The Journal Of Chemical Physics 128, 044317 (2008)
Photofragmentation of argon clusters of average size ranging from 10 up to 1000 atoms is studied using soft x-ray radiation below the 2p threshold and multicoincidence mass spectroscopy technique. For small clusters <N>=10, ionization induces fast fragmentation with neutral emission imparting a large amount of energy.While the primary dissociation takes place on a picosecond time scale, the fragments undergo slow degradation in the spectrometer on a microsecond time scale. For larger clusters <N>>=100 we believe that we observe the fragmentation pattern of multiply charged species on a time-scale which lasts a few hundred nanoseconds. The reason for these slower processes is the large number of neutral atoms which act as an efficient cooling bath where the excess energy heat dissipates among all degrees of freedom. Further degradation of the photoionic cluster in spectrometer then takes place on the microsecond time scale, similar to small clusters.
UpdateBinaryFile(.DS_Store) AddTxtFile(Argon_size_depedence.aux) DelBlock(Argon_size_depedence.bbl,1,1) -- \begin{thebibliography}{30} AddBlock(Argon_size_depedence.bbl,1,1) ++ \begin{thebibliography}{38} DelBlock(Argon_size_depedence.bbl,15,16) -- \bibitem[{\citenamefont{{M. Gisselbrecht} et~al.}(2005)\citenamefont{{M. -- Gisselbrecht}, {A. Lindgren}, {M. Tchaplyguine}, { F. Burmeister}, {G. -- \"{O}hrwall}, {M. Lundwall}, {M. Lundin}, {R. R.T. Marinho}, {A. Naves de -- Brito}, {S. Svensson} et~al.}}]{Gisselbrecht_2005} -- \bibinfo{author}{\bibnamefont{{M. Gisselbrecht}}}, -- \bibinfo{author}{\bibnamefont{{A. Lindgren}}}, -- \bibinfo{author}{\bibnamefont{{M. Tchaplyguine}}}, -- \bibinfo{author}{\bibnamefont{{ F. Burmeister}}}, -- \bibinfo{author}{\bibnamefont{{G. \"{O}hrwall}}}, -- \bibinfo{author}{\bibnamefont{{M. Lundwall}}}, -- \bibinfo{author}{\bibnamefont{{M. Lundin}}}, -- \bibinfo{author}{\bibnamefont{{R. R.T. Marinho}}}, -- \bibinfo{author}{\bibnamefont{{A. Naves de Brito}}}, -- \bibinfo{author}{\bibnamefont{{S. Svensson}}}, \bibnamefont{et~al.}, -- \bibinfo{journal}{J. Chem. Phys.} \textbf{\bibinfo{volume}{123}}, -- \bibinfo{pages}{194301} (\bibinfo{year}{2005}). AddBlock(Argon_size_depedence.bbl,15,7) ++ \bibitem[{\citenamefont{{C. Bobbert} et~al.}(2002)\citenamefont{{C. Bobbert}, ++ {S. Sch\"{u}tte}, {C. Steinbach}, and {U. Buck}}}]{Bobbert_2002} ++ \bibinfo{author}{\bibnamefont{{C. Bobbert}}}, \bibinfo{author}{\bibnamefont{{S. ++ Sch\"{u}tte}}}, \bibinfo{author}{\bibnamefont{{C. Steinbach}}}, ++ \bibnamefont{and} \bibinfo{author}{\bibnamefont{{U. Buck}}}, ++ \bibinfo{journal}{Eur. Phys. J. D} \textbf{\bibinfo{volume}{19}}, ++ \bibinfo{pages}{183} (\bibinfo{year}{2002}). AddBlock(Argon_size_depedence.bbl,23,48) ++ \bibitem[{\citenamefont{{R. Thissen} et~al.}(1998)\citenamefont{{R. Thissen}, ++ {P. Lablanquie}, {R.I. Hall}, {M. Ukai}, and {K. Ito}}}]{Thissen_1998} ++ \bibinfo{author}{\bibnamefont{{R. Thissen}}}, \bibinfo{author}{\bibnamefont{{P. ++ Lablanquie}}}, \bibinfo{author}{\bibnamefont{{R.I. Hall}}}, ++ \bibinfo{author}{\bibnamefont{{M. Ukai}}}, \bibnamefont{and} ++ \bibinfo{author}{\bibnamefont{{K. Ito}}}, \bibinfo{journal}{Eur. Phys. J. D} ++ \textbf{\bibinfo{volume}{4}}, \bibinfo{pages}{335} (\bibinfo{year}{1998}). ++ ++ \bibitem[{\citenamefont{{T. Jahnke} et~al.}(2004)\citenamefont{{T. Jahnke}, {A. ++ Czasch}, {M. S. Sch\"{o}ffler}, {S. Sch\"{o}ssler}, {A. Knapp}, {M. ++ K\"{a}sz}, {J. Titze}, {C. Wimmer}, {K. Kreidi}, {R. E. Grisenti} ++ et~al.}}]{Jahnke_2004} ++ \bibinfo{author}{\bibnamefont{{T. Jahnke}}}, \bibinfo{author}{\bibnamefont{{A. ++ Czasch}}}, \bibinfo{author}{\bibnamefont{{M. S. Sch\"{o}ffler}}}, ++ \bibinfo{author}{\bibnamefont{{S. Sch\"{o}ssler}}}, ++ \bibinfo{author}{\bibnamefont{{A. Knapp}}}, \bibinfo{author}{\bibnamefont{{M. ++ K\"{a}sz}}}, \bibinfo{author}{\bibnamefont{{J. Titze}}}, ++ \bibinfo{author}{\bibnamefont{{C. Wimmer}}}, ++ \bibinfo{author}{\bibnamefont{{K. Kreidi}}}, ++ \bibinfo{author}{\bibnamefont{{R. E. Grisenti}}}, \bibnamefont{et~al.}, ++ \bibinfo{journal}{Phys. Rev. Lett.} \textbf{\bibinfo{volume}{93}}, ++ \bibinfo{pages}{163401} (\bibinfo{year}{2004}). ++ ++ \bibitem[{\citenamefont{{T. Aoto} et~al.}(2006)\citenamefont{{T. Aoto}, {K. ++ Ito}, {Y. Hikosaka}, {E. Shigemasa}, {F. Penent}, and {P. ++ Lablanquie}}}]{Aoto_2006} ++ \bibinfo{author}{\bibnamefont{{T. Aoto}}}, \bibinfo{author}{\bibnamefont{{K. ++ Ito}}}, \bibinfo{author}{\bibnamefont{{Y. Hikosaka}}}, ++ \bibinfo{author}{\bibnamefont{{E. Shigemasa}}}, ++ \bibinfo{author}{\bibnamefont{{F. Penent}}}, \bibnamefont{and} ++ \bibinfo{author}{\bibnamefont{{P. Lablanquie}}}, \bibinfo{journal}{Phys. Rev. ++ Lett} \textbf{\bibinfo{volume}{97}}, \bibinfo{pages}{243401} ++ (\bibinfo{year}{2006}). ++ ++ \bibitem[{\citenamefont{{Y. Morishita} et~al.}(2006)\citenamefont{{Y. ++ Morishita}, {XJ. Liu}, {N. Saito}, {T. Lischke}, {M. Kato}, {G. Prumper}, {M. ++ Oura}, {H. Yamaoka}, {Y. Tamenori}, {IH. Suzuki} et~al.}}]{Morishita_2006} ++ \bibinfo{author}{\bibnamefont{{Y. Morishita}}}, ++ \bibinfo{author}{\bibnamefont{{XJ. Liu}}}, \bibinfo{author}{\bibnamefont{{N. ++ Saito}}}, \bibinfo{author}{\bibnamefont{{T. Lischke}}}, ++ \bibinfo{author}{\bibnamefont{{M. Kato}}}, \bibinfo{author}{\bibnamefont{{G. ++ Prumper}}}, \bibinfo{author}{\bibnamefont{{M. Oura}}}, ++ \bibinfo{author}{\bibnamefont{{H. Yamaoka}}}, ++ \bibinfo{author}{\bibnamefont{{Y. Tamenori}}}, ++ \bibinfo{author}{\bibnamefont{{IH. Suzuki}}}, \bibnamefont{et~al.}, ++ \bibinfo{journal}{Phys. Rev. Lett.} \textbf{\bibinfo{volume}{96}}, ++ \bibinfo{pages}{243402} (\bibinfo{year}{2006}). ++ AddBlock(Argon_size_depedence.bbl,100,17) ++ \bibitem[{\citenamefont{{M. Gisselbrecht} et~al.}(2005)\citenamefont{{M. ++ Gisselbrecht}, {A. Lindgren}, {M. Tchaplyguine}, { F. Burmeister}, {G. ++ \"{O}hrwall}, {M. Lundwall}, {M. Lundin}, {R. R.T. Marinho}, {A. Naves de ++ Brito}, {S. Svensson} et~al.}}]{Gisselbrecht_2005} ++ \bibinfo{author}{\bibnamefont{{M. Gisselbrecht}}}, ++ \bibinfo{author}{\bibnamefont{{A. Lindgren}}}, ++ \bibinfo{author}{\bibnamefont{{M. Tchaplyguine}}}, ++ \bibinfo{author}{\bibnamefont{{ F. Burmeister}}}, ++ \bibinfo{author}{\bibnamefont{{G. \"{O}hrwall}}}, ++ \bibinfo{author}{\bibnamefont{{M. Lundwall}}}, ++ \bibinfo{author}{\bibnamefont{{M. Lundin}}}, ++ \bibinfo{author}{\bibnamefont{{R. R.T. Marinho}}}, ++ \bibinfo{author}{\bibnamefont{{A. Naves de Brito}}}, ++ \bibinfo{author}{\bibnamefont{{S. Svensson}}}, \bibnamefont{et~al.}, ++ \bibinfo{journal}{J. Chem. Phys.} \textbf{\bibinfo{volume}{123}}, ++ \bibinfo{pages}{194301} (\bibinfo{year}{2005}). ++ DelBlock(Argon_size_depedence.bbl,142,9) -- \bibitem[{\citenamefont{{E. R\"{u}hl} et~al.}(1992)\citenamefont{{E. R\"{u}hl}, -- {C. Schmale}, {H.C. Schmelz}, and {H. Baumg\"{a}rtel}}}]{Ruhl_1992} -- \bibinfo{author}{\bibnamefont{{E. R\"{u}hl}}}, -- \bibinfo{author}{\bibnamefont{{C. Schmale}}}, -- \bibinfo{author}{\bibnamefont{{H.C. Schmelz}}}, \bibnamefont{and} -- \bibinfo{author}{\bibnamefont{{H. Baumg\"{a}rtel}}}, \bibinfo{journal}{Chem. -- Phys. Lett.} \textbf{\bibinfo{volume}{191}}, \bibinfo{pages}{430} -- (\bibinfo{year}{1992}). -- DelBlock(Argon_size_depedence.bbl,187,6) -- \bibitem[{\citenamefont{{K. Stephan} et~al.}(1983)\citenamefont{{K. Stephan}, -- {A. Stamatovic}, and {T.D. M\"{a}rk}}}]{Stephan_1983} -- \bibinfo{author}{\bibnamefont{{K. Stephan}}}, \bibinfo{author}{\bibnamefont{{A. -- Stamatovic}}}, \bibnamefont{and} \bibinfo{author}{\bibnamefont{{T.D. -- M\"{a}rk}}}, \bibinfo{journal}{Phys. Rev. A} \textbf{\bibinfo{volume}{28}}, -- \bibinfo{pages}{3105} (\bibinfo{year}{1983}). AddBlock(Argon_size_depedence.bbl,187,15) ++ \bibitem[{\citenamefont{{M. Tchaplyguine} et~al.}(2004)\citenamefont{{M. ++ Tchaplyguine}, {RR. Marinho}, {M. Gisselbrecht}, {J. Schulz}, {N. ++ Martensson}, {SL. Sorensen}, {AN. de Brito}, {Feifel R}, {G. \"{O}hrwall}, ++ {M. Lundwall} et~al.}}]{Tchaplyguine_2004} ++ \bibinfo{author}{\bibnamefont{{M. Tchaplyguine}}}, ++ \bibinfo{author}{\bibnamefont{{RR. Marinho}}}, ++ \bibinfo{author}{\bibnamefont{{M. Gisselbrecht}}}, ++ \bibinfo{author}{\bibnamefont{{J. Schulz}}}, ++ \bibinfo{author}{\bibnamefont{{N. Martensson}}}, ++ \bibinfo{author}{\bibnamefont{{SL. Sorensen}}}, ++ \bibinfo{author}{\bibnamefont{{AN. de Brito}}}, ++ \bibinfo{author}{\bibnamefont{{Feifel R}}}, \bibinfo{author}{\bibnamefont{{G. ++ \"{O}hrwall}}}, \bibinfo{author}{\bibnamefont{{M. Lundwall}}}, ++ \bibnamefont{et~al.}, \bibinfo{journal}{J. Chem. Phys} ++ \textbf{\bibinfo{volume}{120}}, \bibinfo{pages}{345} (\bibinfo{year}{2004}). DelBlock(Argon_size_depedence.bbl,203,15) -- \bibitem[{\citenamefont{{P.G. Lethbridge} and {A.J. -- Stace}}(1988)}]{Lethbridge_1988} -- \bibinfo{author}{\bibnamefont{{P.G. Lethbridge}}} \bibnamefont{and} -- \bibinfo{author}{\bibnamefont{{A.J. Stace}}}, \bibinfo{journal}{J. Chem Phys} -- \textbf{\bibinfo{volume}{89}}, \bibinfo{pages}{4062} (\bibinfo{year}{1988}). -- -- \bibitem[{\citenamefont{{W.H. Press} et~al.}(1992)\citenamefont{{W.H. Press}, -- {S.A. Teukolsky}, {W.T. Vetterling}, and {B.P. Flannery}}}]{NumericalRecipes} -- \bibinfo{author}{\bibnamefont{{W.H. Press}}}, -- \bibinfo{author}{\bibnamefont{{S.A. Teukolsky}}}, -- \bibinfo{author}{\bibnamefont{{W.T. Vetterling}}}, \bibnamefont{and} -- \bibinfo{author}{\bibnamefont{{B.P. Flannery}}}, -- \emph{\bibinfo{title}{Numerical Recipes}} (\bibinfo{publisher}{Cambridge -- University Press}, \bibinfo{year}{1992}). -- DelBlock(Argon_size_depedence.bbl,214,8) -- \bibitem[{\citenamefont{{R. Thissen} et~al.}(1998)\citenamefont{{R. Thissen}, -- {P. Lablanquie}, {R.I. Hall}, {M. Ukai}, and {K. Ito}}}]{Thissen_1998} -- \bibinfo{author}{\bibnamefont{{R. Thissen}}}, \bibinfo{author}{\bibnamefont{{P. -- Lablanquie}}}, \bibinfo{author}{\bibnamefont{{R.I. Hall}}}, -- \bibinfo{author}{\bibnamefont{{M. Ukai}}}, \bibnamefont{and} -- \bibinfo{author}{\bibnamefont{{K. Ito}}}, \bibinfo{journal}{Eur. Phys. J. D} -- \textbf{\bibinfo{volume}{4}}, \bibinfo{pages}{335} (\bibinfo{year}{1998}). -- AddBlock(Argon_size_depedence.bbl,228,23) ++ \bibitem[{\citenamefont{{O. Bj\"{o}rneholm} et~al.}(1995)\citenamefont{{O. ++ Bj\"{o}rneholm}, {F. Federmann}, {F. F\"{o}ssing}, and {T. ++ M\"{o}ller}}}]{Olle_1995} ++ \bibinfo{author}{\bibnamefont{{O. Bj\"{o}rneholm}}}, ++ \bibinfo{author}{\bibnamefont{{F. Federmann}}}, ++ \bibinfo{author}{\bibnamefont{{F. F\"{o}ssing}}}, \bibnamefont{and} ++ \bibinfo{author}{\bibnamefont{{T. M\"{o}ller}}}, \bibinfo{journal}{Phys. Rev. ++ Lett.} \textbf{\bibinfo{volume}{74}}, \bibinfo{pages}{3017} ++ (\bibinfo{year}{1995}). ++ ++ \bibitem[{\citenamefont{{S. Kakar} et~al.}(1997)\citenamefont{{S. Kakar}, {O. ++ Bj\"{o}rneholm}, {J. Weigelt}, {A. R. B. de Castro}, {L. Trger}, {R. Frahm}, ++ {T. M\"{o}ller}, {A. Knop}, and {E. R\"{u}hl}}}]{Kakar_1997} ++ \bibinfo{author}{\bibnamefont{{S. Kakar}}}, \bibinfo{author}{\bibnamefont{{O. ++ Bj\"{o}rneholm}}}, \bibinfo{author}{\bibnamefont{{J. Weigelt}}}, ++ \bibinfo{author}{\bibnamefont{{A. R. B. de Castro}}}, ++ \bibinfo{author}{\bibnamefont{{L. Trger}}}, ++ \bibinfo{author}{\bibnamefont{{R. Frahm}}}, \bibinfo{author}{\bibnamefont{{T. ++ M\"{o}ller}}}, \bibinfo{author}{\bibnamefont{{A. Knop}}}, \bibnamefont{and} ++ \bibinfo{author}{\bibnamefont{{E. R\"{u}hl}}}, \bibinfo{journal}{Phys. Rev. ++ Lett} \textbf{\bibinfo{volume}{78}}, \bibinfo{pages}{1675} ++ (\bibinfo{year}{1997}). ++ AddBlock(Argon_size_depedence.bbl,263,41) ++ \bibitem[{\citenamefont{{M. Lundwall} et~al.}(2006)\citenamefont{{M. Lundwall}, ++ {A. Lindblad}, {H. Bergersen}, {T. Rander}, {G. Ohrwall}, {M. Tchaplyguine}, ++ {S. Peredkov}, {S. Svensson}, and {O. Bjorneholm}}}]{Lundwall_2006} ++ \bibinfo{author}{\bibnamefont{{M. Lundwall}}}, ++ \bibinfo{author}{\bibnamefont{{A. Lindblad}}}, ++ \bibinfo{author}{\bibnamefont{{H. Bergersen}}}, ++ \bibinfo{author}{\bibnamefont{{T. Rander}}}, ++ \bibinfo{author}{\bibnamefont{{G. Ohrwall}}}, ++ \bibinfo{author}{\bibnamefont{{M. Tchaplyguine}}}, ++ \bibinfo{author}{\bibnamefont{{S. Peredkov}}}, ++ \bibinfo{author}{\bibnamefont{{S. Svensson}}}, \bibnamefont{and} ++ \bibinfo{author}{\bibnamefont{{O. Bjorneholm}}}, \bibinfo{journal}{J. Phys. ++ B.} \textbf{\bibinfo{volume}{39}}, \bibinfo{pages}{3321} ++ (\bibinfo{year}{2006}). ++ ++ \bibitem[{\citenamefont{{K. Stephan} et~al.}(1983)\citenamefont{{K. Stephan}, ++ {A. Stamatovic}, and {T.D. M\"{a}rk}}}]{Stephan_1983} ++ \bibinfo{author}{\bibnamefont{{K. Stephan}}}, \bibinfo{author}{\bibnamefont{{A. ++ Stamatovic}}}, \bibnamefont{and} \bibinfo{author}{\bibnamefont{{T.D. ++ M\"{a}rk}}}, \bibinfo{journal}{Phys. Rev. A} \textbf{\bibinfo{volume}{28}}, ++ \bibinfo{pages}{3105} (\bibinfo{year}{1983}). ++ ++ \bibitem[{\citenamefont{{P.G. Lethbridge} and {A.J. ++ Stace}}(1988)}]{Lethbridge_1988} ++ \bibinfo{author}{\bibnamefont{{P.G. Lethbridge}}} \bibnamefont{and} ++ \bibinfo{author}{\bibnamefont{{A.J. Stace}}}, \bibinfo{journal}{J. Chem Phys} ++ \textbf{\bibinfo{volume}{89}}, \bibinfo{pages}{4062} (\bibinfo{year}{1988}). ++ ++ \bibitem[{\citenamefont{{W.H. Press} et~al.}(1992)\citenamefont{{W.H. Press}, ++ {S.A. Teukolsky}, {W.T. Vetterling}, and {B.P. Flannery}}}]{NumericalRecipes} ++ \bibinfo{author}{\bibnamefont{{W.H. Press}}}, ++ \bibinfo{author}{\bibnamefont{{S.A. Teukolsky}}}, ++ \bibinfo{author}{\bibnamefont{{W.T. Vetterling}}}, \bibnamefont{and} ++ \bibinfo{author}{\bibnamefont{{B.P. Flannery}}}, ++ \emph{\bibinfo{title}{Numerical Recipes}} (\bibinfo{publisher}{Cambridge ++ University Press}, \bibinfo{year}{1992}). ++ ++ \bibitem[{\citenamefont{{M. Gisselbrecht {\it et al.}}}()}]{Gisselbrecht_2007} ++ \bibinfo{author}{\bibnamefont{{M. Gisselbrecht {\it et al.}}}}, ++ \bibinfo{note}{to be published}. ++ AddBlock(Argon_size_depedence.bbl,330,21) ++ \bibitem[{\citenamefont{{V. Lepere} et~al.}(2005)\citenamefont{{V. Lepere}, ++ {IM. Ismail}, {M. Barat}, {JA. Fayeton}, {YJ. Picard}, {K. Wohrer}, {C. ++ Jouvet}, and {S. Martrenchard}}}]{Lepere_2005} ++ \bibinfo{author}{\bibnamefont{{V. Lepere}}}, \bibinfo{author}{\bibnamefont{{IM. ++ Ismail}}}, \bibinfo{author}{\bibnamefont{{M. Barat}}}, ++ \bibinfo{author}{\bibnamefont{{JA. Fayeton}}}, ++ \bibinfo{author}{\bibnamefont{{YJ. Picard}}}, ++ \bibinfo{author}{\bibnamefont{{K. Wohrer}}}, ++ \bibinfo{author}{\bibnamefont{{C. Jouvet}}}, \bibnamefont{and} ++ \bibinfo{author}{\bibnamefont{{S. Martrenchard}}}, \bibinfo{journal}{J. Chem. ++ Phys.} \textbf{\bibinfo{volume}{123}}, \bibinfo{pages}{174307} ++ (\bibinfo{year}{2005}). ++ ++ \bibitem[{\citenamefont{{M. Barat} et~al.}(2002)\citenamefont{{M. Barat}, {JC. ++ Brenot JC}, {JA. Fayeton}, and {YJ. Picard}}}]{Barat_2002} ++ \bibinfo{author}{\bibnamefont{{M. Barat}}}, \bibinfo{author}{\bibnamefont{{JC. ++ Brenot JC}}}, \bibinfo{author}{\bibnamefont{{JA. Fayeton}}}, ++ \bibnamefont{and} \bibinfo{author}{\bibnamefont{{YJ. Picard}}}, ++ \bibinfo{journal}{J. Chem. Phys.} \textbf{\bibinfo{volume}{117}}, ++ \bibinfo{pages}{1497} (\bibinfo{year}{2002}). ++ DelBlock(Argon_size_depedence.bbl,363,9) -- \bibitem[{\citenamefont{{G. Dujardin} et~al.}(1990)\citenamefont{{G. Dujardin}, -- {L. Hellner}, {M.J. Besnardramage}, and {R. Azria}}}]{Dujardin_1990} -- \bibinfo{author}{\bibnamefont{{G. Dujardin}}}, -- \bibinfo{author}{\bibnamefont{{L. Hellner}}}, -- \bibinfo{author}{\bibnamefont{{M.J. Besnardramage}}}, \bibnamefont{and} -- \bibinfo{author}{\bibnamefont{{R. Azria}}}, \bibinfo{journal}{Phys. Rev. -- Lett} \textbf{\bibinfo{volume}{64}}, \bibinfo{pages}{1289} -- (\bibinfo{year}{1990}). -- DelBlock(Argon_size_depedence.bbl,370,8) -- \bibitem[{\citenamefont{{T. Moller} et~al.}(1999)\citenamefont{{T. Moller}, {K. -- von Haeften}, {T. Laarman}, and {R. von Pietrowski}}}]{Moller_99} -- \bibinfo{author}{\bibnamefont{{T. Moller}}}, \bibinfo{author}{\bibnamefont{{K. -- von Haeften}}}, \bibinfo{author}{\bibnamefont{{T. Laarman}}}, -- \bibnamefont{and} \bibinfo{author}{\bibnamefont{{R. von Pietrowski}}}, -- \bibinfo{journal}{Eur. J. Phys. D} \textbf{\bibinfo{volume}{9}}, -- \bibinfo{pages}{5} (\bibinfo{year}{1999}). -- AddTxtFile(Argon_size_depedence.blg) UpdateBinaryFile(Argon_size_depedence.dvi) AddTxtFile(Argon_size_depedence.log) UpdateBinaryFile(Argon_size_depedence.pdf) DelBlock(Argon_size_depedence.tex,14,1) -- \title{Size dependence fragmentation of argon clusters} AddBlock(Argon_size_depedence.tex,14,1) ++ \title{Size dependence fragmentation of argon clusters in the X-ray ionization regime} DelBlock(Argon_size_depedence.tex,54,1) -- Photo-fragmentation of argon clusters of average size ranging from 10 up to 1000 atoms is reported at a photon energy of 116 eV using multi-coincidence technique with a mass spectrometer. A spectacular change in fragmentation pattern is observed when the cluster size increases, arising from a change in the dissociation time-scale. For small clusters ($<$10$>$), after ionization a fast fragmentation with neutral emission imparting large amount of energy in the ps time scale occurs, then slow degradation of the photo-cluster ions is observed in the $\mu$s time scale. For larger clusters ($\geq <$100$>$) we believe that we observe the fragmentation pattern of large unstable multiply charged species on a time-scale which lasts a few hundred ns. The reason for these apparent slow processes could be that the large number of neutral atoms acts as an efficient cooling bath which tends to dissipate the excess of energy ("heat") among all degrees of freedom. Degradation of the photo-cluster ions takes place in the $\mu$s time scale as for small clusters. AddBlock(Argon_size_depedence.tex,54,1) ++ Photo-fragmentation of argon clusters of average size ranging from 10 up to 1000 atoms is studied at a photon energy of 216 eV using multi-coincidence mass spectroscopy technique. For small clusters ($<$N$>$=10), ionization induces fast fragmentation with neutral emission imparting large amount of energy. While the primary dissociation takes place on a ps time scale, the fragments undergo slow degradation in the spectrometer on a $\mu$s time scale. For larger clusters ($<$N$>\geq$100) we believe that we observe the fragmentation pattern of large multiply charged species on a time-scale which lasts a few hundred ns. The reason for these apparent slower processes is the large number of neutral atoms which act as an efficient cooling bath where the excess energy ("heat") dissipates among all degrees of freedom. Further degradation of the photo-ionic-cluster in spectrometer then takes place on the $\mu$s time scale, as for small clusters. AddBlock(Argon_size_depedence.tex,62,1) ++ Mass spectroscopy is one of the most common methods to study clusters, however to analyze the simple mass spectra of van der Waals cluster quantitative information on the ionization process itself is necessary. In contrast to electron impact ionization, X-ray photo-ionization do not produce a binary collision which results in massive neutral evaporation or fragmentation (e.g.\cite{Bobbert_2002}). Hence the fragmentation dynamics of ionized clusters by X-ray give deeper insight into the interplay between the electronic and nuclear relaxations\cite{Thissen_1998, Jahnke_2004, Aoto_2006, Morishita_2006}. Upon resonant inner-shell excitation and ionization in the vicinity of the L-edge threshold, argon clusters are produced in specific ionic states mainly below or above the vertical double ionization potential \cite{Maxim_2003, Lundwall_05}. In a previous publication \cite{Gisselbrecht_2005}, we presented the general fragmentation pattern of small argon clusters in this X-ray ionization regime. Argon clusters undergo dissociation departing from the Coulomb explosion picture, revealing the role of the internal energy left in the system. \\ DelBlock(Argon_size_depedence.tex,64,3) -- In a recent publication \cite{Gisselbrecht_2005} we presented the general fragmentation pattern of small argon clusters for resonant inner shell excitation and ionization. We showed that the inner shell photo-absorption selectively prepared ionic species below or above the vertical double ionization potential \cite{Maxim_2003, Lundwall_05}, respectively Ar$_m^{+*}$ and Ar$_m^{2+}$. In both case theses species undergo dissociation leading to two or more charged fragments pointing out the importance of the nuclear relaxation as well as the electronic relaxation. -- -- This study focus on the cluster-size dependent fragmentation with a VUV photon of 116~eV. We perform a multicoincidence measurement Photo-Electron-n-Photo-Ions COincidence PE(PI)$_n$CO with a mass spectrometer. AddBlock(Argon_size_depedence.tex,64,1) ++ This study focuses on the cluster-size dependent fragmentation irradiated by 216~eV photons. We performed a multi-coincidence measurement Photo-Electron-n-Photo-Ions COincidence PE(PI)$_n$CO with a mass spectrometer. DelBlock(Argon_size_depedence.tex,68,1) -- \caption{\label{Fig1} Photo-ionization branching ratio for free argon atoms and schematic decay channels for clusters.} AddBlock(Argon_size_depedence.tex,68,1) ++ \caption{\label{Fig1} Schematic fragmentation pathway after primary ionization with 216 eV photon of an argon atom in the cluster. Note that no scattering of the primary electron is considered in this scheme.} DelBlock(Argon_size_depedence.tex,71,5) -- The chosen photon energy implies that only the $3p$ valence and $3s$ inner valence shells can be ionized and Auger relaxation is energetically not possible. For free atoms, we are well above the double-ionization threshold 43.4~eV \cite{Nist}, the $3s$ Cooper minimum between 45-50~eV, and even exceeds the triple ionization threshold 84.3~eV\cite{Nist}. The branching ratios are known to be 83\% for single photo-ionization, 16\% for double photo-ionization, and less than 1\% for triple photo-ionization \cite{Holland_1979}. In the current picture of cluster ionization, called Haberland's model \cite{Haberland_book_1995, Haberland_book_1994}, the system does not have time for nuclear rearrangement and states close to the dissociation limit are populated. Thus the cluster photo-ionization branching ratio should mimic the atomic one. However, in our experiment the time scale is long enough for nuclear relaxation to take place and adiabatic potentials to be relevant \cite{Ruhl_1992}. Hence, among the singly charged species a few of them ($\sim$15\%) prepared with two holes and one particle in the outer valence shell, should decay in the double ionization continuum as we have already implied \cite{Gisselbrecht_2005}. Hence, one could speculate that the fragmentation depends on the cluster size. -- %==== mathieu@g3 / andreas@work -- %>The chosen photon energy implies that only the $3p$ valence and $3s$ inner valence shells can be ionized and Auger relaxation is energetically not possible. For free atoms, we are well above the double-ionization threshold 43.4~eV \cite{Nist}, the $3s$ Cooper minimum between 45-50~eV, and even exceeds the triple ionization threshold 84.3~eV. The branching ratios are known to be 83\% for single photo-ionization, 16\% for double photo-ionization, and less than 1\% for triple photo-ionization \cite{Holland_1979}. In the current picture of cluster ionization, so called Haberland's model \cite{Haberland_book_1995, Haberland_book_1994}, the system does not have time for nuclear rearrangement and states close to the dissociation limit are populated. Thus the cluster photo-ionization branching ratio should mimic the atomic one. However in our experiment the time scale is long enough for nuclear relaxation to take place and adiabatic potentials to be relevant \cite{Ruhl_1992}. Hence, among the singly charge species a few of them ($\sim$15\%) prepared with two holes and one particle in the outer valence shell, should decay in the double ionization continuum as we have already eluded \cite{Gisselbrecht_2005}. Hence, one could speculate that the fragmentation depend on the cluster size. -- -- In Fig.~\ref{Fig1} the photo-ionization branching ratio for free argon atoms and corresponding fragmentation channels in clusters are shown. Our aim is to investigate the photo-fragmentation over a size range from a few up to thousands of atoms in order to determine whether the fragmentation dynamics is a sensitive probe to the formation of stable multiply ionized clusters. AddBlock(Argon_size_depedence.tex,71,1) ++ The chosen photon energy implies that only the $3p$ valence and $3s$ inner valence shells can be ionized and Auger relaxation is energetically not possible. For free atoms, we are well above the double-ionization threshold at 43.4~eV \cite{Nist}, the $3s$ Cooper minimum between 45-50~eV, and we even exceed the triple ionization threshold at 84.3~eV\cite{Nist}. The branching ratios are known to be 83\% for single photo-ionization, 16\% for double photo-ionization, and less than 1\% for triple photo-ionization \cite{Holland_1979}. In the accepted picture of cluster ionization, so-called Haberland's model \cite{Haberland_book_1995, Haberland_book_1994}, the system does not have time for nuclear rearrangement after ionization and states close to the dissociation limit are populated. Thus the cluster photo-ionization branching ratio should mimic the atomic one and be independent of the size and geometry of the cluster. In Fig.~\ref{Fig1} we present a summary of the most probable fragmentation pathway after primary photo-ionization of an atom in the cluster neglecting scattering processes. Among the singly charged species, those prepared with two holes and one particle in the outer valence shell would fragment in the double ionization continuum as we have already suggested \cite{Gisselbrecht_2005}, while other singly ionized species would fragment in the single ionization continuum\cite{Thissen_1998}. Hence, one could speculate that the fragmentation pathway changes with the cluster size, especially if one can unambiguously study the decay of multiple ionized species. We show that over a size range from a few up to thousands of atoms, the multi-coincidence technique is a sensitive probe to study the photo-fragmentation dynamics of multiply ionized clusters. A spectacular change in the fragmentation pattern is observed when the cluster size increases, due mainly to a change in the dissociation time-scale. Furthermore, at a fixed photon energy, the degree of ionization increases as the function of the cluster size as the result of secondary ionization processes, namely auto-ionization and electron scattering within the cluster. AddBlock(Argon_size_depedence.tex,74,5) ++ The experiment was carried out at the beam line I411 of the MAX II electron storage ring at the Swedish National Synchrotron Radiation Laboratory MAX-lab in Lund, Sweden \cite{Svensson_1996}. The undulator beamline was equipped with a modified SX-700 plane-grating monochromator. A chamber with a 2-field electron-ion coincidence spectrometer was mounted on the beam line upstream of the permanent end station. ++ Argon clusters were produced in a supersonic expansion with different experimental conditions (flat or conical nozzle at room or liquid nitrogen temperature). The beam contained a mixture of atoms and clusters, characterized by an average cluster size of $<$N$>$ atoms per cluster and the full-width at half-maximum (FWHM) of the size distribution is $\sim N/2$. The average cluster size $<$N$>$ was estimated according to the $\Gamma^{\ast}$-formalism \cite{Karnbach_1993}. One should keep in mind that the uncertainty in the absolute size determintation can be of a factor of 2, depending on the experimental parameter uncertainties and which of the published scaling laws is used \cite{Karnbach_1993, Buck_1996}. ++ Monochromatic synchrotron light crossed the cluster jet at right angles in the center of the source region of the spectrometer. A continuous field (U$_\mathrm{ext}$=1666~V/cm) extracts the ++ electrons and the ions from this region. Electrons with kinetic energy up to 500~eV can be collected over a solid angle of 4$\pi$ steradian. In order to satisfy the so-called 'space-time focusing' \cite{Wiley_1955} criterion, ions were post-accelerated before they passed into a field free drift tube. The spectrometer was positioned perpendicular to the polarization plane of the light. Thus, the spatial extent of the source volume along the spectrometer axis is negligible since it is defined by the vertical size of the light spot ($\sim$0.4~mm) and is independent of the expansion conditions of the cluster source. ++ Electrons and ions, detected by micro channel plate (MCP) pairs in a chevron configuration, provide start and stop signals for the Time-to-Digital Converter (TDC) in the set-up. The time of flight of ions arising from single, up to quadruple ionization events, was recorded and treated in real time. For all measurements the total ion count rate was essentially constant, less than 2~kHz, keeping theoretically the detection probability of a random ion (false coincidence) at about 1\% within our acquisition time window (5~$\mu$s). This probability is in practice affected by the fact that the density of uncondensed atoms in the cluster source is 10 to 20 times higher than the density of clusters. Calibration on rare gases (argon, krypton, and xenon) has shown that the ion detection efficiency decreases for masses above $\sim$150 a.u.due to the use of discriminators in the electronics scheme which cut-off a part of the pulse height distribution of the MCP signal arising from heavy particles \cite{Furuya_2002}. DelBlock(Argon_size_depedence.tex,80,2) -- \subsection{Experimental equipment} -- The experiment was carried out at the beam line I411 on the MAX II electron storage ring at the Swedish National Synchrotron Radiation Laboratory MAX-lab in Lund, Sweden \cite{Svensson_1996}. The undulator beamline was equipped with a modified SX-700 plane-grating monochromator, which allowed photon energy tuning from 61 to 1500~eV. A chamber with a 2-field electron-ion coincidence spectrometer was mounted on the beam line upstream of the permanent end station. DelBlock(Argon_size_depedence.tex,81,1) -- Argon clusters were produced in a supersonic expansion with different experimental conditions (flat or conical nozzle at room or liquid nitrogen temperature). The beam consisted of a mixture of atoms and clusters, characterized by an average cluster size of $<$N$>$ atoms per cluster and the full-width at half-maximum (FWHM) of the size distribution is $N/2$. The average cluster size $<$N$>$ was estimated according to the $\Gamma^{\ast}$-formalism \cite{Karnbach_1993}. One should keep in mind that the uncertainty in the absolute size determintation can be of a factor of 2, depending on experimental parameter uncertainties and which of the published scaling law are used \cite{Karnbach_1993, Buck_1996}. We present Figure~\ref{Fig2} in log-log scale the theoretical intensity distribution of neutral clusters for different average sizes. It has been arbitrary normalized for $<$N$>$=10 for sake of clarity. The spectrum shows that between the smallest and the largest average size, the relative intensity of small clusters (e.g. dimers, trimers...) is a few order of magnitude more for smallest size. This means that in our experiment the physical origins of small photo-clusters changes gradually with the cluster size. For the smallest cluster size, the photo-clusters arise from direct photo-ionization and photo-fragmentation, while for largest cluster size photo-clusters arise exclusively from photo-fragmentation. The use of multi-coincidence technique allow us then to ensure that the measured photo-clusters are related to multiply charged mother clusters. AddBlock(Argon_size_depedence.tex,81,1) ++ \section{Results and Discussion} DelBlock(Argon_size_depedence.tex,85,2) -- \scalebox{1}{\includegraphics{figure2.eps}} -- \caption{\label{Fig2} Distribution of neutral clusters for different cluster sizes. The relative intensity should reflect the intensity of direct photo-ionization in our measurement. } AddBlock(Argon_size_depedence.tex,85,2) ++ \scalebox{1}{\includegraphics{figure4.eps}} ++ \caption{\label{Fig2} Mass spectra for cluster with 10 up to 1000 atoms at 216~eV. The spectra are normalized with respect to the total number of electrons (starts) and to the acquisition time, so the intensity of each peak reflects the partial cross section of each photo-ions multiplied with its detection probability. In the insert we present the log-normal distribution of neutral clusters for different cluster sizes in log-log scale in order to illustrate the general trend expected from simple XUV photo-ionization} AddBlock(Argon_size_depedence.tex,88,2) ++ ++ \subsection{Mass Spectra} DelBlock(Argon_size_depedence.tex,91,2) -- Monochromatic synchrotron light crossed the cluster jet at right angles in the center of the source region of the spectrometer. A continuous field (U$_\mathrm{ext}$=1666~V/cm) extracts the -- electrons and the ions from this region. Electrons with kinetic energy up to 500~eV can be collected over a solid angle of 4$\pi$ steradian. In order to satisfy the so-called 'space-time focusing' \cite{Wiley_1955} criterion, ions were post-accelerated before they passed into a field free drift tube. The spectrometer was positioned perpendicular to the polarization plane of the light. Thus, the spatial extent of the source volume along the spectrometer axis is negligible since it is defined by the vertical size of the light spot ($\sim$0.4~mm) and is independent of the expansion conditions of the cluster source. A resolving power of $m/\delta m \sim 500$ was achieved. AddBlock(Argon_size_depedence.tex,91,2) ++ \subsubsection{Overview} ++ As it has been discussed \cite{Haberland_book_1995, Haberland_book_1994} the unambiguous interpretation of mass spectrum requires its connection to the original cluster size distribution taking into account experimental effects and physical processes. In figure~\ref{Fig2} mass spectra after ionization by 216~eV photons are shown for a series of clusters of average sizes $<$N$>$ = 10, 20, 100 and 1000. The signal intensity diminishes strongly as the function of the time-of-flight (see scaling factor 1:60:1200) as a result of lower ion detection efficiency for heavy particles. At short time of flight ($<$ 1400 ns) a large amount atomic ions is located in the spectra due to uncondensed argon atoms which remain in the cluster beam. All heavier ions (time of flight $>$1400~ns) arise only from ionization or fragmentation of neutral clusters. For the small photo-ionic-clusters (2$\leq$N$\leq$5), the peak heights are very similar for $<$N$>$=10 and 20 atoms, but decreases quickly for $<$N$>$=100 and 1000 atoms. From simple consideration, this overall behavior reflects the neutral cluster abundance in the beam when the average cluster size increases. In the inset figure~\ref{Fig2}, we present in log-log scale, a log-normal intensity distribution of neutral clusters for different average sizes. The neutral intensity distribution shows that between $<$N$>$=10 and $<$N$>$=1000, the relative intensity of small clusters (e.g. dimers, trimers...) is at least 3 orders of magnitude lower. Note that we assume a single log-normal distribution because the determination of the average cluster size by electron spectroscopy measurement \cite{Tchaplyguine_2004} and by partial ion yield (PIY) measurement \cite{Gisselbrecht_2005} scaled in very good agreement according to the $\Gamma^{\ast}$-formalism\cite{Karnbach_1993}. A deeper analysis of the mass spectra reveals however that we observe not more than one order of magnitude difference when we integrate the signal over the whole peak. This would mean that in our experiment the physical origins of small photo-ionic-clusters change gradually with the cluster size. For $<$N$>$=10 and 20, the photo-ionic-clusters arise from direct photo-ionization and photo-fragmentation, while $<$N$>$=100 and 1000 photo-ionic-clusters arise exclusively from photo-fragmentation. One should emphasize that these observations are independent of the expansion conditions as it was checked with a different set of nozzle, pressure and temperature. \\ DelBlock(Argon_size_depedence.tex,94,1) -- Electrons and ions, detected by micro channel plate (MCP) pairs in a chevron configuration, provide start and stop signals for the Time-to-Digital Converter (TDC) in the set-up. The time of flight of ions arising from single, up to quadruple ionization events, was recorded and treated in real time. For all measurements the ion count rate was essentially constant, less than 2~kHz, keeping theoretically the detection probability of a random ion (false coincidence) at about 1\% within our acquisition time window (5~$\mu$s). This probability is in practice degraded by the fact that the density of uncondensed atoms in the cluster source is 10 to 20 times higher than the density of clusters. Calibration on rare gases (argon, krypton, and xenon) has shown that the ion efficiency decreases for masses above $\sim$150 a.u. even though the photo-ions are accelerated up to 4~keV. This is due to the use of discriminators in the electronics scheme which cut-off a part of the pulse height distribution of the MCP signal for heavy particles \cite{Furuya_2002}. Thus the detection efficiencies of argon dimers and trimers are comparable, but heavier ions have lower detection efficiency. Calibration of the cluster source has shown that cluster sizes larger than 35 atoms can easily be observed with the present spectrometer. AddBlock(Argon_size_depedence.tex,94,2) ++ \subsubsection{Peak Shape} ++ In the mass spectra, the peak shape of photo-ionic-cluster changes from a relatively narrow profile for $<$N$>$=10 and $<$N$>$=20, to a broad one for larger clusters. In the $<$N$>$=100 and $<$N$>$=1000 spectra, photo-ionic-monomer and photo-ionic-dimer peak shapes become distinctly asymmetric while all other peaks remain mostly symmetric. These changes in the series of spectra with $<$N$> \geq$100 cannot be explained simply by the fragmentation of singly ionized clusters in the ground state. Indeed using the model developed by Haberland \cite{Haberland_book_1994,Haberland_book_1995}, cluster ionization is followed by neutral evaporation which tends to cool down the cluster. Although it is known that other dissociation mechanisms are possible at this photon energy, for instance due to inner-valence shell ionization \cite{Thissen_1998}, the dominant fragmentation pathway is related to single vacancy in the outer electronic shell. Hence in the present study large clusters should fragment statistically: the excess energy is shared among all degrees of freedom and the kinetic energy of the fragment does not increase as a function of the cluster size. The typical energy released in this unimolecular fragmentation is on the order of 60-200~meV \cite{Ikegami_1993,Hrivnak_2001}. This is in contradiction with our observation where a substantial amount of kinetic energy is imparted to the photo-ionic-clusters. AddBlock(Argon_size_depedence.tex,97,5) ++ \begin{figure} ++ \centering ++ \scalebox{1}{\includegraphics{figure5.eps}} ++ \caption{\label{Fig4} The Ar$_2^+$ and Ar$_3^+$ photo-ion peaks from Fig~\ref{Fig4} are shown using a solid line. The dashed line represents the line shape for the same ion measures in a double, triple and quadruple ion-coincidence event. } ++ \end{figure} AddBlock(Argon_size_depedence.tex,103,6) ++ In figure \ref{Fig4}, a detailed view (solid lines) of the dimer (Ar$_2^+$) and trimer (Ar$_3^+$) photo-ionic-clusters is presented for the same average sizes as in figure~\ref{Fig2}. Ar$_2^+$ and Ar$_3^+$ are selected because they illustrate the two characteristic features observed in our spectra. The dashed lines shown in each plot are the sum of time-of-flight distributions of the same fragment measured in multiple-coincidence event, where several photo-ions are detected together. \\ ++ For the smallest cluster sizes ($<$N$>$=10, 20), single ionization dominates, but there is a contribution from multiply-charged species which corresponds certainly to the wing broadening. For the average cluster sizes $\geq$100 atoms, the real mass spectra (solid lines) mimic almost perfectly the time-of-flight distributions arising from multiple charged species (dashed lines). This means that these photo-ionic-clusters arise mainly from fragmentation of large multiply charged clusters. In general, multiply ionized clusters are expected to be stable when a critical size (N$_\text{c}$) is reached: for argon clusters, the first stable doubly charged species is at N$^{(2)}_c=$89 \cite{Gotts_1992} and the first stable triply charged species is at N$^{(3)}_c=$226 \cite{Scheier_87}. Thus, for the largest cluster sizes in our experiment, the most likely origin for the photo-ionic-clusters would be the fragmentation of unstable doubly/triply charged clusters which are always produced due to the broad neutral cluster size distributions. Hence, a maximum of production of unstable multiply charged species for the size $<$N$>$=100 should be expected since all clusters with a size below 89 or 226 undergo fragmentation if they are doubly or triply charged. This is agreement with our observation where the total amount of multiple-coincidence events increases from $<$N$>$=10 to $<$N$>$=100, and decreases from $<$N$>$=100 to $<$N$>$=1000. However one should keep in mind that measurements in the vicinity of the L-edges dimer PIY \cite{Olle_1995, Gisselbrecht_2005} exhibit characteristic structures which are related to the largest clusters. This implies that also the "stable" multiply-charged clusters undergo fast fragmentation certainly due to further ionization.\\ ++ This astounding importance of multiply charged species deserves a more detailed discussion. Although at this photon energy the double ionization cross section for free atoms is a very low channel, for clusters there are actually two more mechanisms that enhance the formation of multiply charged species. On the one hand, the double ionization continuum in 3p shell decreases from 43~eV in atoms to 32~eV in clusters of size N=101 \cite{Scheier_87}. Due to this lowering of the adiabatic ionization potentials, high ionic excited states (e.g. Ar$_m^{*+}$) auto-ionize into the double ionization continuum. Auto-ionization mechanism is certainly significant for rather small clusters N$<$20 and may evolve as long as structural changes occur in the neutral clusters ($<$N$> <$ 200 \cite{Kakar_1997}), but it is not supposed to strongly influence the fragmentation dynamics of the larger clusters. On the other hand, ÒindirectÓ processes like scattering of a primary electron on another atom can occur as it has been pointed out in studies on large clusters by electron impact and photo-ionization\cite{Hergenhahn_2002,Lundwall_2006}. Here, direct photo-ionization can produce either one electron from the ($3p/3s$) shells, or two/three electrons from the 3p shell, thus the electron kinetic energies can range from 0-200~eV. This corresponds to an inelastic mean free path which can be smaller than the cluster size. Inelastic scattering is known to be significant close to the atomic ionization thresholds as it has been shown in Ne clusters \cite{Hergenhahn_2002} and electron spectroscopy of Auger electron in Ar clusters supports also the presence of this mechanism at higher photo-ionization energy\cite{Lundwall_2006}. Thus inelastic scattering mechanism could be emphasized by the auto-ionization of high ionic excited states (e.g. Ar$_m^{*+}$) which would produce low kinetic energy electrons and cascade processes may occur for large clusters. ++ ++ \subsection{Fragmentation} ++ DelBlock(Argon_size_depedence.tex,112,1) -- \caption{\label{Fig3} Time of flight distribution for daughter ion for different lifetime of the mother ion. t$_m$ and t$_d$ represent respectively the mother and daughter time-of flight if these ions where produced at the source point without kinetic energy. The scaling factor is given to compare the absolute peak height. For this simulation the t$_{acc}=$350~ns, $\tau_{m}=$50, 300, 3600~ns and $m_d/m_m$=1/2 } AddBlock(Argon_size_depedence.tex,112,1) ++ \caption{\label{Fig5} Time of flight distribution for daughter ion for different lifetime of the mother ion. t$_m$ and t$_d$ represent respectively the mother and daughter time-of flight if these ions where produced at the source point without kinetic energy. The scaling factor is given to compare the absolute peak height. For this simulation the t$_{acc}=$350~ns, $\tau_{m}=$50, 300, 3600~ns and $m_d/m_m$=1/2 } DelBlock(Argon_size_depedence.tex,115,1) -- \subsection{Data analysis} AddBlock(Argon_size_depedence.tex,115,1) ++ \subsubsection{Theoretical time-of-flight distribution} DelBlock(Argon_size_depedence.tex,117,1) -- From studies on cluster ion dynamics \cite{Stephan_1983, Lethbridge_1988}, the peak shape at this photon energy is the best described by meta-stable decay of the photo-clusters and photo-fragments within our time scale of observation. Therefore we developed a full numerical calculation of the time-of-flight distribution in our spectrometer. The trajectories of the particles are calculated by solving the classical motion equation of charged particles with a 4th-order Runge-Kutta algorithm \cite{NumericalRecipes}. Due to a large variety in orientation, geometry and size of the clusters in the beam, no alignment of the clusters is {\it a-priori} expected. Thus the initial condition is an isotropic distribution of particles emitted in space. The mother ion is defined by its lifetime $\tau_m$ and its initial kinetic energy distribution (KE$_1$). The number of mother ions decreases in time as: AddBlock(Argon_size_depedence.tex,117,1) ++ According to cluster ion dynamics studies (e.g. \cite{Stephan_1983, Lethbridge_1988}), it is reasonable to consider that that the peak shape in our experiment is best described by meta-stable decay of the photo-ionic-clusters within our time scale of observation (0$\rightarrow2\mu$s). Therefore we developed a full numerical calculation of the time-of-flight distribution in our spectrometer. The trajectories of the particles are calculated by solving the classical motion equation of charged particles with a 4th-order Runge-Kutta algorithm \cite{NumericalRecipes}. Due to a large variety in orientation, geometry and size of the clusters in the beam, no alignment of the clusters is {\it a-priori} expected. Hence the initial condition is an isotropic distribution of particles emitted in space. The mother ion is defined by its lifetime $\tau_m$ and its initial kinetic energy distribution (KE$_1$). The number of mother ions decreases in time as: DelBlock(Argon_size_depedence.tex,121,1) -- and the dissociation rate, i.e. number of daughter ion produced, at any time is given by: AddBlock(Argon_size_depedence.tex,121,1) ++ and the dissociation rate, i.e. the number of daughter ion produced, at any time is given by: DelBlock(Argon_size_depedence.tex,126,1) -- The daughter ion is assumed to be emitted with an isotropic distribution and we considered the case of variable kinetic energy released (KE$_2$) in the dissociation. One should notice that from momentum conservation, the kinetic energy of the daughter ion is expressed as: KE$_d=(m_m-m_d)/m_m$KE$_2$. The final time of flight is constructed with Monte-Carlo integration and we convolute the numerical peak shape with our experimental broadening. To understand the result of the simulation, two cases ought to be considered. If the mother ion dissociates in the drift tube the daughter ion arrives at the time of flight of the mother ion (t$_m$). The peak is symmetric and the time spread is related to kinetic energy imparted to the daughter ion, the field strength as well as the length of the drift tube. If the mother ion dissociation happens before the drift tube, the daughter ion arrive with a short time of flight (t$_d$). The peak is asymmetric and looks like an exponential decay which actually follows the dissociation rate eqn~(\ref{eqn:daughters}). The peak shape is in that case independent of the extraction condition as well as the kinetic energy KE$_1$ and KE$_2$ but depends on the ratio $m_d/m_m$. AddBlock(Argon_size_depedence.tex,126,6) ++ The daughter ion is assumed to be emitted isotropically and we considered the case of variable kinetic energy released (KE$_2$) in the dissociation. One should notice that from momentum conservation, the kinetic energy of the daughter ion is expressed as: KE$_d=(m_m-m_d)/m_m$KE$_2$. The final time of flight is constructed with Monte-Carlo integration and we convolute the numerical peak shape with our experimental broadening. To understand the result of the simulation, different cases ought to be considered. We present in figure the characteristic peak shapes obtained when the $\tau_m>>$t$_{acc}$, $\tau_m\sim $t$_{acc}$ and $\tau_m<<$t$_{acc}$ where t$_{acc}$ is the travel time of the mother ion from source point to the entrance of the drift tube. ++ \begin{itemize} ++ \item[-] For $\tau_m>>$t$_{acc}$, the mother ion mostly dissociates in the drift tube and the daughter ion arrives at the time of flight of the mother ion (t$_m$). The daughter ion peak is symmetric and exhibit a typical "eiffel tower" shape which correspond exactly to our observation in figure \ref{Fig4}, when the photo-ionic-dimers and the photo-ionic-trimers arise from the smallest cluster sizes ($<$N$>$=10,20). The time spread is related to kinetic energy imparted to the daughter ion, to the field strength as well as to the length of the drift tube. ++ \item[-] If $\tau_m\sim $t$_{acc}$, a significant amount of daughter ions can reach the detector at the flight time of the mother ion ($t_m$) and at a shorter flight time (t$_d$). For ions arriving at $t_m$, the peak shape is still symmetric but roundish and the time spread informs on the kinetic energy imparted to the daughter ion. The "round" shape and the ratio between the amount of daughter ions at $t_m$ and $t_d$ are strongly related to $\tau_m$. This situation is clearly seen in figure \ref{Fig4} for the photo-ionic-trimers with average cluster sizes of $<$N$>$=100, 1000. A similar trend is also suggested for photo-ionic-dimers. ++ \item[-] For $\tau_m<<$t$_{acc}$, the mother ion dissociates mostly before the drift tube and the daughter ion arrives with a short time of flight (t$_d$). The daughter ion peak is asymmetric and looks like an exponential decay which actually follows the dissociation rate eqn~(\ref{eqn:daughters}). The peak shape is in that case independent of the extraction condition as well as the kinetic energy KE$_1$ and KE$_2$ but depends on the ratio $m_d/m_m$. Such exponential decay is observed in figure \ref{Fig4} for the photo-ionic-dimer with average cluster sizes of $<$N$>$=100, 1000. ++ \end{itemize} DelBlock(Argon_size_depedence.tex,133,9) -- We present in figure the characteristic peak shapes obtained when the $\tau_m<<$t$_{acc}$, $\tau_m\sim $t$_{acc}$ and $\tau_m>>$t$_{acc}$ where t$_{acc}$ is the travel time of the mother ion from source point to the entrance of the drift tube. -- -- \begin{figure}[t] -- \centering -- \scalebox{1}{\includegraphics{figure4.eps}} -- \caption{\label{Fig4} Mass spectra for cluster with 10 up to 1000 atoms at 116~eV. The spectra are normalized with respect to the total number of electrons (starts) and to the acquisition time, so the intensity of each peak reflects the partial cross section of each photo-ions multiplied with its detection probability} -- \end{figure} -- -- \section{Results and Discussion} AddBlock(Argon_size_depedence.tex,133,2) ++ \subsubsection{On metastable decay} ++ In the following we focus our analysis on the peaks arising from the multi-coincidence events because they can be unambiguously interpreted at the origin of our observation. Furthermore we can determine the size of mother ionic clusters from the multi-coincidence spectra \cite{Gisselbrecht_2007}. Time-dependent fragmentation dynamics of large multiply charged van-der-Walls clusters has been studied theoretically \cite{Casero_1988}. Asymmetric Coulomb fission of doubly charged clusters is expected to take place in the picosecond time scale below their critical size ($N_c$=89), while above the critical size it occurs in a tenth of microsecond. This theoretical results is in agreement with earlier experimental results performed above the $L$-edges \cite{Ruhl_1994} and our own observation in PEPIPICO spectra. Thus the primary fragmentation, which occurs in the ps time scale, introduces only kinetic energy to the mother cluster (KE$_1$). Meta-stable decays of photo-ionic-clusters from a few ns to the microsecond time scale are then assumed to be the reasons for the specific peak shape. With our present statistics, the shapes in different fragmentation channels have the same behavior, and we can only apply a simple model to extrapolate typical time scales for various processes. We present in table I, the result of our simulation for photo-ionic-dimer and photo-ionic-trimer species DelBlock(Argon_size_depedence.tex,136,27) -- \subsection{Mass spectra} -- -- In figure~\ref{Fig4}, mass spectra after ionization by 116~eV photons are shown for a series of clusters of average sizes $<$N$>$ = 10, 20, 100 and 1000. Since the cluster beam contains a large amount of uncondensed argon atoms, which produce atomic ions (even multiply charged) in the spectrum, we assume that most, but not all such ions, come from atoms in the sample. All heavier ions (time of flight $>$1400~ns) arise only from clusters. As we can see, the peak height of the ionic cluster fragments is almost constant between $<$N$>$=10 and 20 atoms, then decreases drastically for average cluster sizes above 20 atoms. This decrease in height is combined with a change in width. The peaks change from relatively narrow profile lines for $<$N$>$=10 and $<$N$>$=20, to broad features for larger clusters. In the $<$N$>$=100 and $<$N$>$=1000 spectra, all cluster peaks are affected, and the peak widths are broader for heavier fragments (see the insert Fig~\ref{Fig4}). Furthermore monomer and dimer peak shapes for large clusters becomes distinctly asymmetric while all other peaks stay mostly symmetric. One should note that these observations are independent of the expansion conditions as it was checked with different set of nozzle, pressure and temperature. -- -- \subsection{Peak shape} -- The broadening of the peak in these series of spectra cannot be explained simply as the fragmentation of singly ionized clusters in the ground state. Indeed using the model developed by Haberland \cite{Haberland_book_1994,Haberland_book_1995}, cluster ionization is followed simply by neutral evaporation which tends to cool down the cluster. The typical energy released in this unimolecular fragmentation is typically 60-200~meV \cite{Ikegami_1993,Hrivnak_2001}. Although it is known that other dissociation mechanisms are possible at this photon energy, for instance after inner-valence shell ionization \cite{Thissen_1998}, one can assume that the dominant decay channel observed is related to one vacancy in the outer shell. Hence large clusters fragment statistically: the excess energy is shared among all degrees of freedom and the kinetic energy of the fragment does not increase as a function of the cluster size. The observed fragmentation processes would imply a substantial amount of stored internal energy. -- -- Another hint which supports that our observation does not follow the classical picture of single ionization is that the neutral cluster size distribution (see fig~\ref{Fig2}) tells us that one should expect at least 3 orders of magnitude less signal between small and large clusters. In fact we observe not more than one order of magnitude difference when we integrate the signal over the whole peak. The origin of photo-cluster ions has to change from small to large clusters. -- -- \begin{figure} -- \centering -- \scalebox{1}{\includegraphics{figure5.eps}} -- \caption{\label{Fig5} The Ar$_2^+$ and Ar$_3^+$ photo-ion peaks Fig~\ref{Fig4} are shown using a solid line. The dashed line represents the line shape for the same ion measures in a double, triple and quadruple ion-coincidence event. } -- \end{figure} -- -- \subsubsection{Origin} -- In figure \ref{Fig5}, a detailed view of the dimer (Ar$_2^+$) and trimer (Ar$_3^+$) fragments is presented for the same average sizes as in figure~\ref{Fig4}. Ar$_2^+$ and Ar$_3^+$ fragments are selected because they nicely illustrate our observations. The dashed lines shown in each plot are the sum of time-of-flight distributions of the same fragment measured in multiple-coincidence event, where several photo-ions are detected together [sum of projected PE(PI)$_n$CO spectra n$>$1]. The peak shape in these spectra is unambiguously related to fragmentation of multiply charged clusters. -- -- For the smallest clusters size ($<$N$>$=10, 20), the single ionization dominates, but there is certainly a contribution from multiply-charged species which corresponds to the wing broadening in the real mass spectra. For average cluster sizes $\geq$100 atoms, the real mass spectra mimic almost perfectly the time-of-flight distributions arising from multiple charged species. This means that these photo-ions are actually fragments arising from large multiply charged clusters. Multiply ionized clusters are expected to be stable when a critical size (N$_\text{c}$) is reached: for argon clusters, the first stable doubly charged species is at N$^{(2)}_c=$89 \cite{Gotts_1992} and the first stable triply charged species is at N$^{(3)}_c=$226 \cite{Scheier_87}. Thus, for the largest cluster sizes in our experiment, the most likely origin for the photo-ions is the fragmentation of unstable doubly/triply charged clusters which are always produced due to the broad neutral cluster size distributions. Assuming this, one should expect a maximum production of unstable multiply charged species for a size $<$N$>$=100 since all clusters with a size below 89 or 226 undergo fragmentation if they are doubly or triply charged. It is actually what is observed in the time-of-flight distributions of fragments measured in multiple-coincidence event. The count rate increases from $<$N$>$=10 to $<$N$>$=100, and decreases from $<$N$>$=100 to $<$N$>$=1000. -- -- This astounding importance of multiply charged species deserve further discussion. Although at this photon energy the double photo ionization cross section for free atoms is a minor channel, for clusters there are actually two more mechanisms that lead to the formation of multiply charged species. First, the double ionization continuum in 3p shell decreases from 43~eV in atoms to 32~eV in clusters of size N=101 \cite{Scheier_87}. Due to this lowering of the adiabatic ionization potentials, high ionic excited states (e.g. Ar$_m^{*+}$) auto-ionize into the double ionization continuum. For instance, a single charge exchange between atoms can occur, opening dissociation channels Ar$_p^+$ + Ar$_q^+$ located around $\sim$31~eV (depending on the cluster size). Secondly, ÒindirectÓ processes like scattering of a primary electron on another atom can also occur as it has been pointed out in studies on large clusters. In our case, direct photo-ionization can produce either one electron from the ($3p/3s$) shells, or two/three electrons from the 3p shell, thus the electron kinetic energies can range from 0-100~eV. This corresponds to an inelastic mean free path which can be smaller than the cluster size. Inelastic scattering is expected to be mainly significant close to atomic ionization thresholds as it has been shown in Ne \cite{Hergenhahn_2002}, but this mechanism could be emphasized by the auto-ionization of high ionic excited states (e.g. Ar$_m^{*+}$) which would produced low kinetic energy electrons. Such mechanism would heat up the cluster, increase the overall degree of ionization and strengthen Coulomb repulsion forces. -- % copy paste the last sentence "Such mechanism..." -- -- \subsubsection{Analysis: influence of meta-stable decay} -- Our aim is to understand the fragmentation of the multiply charged clusters; we will in the following only treat the peaks arising from multi-coincidence events. Time dependent fragmentation dynamics of large multiply charged van-der-Walls clusters have been studied theoretically \cite{Casero_1988}. Asymmetric Coulomb fission of doubly charged clusters is expected below their critical size ($N_c$=89) to take place in the picosecond time scale, while above the critical size it occurs in a tenth of microsecond. This is in agreement with previous experimental results performed above the $L$-edges \cite{Ruhl_1994} and our own observation in PEPIPICO spectra. Thus we will assume that only meta-stable decays of clusters are the reasons for the peak shape since the fragmentation which happen in the ps time scale just introduce kinetic energy to the mother ion. Furthermore, with our present statistics, shapes in different fragmentation channels have the same behavior, thus we use a simple model to extrapolate a typical time scale for various process using numerical simulation. -- -- \begin{table}[t] AddBlock(Argon_size_depedence.tex,136,1) ++ \begin{table}[t] DelBlock(Argon_size_depedence.tex,157,2) -- In figure \ref{Fig5}, the Ar$_2^+$ and Ar$_3^+$ peaks (dashed-line) arising from the smallest cluster -- sizes ($<$N$>$=10,20), exhibit a typical peak shape with "eiffel tower" signature of decay in the drift tube. For dimer channels, it corresponds to the degradation of Ar$^+_2\rightarrow$Ar$^+$+Ar. According to Whitaker~\textit{et al.} \cite{Whitaker_93} this process can arise from radiative decay from the electronic $\Pi$(1/2)$_u$ state of the ion to the I(1/2)$_g$. Such decay is reasonable in our experiment since there is no particular reason to produce dimer fragments arising from the fragmentation of multiply charge clusters only in its ground state. However, one should keep in mind that collision induced dissociation (CID) is very a likely reason for cluster-ion degradation for background pressure above 10$^{-7}$~mbar which was the case. Our experimental resolution is not good enough to properly quantify the importance of such process but we think that at least both processes can happen. For the trimer, the gaussian like distribution is due to a more complex fragmentation mechanisms which can lead either to formation of monomer or dimer depending on the internal energy left in the trimer, blurring hence the "Eiffel-tower" distribution. We present in table I, the result of our simulation in order to give an estimation of the time scale associated the degradation of this species. Accurate values for the kinetic energy KE$_1$ and KE$_2$ are hard to extract since both parameters behave similarly, however one can estimate that they are in the order of 500~meV down to 100~meV. DelBlock(Argon_size_depedence.tex,158,7) -- In the case of large clusters (from 100 to 1000), these peaks are no longer sharp. The shape can be explained either considering that fragments carry away measurable kinetic energy upon fragmentation of multiply charged species or meta-stable decay leading to neutral evaporation. -- % sentence rearranged -- To reproduce the roundish-shape of the peak with the simulation, the time-scale of such process has to be on the order of time-of-flight until the drift tube (t$^{dimer/trimer}_{acc}$) . -- % -- The typical kinetic energy KE$_1$ and KE$_2$ is on the order of 2~eV down to 300~meV. Another peculiar feature is observed in the fragmentation of large clusters, the Ar$_2^+$ line profile exhibits an asymmetric wing (tail) extending towards longer time-of-flight while Ar$_3^+$ is symmetric. This tail is a clear signature of decay producing dimer in a time scale shorter then t$^{dimer}_{acc}$: Ar$^+_m\rightarrow$Ar$^+_2$+X. The fact that this tail occurs in dimer channels may reflect that dimer ionic core is the most likely unit formed inside large argon clusters as it has been observed on xenon clusters \cite{Laarmann_2002}. We performed measurement at a lower extraction field to increase the flight time for dimers in the extraction region from 150~ns to 320~ns and no change from the tail was observed, as it should be expected. %(trimer peak change from roundish shape to square shape ?) -- Since different mother ions can lead to the formation of the dimer the determination of the life-time cannot be accurate but has to be in the order of hundred ns. \\ -- The times-scale found for small cluster are typical for usual meta-stable unimolecular degradation of van-der-Waals clusters \cite{Stephan_1983, Lethbridge_1988}. In the case of large clusters, the time-scale is relatively short and it shows that there are strong interactions within the cluster. One should point out that for clusters of $<$N$>$=100 and 1000 atoms, the similarity of the two time-scales within the error bars implies that the fragmentation mechanism does not change drastically with cluster size. This corroborate that the observed mechanisms originate from the same species: unstable multiple charged clusters. It shows also that another dissociation mechanism is energetically possible when a certain size is reached. Note the small contribution from slow meta-stable decay as we have seen for small clusters. AddBlock(Argon_size_depedence.tex,158,4) ++ In the case of small clusters (from 10 to 20), the photo-ionic-dimer is produced essentially after the fast fragmentation of a doubly charged trimer in a picosecond time-scale. The photo-ionic-dimer undergoes further dissociation in the drift tube such as Ar$^+_2\rightarrow$Ar$^+$+Ar in microsecond time scale. A number studies \cite{Whitaker_93, Barat_2002, Lepere_2005} report on such unimolecular dissociation which can arise from the decay of the electronic II(1/2)$_u$ state of the ion to the I(1/2)$_g$ state. Furthemore, Collision induced dissociation (CID) of small argon cluster is also very probable mechanism for cluster-ion degradation at a background pressure above 10$^{-7}$~mbar as it was the case during the measurement\cite{Whitaker_93}. Although a detailed comparison with other mass selected clusters studies cannot be achieved because the usual observation time widow is at much longer time scale then in the present experiment, we think that not only CID mechanism occurs but our resolution is not good enough to properly quantify the importance of various mechanisms. Indeed, the fragmentation of doubly charged trimers is likely to produce photo-ionic-dimer with wide distribution of electronic and vibrational states. Photo-ionic-trimers arise mostly from the fast fragmentation of doubly and triply charged quadrimer. More complex dissociation mechanisms ought to be considerer because photo-ionic-trimer fragmentation can lead either to the formation of a monomer or a dimer in the drift tube. Accurate values for the kinetic energy KE$_1$ and KE$_2$ are hard to extract since both parameters behave similarly, however one can estimate that they are in the order of 500~meV down to 100~meV.\\ ++ Concerning large clusters (from 100 to 1000), a strong enhancement of the degree of ionization is observed, especially when the cluster size increase from 100 to 1000 atoms. The mother ionic clusters leading to the formation of photo-ionic-dimer and photo-ionic-trimer can either be doubly, triply or quadruply charged species. Hence, one can expect that the fragments carry away measurable kinetic energy upon the dissociation of multiply charged species. While in the doubly ionization channel mostly trimer and quintamer are the most relevant mother species, in the triply and quadruply ionization channel a large distribution of multiply charged mother clusters are observed. To reproduce the overall peak shapes with the simulation, the dissociation has to occur with a time-scale on the order of the time-of-flight until the drift tube (t$^{dimer/trimer}_{acc}$) . The typical kinetic energies KE$_1$ and KE$_2$ are of the order of 2~eV down to 300~meV. The peculiar asymmetric wing (tail) extending towards longer time-of-flight of Ar$_2^+$ is a clear signature of a decay producing dimer on a time scale shorter then t$^{dimer}_{acc}$: Ar$^+_m\rightarrow$Ar$^+_2$+X. The fact that this tail occurs only in the dimer channels may reflect that this ionic core is the most likely unit formed inside large argon clusters as it has been observed on xenon clusters \cite{Laarmann_2002}. We performed measurement at a lower extraction field to increase the flight time for dimers in the extraction region from 150~ns to 320~ns and no change from the tail was observed, as it should be expected. Note that a rather large size of mother ions contribute to the formation of the photo-ionic-dimer, thus the life-time cannot be extracted accurately but has to be in the order of hundred ns. \ \ ++ ++ In the case of large clusters, the time-scale of fragmentation is unusually short and shows that strong interactions lie within the cluster. The similarity of the time-scales (within the errors bars) for clusters of $<$N$>$=100 and 1000 atoms implies that a specific dissociation mechanism is reached. This threshold behavior corroborates that such a mechanism originates from similar physical origins. If electron scattering drives the dissociation mechanisms, the observed fragmentation depends on the location of the scattered electron with respect to the original site as well as the localization of the charges in the cluster (bulk or surface). The proximity of two charges would lead to reach locally the boiling point of the argon cluster, while a large separation between charges would leave more time for energy dissipation. The localization of charges close to the surface would result in the expulsion of a dimer, as it has been seen by A. Stace~\textit{et al.} \cite{Stace_1991} for large clusters. Other mechanisms can be considered since the time scale is long enough to localize a charged in the cluster and to create a self-trapped atomic or molecular excitons. Radiative decays from a molecular exciton (excimer), via bound-to-free transitions, are known to open dissociation channels. Studies on doubly charged clusters \cite{Ruhl_1993} have revealed the presence of a third continuum related to the decay from a dication excimer to Ar$^+$+ Ar$^+$ limit. To the best of our knowledge, XUV decay from excited cation excimer to the dissociation limit to Ar$^+$+ Ar has not been reported. The lifetimes can be however inferred through atomic radiative transitions \cite{Nist}, and estimated to vary from 300~ps to 200~ns which is in agreement with our measurement. DelBlock(Argon_size_depedence.tex,163,13) -- \begin{figure*}[t] -- \centering -- \scalebox{1}{\includegraphics{figure6.eps}} -- \caption{\label{Fig6} Schematic diagram of the photo-ionization at 116~eV. Only the channels producing unstable multiply charged species are considered. See text for details } -- \end{figure*} -- -- In Fig.~\ref{Fig6}, we present a summary of the possible mechanisms that we observe. At 116~eV photon energy, direct photo-ionization can produce about 15 \% of excited singly charged clusters Ar$_m^{+*}$ and about 16\% of doubly charged clusters Ar$_m^{2+}$ with or without additional energy. This species can relax into the double ionization continuum of the clusters. Inelastic scattering can also contribute to the formation multiply charged species to a certain extend. -- -- After fission, the extra internal energy of the cluster is released in different ways. For small clusters, it is likely that neutral evaporation (neutral expulsion) imparts most of the kinetic energy, while for large cluster this energy would be more dissipated among all the degrees of freedom. For instance molecular-dynamics in a liquid droplet model\cite{Casero_1988} shows that only fission due to Coulomb repulsion -- of triply ionized clusters could justify a delayed or thermal fragmentation. After ionization, the three charges would tend to form an equilateral triangle (minimum energy configuration), repelling simultaneously outwards, while the most favorable pathway to fission would preferably be that two of the charges approach each other while the other ones move outwards. This effect would leave time for thermal excitation to spread all over the cluster. This is in agreement with our observation since the tails in dimer are observed in coincidence spectra up to the 3rd degree, although these channels are very weak. In multi-layer argon surfaces, the energy dissipation of high lying ionic states is known to be the dominant primary electronic process for photo-desorption \cite{Dujardin_1990}. One could speculate that the same behavior is present here with the expulsion of dimer, as it has been seen by A. Stace~\textit{et al.} \cite{Stace_1991} for large clusters. Although the time scale is not the same, it may be that the internal energy in our experiment is high enough to enhance this mechanism. To the best of our knowledge, there is no evidence of such a relaxation mechanism in argon clusters but it has been found in He clusters \cite{Moller_99}. One should point out that the estimated typical time scale is long enough to localize a charged in the cluster followed by the formation of self-trapped atomic or molecular excitons. Radiative decays from a molecular exciton (excimer), via bound-to-free transitions, are known to open dissociation channels: for example for a neutral excited cluster to Ar+ Ar limit. Studies on doubly charged clusters \cite{Ruhl_1993} have revealed the presence of a third continuum related to the decay from a dication excimer to Ar$^+$+ Ar$^+$ limit. To the best of our knowledge, decay from excited cation excimer has not been reported but a likely dissociation limit to Ar$^+$+ Ar can be inferred through atomic radiative transitions \cite{Nist}. Lifetimes for these excitons can be estimated to vary from 300~ps to 200~ns which could be is in agreement with our measurement. -- -- Finally, after energy dissipation, the small photo-clusters are produced and travel toward the spectrometer. During this time they can undergo further degradation. -- AddBlock(argonbib.bib,52,12) ++ @ARTICLE{Bobbert_2002, ++ author = {{C. Bobbert} and {S. Sch\"{u}tte} and {C. Steinbach} and {U. Buck}}, ++ title = {Fragmentation and reliable size distribution of large ammonia and ++ water clusters}, ++ journal = {Eur. Phys. J. D}, ++ year = {2002}, ++ volume = {19}, ++ pages = {183}, ++ owner = {mathieu}, ++ timestamp = {2007.03.15}, ++ } ++ AddBlock(argonbib.bib,297,18) ++ @ARTICLE{Barat_2002, ++ author = {{M. Barat} and {JC. Brenot JC} and {JA. Fayeton} and {YJ. Picard}}, ++ title = {Collision induced fragmentation of small ionic argon clusters}, ++ journal = {J. Chem. Phys.}, ++ year = {2002}, ++ volume = {117}, ++ pages = {1497}, ++ owner = {mathieu}, ++ timestamp = {2007.03.15}, ++ } ++ ++ @UNPUBLISHED{Gisselbrecht_2007, ++ author = {{M. Gisselbrecht {\it et al.}}}, ++ note = {to be published}, ++ owner = {mathieu}, ++ timestamp = {2007.03.26}, ++ } ++ AddBlock(argonbib.bib,340,14) ++ @ARTICLE{Lundwall_2006, ++ author = {{M. Lundwall} and {A. Lindblad} and {H. Bergersen} and {T. Rander} ++ and {G. Ohrwall} and {M. Tchaplyguine} and {S. Peredkov} and {S. ++ Svensson} and {O. Bjorneholm}}, ++ title = {Photon energy dependent intensity variations observed in Auger spectra ++ of free argon clusters}, ++ journal = {J. Phys. B.}, ++ year = {2006}, ++ volume = {39}, ++ pages = {3321}, ++ owner = {mathieu}, ++ timestamp = {2007.03.26}, ++ } ++ AddBlock(argonbib.bib,394,15) ++ @ARTICLE{Tchaplyguine_2004, ++ author = {{M. Tchaplyguine} and {RR. Marinho} and {M. Gisselbrecht} and {J. ++ Schulz} and {N. Martensson} and {SL. Sorensen} and {AN. de Brito} ++ and {Feifel R} and {G. \"{O}hrwall} and {M. Lundwall} and {S. Svensson} ++ and {O. Bj\"{o}orneholm}}, ++ title = {The size of neutral free clusters as manifested in the relative bulk-to-surface ++ intensity in core level photoelectron spectroscopy}, ++ journal = {J. Chem. Phys}, ++ year = {2004}, ++ volume = {120}, ++ pages = {345}, ++ owner = {mathieu}, ++ timestamp = {2007.03.15}, ++ } ++ DelBlock(argonbib.bib,462,1) -- note = {to be published }, AddBlock(argonbib.bib,462,1) ++ note = {to be published}, AddBlock(argonbib.bib,556,13) ++ @ARTICLE{Kakar_1997, ++ author = {{S. Kakar} and {O. Bj\"{o}rneholm} and {J. Weigelt} and {A. R. B. ++ de Castro} and {L. Trger} and {R. Frahm} and {T. M\"{o}ller} and ++ {A. Knop} and {E. R\"{u}hl}}, ++ title = {Size-dependent K-edge EXAFS study of the structure of free Ar clusters}, ++ journal = {Phys. Rev. Lett}, ++ year = {1997}, ++ volume = {78}, ++ pages = {1675}, ++ owner = {mathieu}, ++ timestamp = {2007.03.14}, ++ } ++ AddBlock(argonbib.bib,585,12) ++ @ARTICLE{Aoto_2006, ++ author = {{T. Aoto} and {K. Ito} and {Y. Hikosaka} and {E. Shigemasa} and {F. ++ Penent} and {P. Lablanquie}}, ++ title = {Properties of Resonant Interatomic Coulombic Decay in Ne Dimers}, ++ journal = {Phys. Rev. Lett}, ++ year = {2006}, ++ volume = {97}, ++ pages = {243401}, ++ owner = {mathieu}, ++ timestamp = {2007.03.15}, ++ } ++ AddBlock(argonbib.bib,691,11) ++ @ARTICLE{Lepere_2005, ++ author = {{V. Lepere} and {IM. Ismail} and {M. Barat} and {JA. Fayeton} and ++ {YJ. Picard} and {K. Wohrer} and {C. Jouvet} and {S. Martrenchard}}, ++ journal = {J. Chem. Phys.}, ++ year = {2005}, ++ volume = {123}, ++ pages = {174307}, ++ owner = {mathieu}, ++ timestamp = {2007.03.15}, ++ } ++ AddBlock(argonbib.bib,747,14) ++ @ARTICLE{Morishita_2006, ++ author = {{Y. Morishita} and {XJ. Liu} and {N. Saito} and {T. Lischke} and ++ {M. Kato} and {G. Prumper} and {M. Oura} and {H. Yamaoka} and {Y. ++ Tamenori} and {IH. Suzuki} and {K. Ueda}}, ++ title = {Experimental evidence of interatomic Coulombic decay from the Auger ++ final states in argon dimers}, ++ journal = {Phys. Rev. Lett.}, ++ year = {2006}, ++ volume = {96}, ++ pages = {243402}, ++ owner = {mathieu}, ++ timestamp = {2007.03.15}, ++ } ++ AddBlock(argonbib.bib.bak,52,12) ++ @ARTICLE{Bobbert_2002, ++ author = {{C. Bobbert} and {S. Sch\"{u}tte} and {C. Steinbach} and {U. Buck}}, ++ title = {Fragmentation and reliable size distribution of large ammonia and ++ water clusters}, ++ journal = {Eur. Phys. J. D}, ++ year = {2002}, ++ volume = {19}, ++ pages = {183}, ++ owner = {mathieu}, ++ timestamp = {2007.03.15}, ++ } ++ AddBlock(argonbib.bib.bak,297,18) ++ @ARTICLE{Barat_2002, ++ author = {{M. Barat} and {JC. Brenot JC} and {JA. Fayeton} and {YJ. Picard}}, ++ title = {Collision induced fragmentation of small ionic argon clusters}, ++ journal = {J. Chem. Phys.}, ++ year = {2002}, ++ volume = {117}, ++ pages = {1497}, ++ owner = {mathieu}, ++ timestamp = {2007.03.15}, ++ } ++ ++ @UNPUBLISHED{Gisselbrecht_2007, ++ author = {{M. Gisselbrecht {\it et al.}}}, ++ note = {to be published}, ++ owner = {mathieu}, ++ timestamp = {2007.03.26}, ++ } ++ DelBlock(argonbib.bib.bak,340,1) -- @ARTICLE{, AddBlock(argonbib.bib.bak,340,15) ++ @ARTICLE{Lundwall_2006, ++ author = {{M. Lundwall} and {A. Lindblad} and {H. Bergersen} and {T. Rander} ++ and {G. Ohrwall} and {M. Tchaplyguine} and {S. Peredkov} and {S. ++ Svensson} and {O. Bjorneholm}}, ++ title = {Photon energy dependent intensity variations observed in Auger spectra ++ of free argon clusters}, ++ journal = {J. Phys. B.}, ++ year = {2006}, ++ volume = {39}, ++ pages = {3321}, ++ owner = {mathieu}, ++ timestamp = {2007.03.26}, ++ } ++ ++ @ARTICLE{Lundwall_05, AddBlock(argonbib.bib.bak,394,15) ++ @ARTICLE{Tchaplyguine_2004, ++ author = {{M. Tchaplyguine} and {RR. Marinho} and {M. Gisselbrecht} and {J. ++ Schulz} and {N. Martensson} and {SL. Sorensen} and {AN. de Brito} ++ and {Feifel R} and {G. \"{O}hrwall} and {M. Lundwall} and {S. Svensson} ++ and {O. Bj\"{o}orneholm}}, ++ title = {The size of neutral free clusters as manifested in the relative bulk-to-surface ++ intensity in core level photoelectron spectroscopy}, ++ journal = {J. Chem. Phys}, ++ year = {2004}, ++ volume = {120}, ++ pages = {345}, ++ owner = {mathieu}, ++ timestamp = {2007.03.15}, ++ } ++ DelBlock(argonbib.bib.bak,462,1) -- note = {to be published }, AddBlock(argonbib.bib.bak,462,1) ++ note = {to be published}, AddBlock(argonbib.bib.bak,556,13) ++ @ARTICLE{Kakar_1997, ++ author = {{S. Kakar} and {O. Bj\"{o}rneholm} and {J. Weigelt} and {A. R. B. ++ de Castro} and {L. Trger} and {R. Frahm} and {T. M\"{o}ller} and ++ {A. Knop} and {E. R\"{u}hl}}, ++ title = {Size-dependent K-edge EXAFS study of the structure of free Ar clusters}, ++ journal = {Phys. Rev. Lett}, ++ year = {1997}, ++ volume = {78}, ++ pages = {1675}, ++ owner = {mathieu}, ++ timestamp = {2007.03.14}, ++ } ++ AddBlock(argonbib.bib.bak,585,12) ++ @ARTICLE{Aoto_2006, ++ author = {{T. Aoto} and {K. Ito} and {Y. Hikosaka} and {E. Shigemasa} and {F. ++ Penent} and {P. Lablanquie}}, ++ title = {Properties of Resonant Interatomic Coulombic Decay in Ne Dimers}, ++ journal = {Phys. Rev. Lett}, ++ year = {2006}, ++ volume = {97}, ++ pages = {243401}, ++ owner = {mathieu}, ++ timestamp = {2007.03.15}, ++ } ++ AddBlock(argonbib.bib.bak,691,11) ++ @ARTICLE{Lepere_2005, ++ author = {{V. Lepere} and {IM. Ismail} and {M. Barat} and {JA. Fayeton} and ++ {YJ. Picard} and {K. Wohrer} and {C. Jouvet} and {S. Martrenchard}}, ++ journal = {J. Chem. Phys.}, ++ year = {2005}, ++ volume = {123}, ++ pages = {174307}, ++ owner = {mathieu}, ++ timestamp = {2007.03.15}, ++ } ++ AddBlock(argonbib.bib.bak,747,14) ++ @ARTICLE{Morishita_2006, ++ author = {{Y. Morishita} and {XJ. Liu} and {N. Saito} and {T. Lischke} and ++ {M. Kato} and {G. Prumper} and {M. Oura} and {H. Yamaoka} and {Y. ++ Tamenori} and {IH. Suzuki} and {K. Ueda}}, ++ title = {Experimental evidence of interatomic Coulombic decay from the Auger ++ final states in argon dimers}, ++ journal = {Phys. Rev. Lett.}, ++ year = {2006}, ++ volume = {96}, ++ pages = {243402}, ++ owner = {mathieu}, ++ timestamp = {2007.03.15}, ++ } ++ AddBinaryFile(Figures/daughter.eps) UpdateBinaryFile(Figures/Figure1.eps) UpdateBinaryFile(Figures/Figure3.eps) UpdateBinaryFile(Figures/Figure4.eps) AddBinaryFile(Figures/Figure4_v0.eps) AddBinaryFile(Figures/Figure5_v0.eps) AddBinaryFile(Figures/Graph2.eps) AddBinaryFile(Figures/mother.eps) AddBinaryFile(Figures/size_distri.eps) Remove(Figures/Figure5_old.eps)
Copy-paste 1 sentence; rearrange 1sentence; add 1 sentence with inelastic scattering for fig 6
UpdateBinaryFile(Argon_size_depedence.dvi) UpdateBinaryFile(Argon_size_depedence.pdf) DelBlock(Argon_size_depedence.tex,146,1) -- This astounding importance of multiply charged species deserve further discussion. Although at this photon energy the double photo ionization cross section for free atoms is a minor channel, for clusters there are actually two more mechanisms that lead to the formation of multiply charged species. First, the double ionization continuum in 3p shell decreases from 43~eV in atoms to 32~eV in clusters of size N=101 \cite{Scheier_87}. Due to this lowering of the adiabatic ionization potentials, high ionic excited states (e.g. Ar$_m^{*+}$) auto-ionize into the double ionization continuum. For instance, a single charge exchange between atoms can occur, opening dissociation channels Ar$_p^+$ + Ar$_q^+$ located around $\sim$31~eV (depending on the cluster size). Secondly, ÒindirectÓ processes like scattering of a primary electron on another atom can also occur as it has been pointed out in studies on large clusters. In our case, direct photo-ionization can produce either one electron from the ($3p/3s$) shells, or two/three electrons from the 3p shell, thus the electron kinetic energies can range from 0-100~eV. This corresponds to an inelastic mean free path which can be smaller than the cluster size. Such mechanism would heat up the cluster, increase the overall degree of ionization and strengthen Coulomb repulsion forces. Inelastic scattering is expected to be mainly significant close to atomic ionization thresholds as it has been shown in Ne \cite{Hergenhahn_2002}, but this mechanism could be emphasized by the auto-ionization of high ionic excited states (e.g. Ar$_m^{*+}$) which would produced low kinetic energy electrons. AddBlock(Argon_size_depedence.tex,146,2) ++ This astounding importance of multiply charged species deserve further discussion. Although at this photon energy the double photo ionization cross section for free atoms is a minor channel, for clusters there are actually two more mechanisms that lead to the formation of multiply charged species. First, the double ionization continuum in 3p shell decreases from 43~eV in atoms to 32~eV in clusters of size N=101 \cite{Scheier_87}. Due to this lowering of the adiabatic ionization potentials, high ionic excited states (e.g. Ar$_m^{*+}$) auto-ionize into the double ionization continuum. For instance, a single charge exchange between atoms can occur, opening dissociation channels Ar$_p^+$ + Ar$_q^+$ located around $\sim$31~eV (depending on the cluster size). Secondly, ÒindirectÓ processes like scattering of a primary electron on another atom can also occur as it has been pointed out in studies on large clusters. In our case, direct photo-ionization can produce either one electron from the ($3p/3s$) shells, or two/three electrons from the 3p shell, thus the electron kinetic energies can range from 0-100~eV. This corresponds to an inelastic mean free path which can be smaller than the cluster size. Inelastic scattering is expected to be mainly significant close to atomic ionization thresholds as it has been shown in Ne \cite{Hergenhahn_2002}, but this mechanism could be emphasized by the auto-ionization of high ionic excited states (e.g. Ar$_m^{*+}$) which would produced low kinetic energy electrons. Such mechanism would heat up the cluster, increase the overall degree of ionization and strengthen Coulomb repulsion forces. ++ % copy paste the last sentence "Such mechanism..." DelBlock(Argon_size_depedence.tex,174,1) -- % there was a double "a a typical peak shape DelBlock(Argon_size_depedence.tex,176,8) -- In the case of large clusters (from 100 to 1000), these peaks are no longer sharp. The shape can be explained either considering that fragments carry away measurable kinetic energy upon fragmentation of multiply charged species or meta-stable decay leading to neutral evaporation. From the simulation, it is clear that the time-scale of such process a has to be on the order of time-of-flight until the drift tube (t$^{dimer/trimer}_{acc}$) to reproduce the roundish-shape. The typical kinetic energy KE$_1$ and KE$_2$ is on the order of 2~eV down to 300~meV. Another peculiar feature is observed in the fragmentation of large clusters, the Ar$_2^+$ line profile exhibits an asymmetric wing (tail) extending towards longer time-of-flight while Ar$_3^+$ is symmetric. This tail is a clear signature of decay producing dimer in a time scale shorter then t$^{dimer}_{acc}$: Ar$^+_m\rightarrow$Ar$^+_2$+X. The fact that this tail occurs in dimer channels may reflect that dimer ionic core is the most likely unit formed inside large argon clusters as it has been observed on xenon clusters \cite{Laarmann_2002}. We performed measurement at a lower extraction field to increase the flight time for dimers in the extraction region from 150~ns to 320~ns and no change from the tail was observed, as it should be expected. %(trimer peak change from roundish shape to square shape ?) -- Since different mother ions can lead to the formation of the dimer the determination of the life-time cannot be accurate but has to be in the order -- % remove "a few hundred" -- of hundred ns. The times-scale found for small cluster are typical for usual meta-stable unimolecular degradation of van-der-Waals clusters \cite{Stephan_1983, Lethbridge_1988}. In the case of large clusters, the time-scale is relatively short and it shows that there are strong interactions within the cluster. One should point out that for clusters of $<$N$>$=100 and 1000 atoms, the similarity of the two time-scales within the error bars implies that the fragmentation mechanism does not change drastically with cluster size. This corroborate that -- %change: these observed mechanisms likely originates -- the observed mechanisms originate from the same species: unstable multiple charged clusters. -- % change "this shows also that one another" -- It shows also that another dissociation mechanism is energetically possible when a certain size is reached. Note the small contribution from slow meta-stable decay as we have seen for small clusters. AddBlock(Argon_size_depedence.tex,176,7) ++ In the case of large clusters (from 100 to 1000), these peaks are no longer sharp. The shape can be explained either considering that fragments carry away measurable kinetic energy upon fragmentation of multiply charged species or meta-stable decay leading to neutral evaporation. ++ % sentence rearranged ++ To reproduce the roundish-shape of the peak with the simulation, the time-scale of such process has to be on the order of time-of-flight until the drift tube (t$^{dimer/trimer}_{acc}$) . ++ % ++ The typical kinetic energy KE$_1$ and KE$_2$ is on the order of 2~eV down to 300~meV. Another peculiar feature is observed in the fragmentation of large clusters, the Ar$_2^+$ line profile exhibits an asymmetric wing (tail) extending towards longer time-of-flight while Ar$_3^+$ is symmetric. This tail is a clear signature of decay producing dimer in a time scale shorter then t$^{dimer}_{acc}$: Ar$^+_m\rightarrow$Ar$^+_2$+X. The fact that this tail occurs in dimer channels may reflect that dimer ionic core is the most likely unit formed inside large argon clusters as it has been observed on xenon clusters \cite{Laarmann_2002}. We performed measurement at a lower extraction field to increase the flight time for dimers in the extraction region from 150~ns to 320~ns and no change from the tail was observed, as it should be expected. %(trimer peak change from roundish shape to square shape ?) ++ Since different mother ions can lead to the formation of the dimer the determination of the life-time cannot be accurate but has to be in the order of hundred ns. \\ ++ The times-scale found for small cluster are typical for usual meta-stable unimolecular degradation of van-der-Waals clusters \cite{Stephan_1983, Lethbridge_1988}. In the case of large clusters, the time-scale is relatively short and it shows that there are strong interactions within the cluster. One should point out that for clusters of $<$N$>$=100 and 1000 atoms, the similarity of the two time-scales within the error bars implies that the fragmentation mechanism does not change drastically with cluster size. This corroborate that the observed mechanisms originate from the same species: unstable multiple charged clusters. It shows also that another dissociation mechanism is energetically possible when a certain size is reached. Note the small contribution from slow meta-stable decay as we have seen for small clusters. DelBlock(Argon_size_depedence.tex,190,1) -- In Fig.~\ref{Fig6}, we present a summary of the possible mechanisms that we observe. At 116~eV photon energy, direct photo-ionization can produce about 15 \% of excited singly charged clusters Ar$_m^{+*}$ and about 16\% of doubly charged clusters Ar$_m^{2+}$ with or without additional energy. This species can relax into the double ionization continuum of the clusters. AddBlock(Argon_size_depedence.tex,190,1) ++ In Fig.~\ref{Fig6}, we present a summary of the possible mechanisms that we observe. At 116~eV photon energy, direct photo-ionization can produce about 15 \% of excited singly charged clusters Ar$_m^{+*}$ and about 16\% of doubly charged clusters Ar$_m^{2+}$ with or without additional energy. This species can relax into the double ionization continuum of the clusters. Inelastic scattering can also contribute to the formation multiply charged species to a certain extend. DelBlock(Argon_size_depedence.tex,193,1) -- % set the ref for the droplet liquid model\ Remove(Argon_size_depedence.pdf#288) Remove(Argon_size_depedence.log) Remove(Argon_size_depedence.dvi#222) Remove(Argon_size_depedence.blg) Remove(Argon_size_depedence.aux)
AddBlock(Argon_size_depedence.aux,67,1) ++ \@writefile{toc}{\contentsline {section}{\numberline {IV}Conclusion}{6}{}} DelBlock(Argon_size_depedence.aux,102,1) -- \@writefile{toc}{\contentsline {section}{\numberline {IV}Conclusion}{7}{}} UpdateBinaryFile(Argon_size_depedence.dvi) DelBlock(Argon_size_depedence.log,1,1) -- This is e-TeX, Version 3.141592-2.1 (MiKTeX 2.4) (preloaded format=latex 2004.8.20) 27 AUG 2006 18:02 AddBlock(Argon_size_depedence.log,1,1) ++ This is e-TeX, Version 3.141592-2.1 (MiKTeX 2.4) (preloaded format=latex 2004.8.20) 28 AUG 2006 09:48 DelBlock(Argon_size_depedence.log,173,1) -- LaTeX Font Info: Try loading font information for U+lasy on input line 55. AddBlock(Argon_size_depedence.log,173,1) ++ LaTeX Font Info: Try loading font information for U+lasy on input line 54. DelBlock(Argon_size_depedence.log,178,1) -- LaTeX Font Info: Try loading font information for U+msa on input line 55. AddBlock(Argon_size_depedence.log,178,1) ++ LaTeX Font Info: Try loading font information for U+msa on input line 54. DelBlock(Argon_size_depedence.log,182,1) -- LaTeX Font Info: Try loading font information for U+msb on input line 55. AddBlock(Argon_size_depedence.log,182,1) ++ LaTeX Font Info: Try loading font information for U+msb on input line 54. DelBlock(Argon_size_depedence.log,193,1) -- Underfull \hbox (badness 1622) in paragraph at lines 95--96 AddBlock(Argon_size_depedence.log,193,1) ++ Underfull \hbox (badness 1622) in paragraph at lines 94--95 DelBlock(Argon_size_depedence.log,205,1) -- on input line 109. AddBlock(Argon_size_depedence.log,205,1) ++ on input line 108. DelBlock(Argon_size_depedence.log,209,1) -- Overfull \hbox (0.92249pt too wide) in paragraph at lines 121--122 AddBlock(Argon_size_depedence.log,209,1) ++ Overfull \hbox (0.92249pt too wide) in paragraph at lines 120--121 DelBlock(Argon_size_depedence.log,219,1) -- Underfull \hbox (badness 2521) in paragraph at lines 147--148 AddBlock(Argon_size_depedence.log,219,1) ++ Underfull \hbox (badness 2521) in paragraph at lines 146--147 DelBlock(Argon_size_depedence.log,233,2) -- 34222 string characters out of 1195288 -- 107756 words of memory out of 1094637 AddBlock(Argon_size_depedence.log,233,2) ++ 34221 string characters out of 1195288 ++ 107503 words of memory out of 1094384 DelBlock(Argon_size_depedence.log,238,1) -- 29i,8n,22p,2163b,313s stack positions out of 1500i,500n,5000p,200000b,32768s AddBlock(Argon_size_depedence.log,238,1) ++ 29i,8n,22p,2165b,313s stack positions out of 1500i,500n,5000p,200000b,32768s DelBlock(Argon_size_depedence.log,240,1) -- Output written on Argon_size_depedence.dvi (7 pages, 49240 bytes). AddBlock(Argon_size_depedence.log,240,1) ++ Output written on Argon_size_depedence.dvi (7 pages, 49104 bytes). UpdateBinaryFile(Argon_size_depedence.pdf) DelBlock(Argon_size_depedence.tex,54,2) -- Photo-fragmentation of argon clusters with average size ranging from 10 up to 1000 atoms is reported at a photon energy of 116 eV using multi-coincidence technique with a mass spectrometer. A spectacular -- change in fragmentation pattern is observed when the cluster size increases revealing the different time scale of the dissociation mechanisms. For small clusters ($<$10$>$), after ionization a fast fragmentation with neutral emission imparting large amount of energy in the ps time scale occurs, then slow degradation of the photo-cluster ions is observed in the $\mu$s time scale. For larger clusters ($\geq <$100$>$) we believe that we observe the fragmentation pattern of large unstable multiply charged species in time scale which last a few hundred of ns. The reason for these apparent slow processes could be that the large amount of neutral atoms acts as an efficient cooling bath which tend to dissipate the excess of energy ("heat") among all degree of freedom. Degradation of the photo-cluster ions take place in the $\mu$s time scale as for small clusters. AddBlock(Argon_size_depedence.tex,54,1) ++ Photo-fragmentation of argon clusters of average size ranging from 10 up to 1000 atoms is reported at a photon energy of 116 eV using multi-coincidence technique with a mass spectrometer. A spectacular change in fragmentation pattern is observed when the cluster size increases, arising from a change in the dissociation time-scale. For small clusters ($<$10$>$), after ionization a fast fragmentation with neutral emission imparting large amount of energy in the ps time scale occurs, then slow degradation of the photo-cluster ions is observed in the $\mu$s time scale. For larger clusters ($\geq <$100$>$) we believe that we observe the fragmentation pattern of large unstable multiply charged species on a time-scale which lasts a few hundred ns. The reason for these apparent slow processes could be that the large number of neutral atoms acts as an efficient cooling bath which tends to dissipate the excess of energy ("heat") among all degrees of freedom. Degradation of the photo-cluster ions takes place in the $\mu$s time scale as for small clusters. DelBlock(Argon_size_depedence.tex,63,1) -- In a recent publication \cite{Gisselbrecht_2005} we presented the general fragmentation pattern of small argon clusters for resonant inner shell excitation and ionization. We did show that the inner shell photo-absorption prepared selectively ionic species below or above the vertical double ionization potential \cite{Maxim_2003, Lundwall_05}, respectively Ar$_m^{+*}$ and Ar$_m^{2+}$. In both case theses species undergo dissociation leading to two or more charged fragments pointing out the importance of the nuclear relaxation as well as the electronic relaxation. AddBlock(Argon_size_depedence.tex,63,1) ++ In a recent publication \cite{Gisselbrecht_2005} we presented the general fragmentation pattern of small argon clusters for resonant inner shell excitation and ionization. We showed that the inner shell photo-absorption selectively prepared ionic species below or above the vertical double ionization potential \cite{Maxim_2003, Lundwall_05}, respectively Ar$_m^{+*}$ and Ar$_m^{2+}$. In both case theses species undergo dissociation leading to two or more charged fragments pointing out the importance of the nuclear relaxation as well as the electronic relaxation. DelBlock(Argon_size_depedence.tex,72,1) -- The chosen photon energy implies that only the $3p$ valence and $3s$ inner valence shells can be ionized and Auger relaxation is energetically not possible. For free atoms, we are well above the double-ionization threshold 43.4~eV \cite{Nist}, the $3s$ Cooper minimum between 45-50~eV, and even exceeds the triple ionization threshold 84.3~eV\cite{Nist}. The branching ratios are known to be 83\% for single photo-ionization, 16\% for double photo-ionization, and less than 1\% for triple photo-ionization \cite{Holland_1979}. In the current picture of cluster ionization, so called Haberland's model \cite{Haberland_book_1995, Haberland_book_1994}, the system does not have time for nuclear rearrangement and states close to the dissociation limit are populated. Thus the cluster photo-ionization branching ratio should mimic the atomic one. However, in our experiment the time scale is long enough for nuclear relaxation to take place and adiabatic potentials to be relevant \cite{Ruhl_1992}. Hence, among the singly charge species a few of them ($\sim$15\%) prepared with two holes and one particle in the outer valence shell, should decay in the double ionization continuum as we have already eluded \cite{Gisselbrecht_2005}. Hence, one could speculate that the fragmentation depend on the cluster size. AddBlock(Argon_size_depedence.tex,72,1) ++ The chosen photon energy implies that only the $3p$ valence and $3s$ inner valence shells can be ionized and Auger relaxation is energetically not possible. For free atoms, we are well above the double-ionization threshold 43.4~eV \cite{Nist}, the $3s$ Cooper minimum between 45-50~eV, and even exceeds the triple ionization threshold 84.3~eV\cite{Nist}. The branching ratios are known to be 83\% for single photo-ionization, 16\% for double photo-ionization, and less than 1\% for triple photo-ionization \cite{Holland_1979}. In the current picture of cluster ionization, called Haberland's model \cite{Haberland_book_1995, Haberland_book_1994}, the system does not have time for nuclear rearrangement and states close to the dissociation limit are populated. Thus the cluster photo-ionization branching ratio should mimic the atomic one. However, in our experiment the time scale is long enough for nuclear relaxation to take place and adiabatic potentials to be relevant \cite{Ruhl_1992}. Hence, among the singly charged species a few of them ($\sim$15\%) prepared with two holes and one particle in the outer valence shell, should decay in the double ionization continuum as we have already implied \cite{Gisselbrecht_2005}. Hence, one could speculate that the fragmentation depends on the cluster size. DelBlock(Argon_size_depedence.tex,76,1) -- In Fig.~\ref{Fig1} we present the photo-ionization branching ratio for free argon atoms and where the decay channel are expected for cluster. Our aim is to investigate the photo-fragmentation over a size range from a few up to thousands of atoms in order to know whether the fragmentation dynamics is a sensitive probe to the formation of stable multiply ionized clusters. AddBlock(Argon_size_depedence.tex,76,1) ++ In Fig.~\ref{Fig1} the photo-ionization branching ratio for free argon atoms and corresponding fragmentation channels in clusters are shown. Our aim is to investigate the photo-fragmentation over a size range from a few up to thousands of atoms in order to determine whether the fragmentation dynamics is a sensitive probe to the formation of stable multiply ionized clusters. DelBlock(Argon_size_depedence.tex,105,1) -- From studies on cluster ion dynamic \cite{Stephan_1983, Lethbridge_1988}, the peak shape at this photon energy is the best described by meta-stable decay of the photo-clusters and photo-fragments within our time scale of observation. Therefore we developed a full numerical calculation of the time-of-flight distribution in our spectrometer. The trajectories of the particles are calculated by solving the classical motion equation of charged particles with a 4rth order Runge-Kutta algorithm \cite{NumericalRecipes}. Due to a large variety in orientation, geometry and size of the clusters in the beam, no alignment of the clusters is {\it a-priori} expected. Thus we used as initial condition an isotropic distribution of particles emitted in space. The mother ion is defined by its lifetime $\tau_m$ and its initial kinetic energy distribution (KE$_1$). The number of mother ions decreases in time as: AddBlock(Argon_size_depedence.tex,105,1) ++ From studies on cluster ion dynamics \cite{Stephan_1983, Lethbridge_1988}, the peak shape at this photon energy is the best described by meta-stable decay of the photo-clusters and photo-fragments within our time scale of observation. Therefore we developed a full numerical calculation of the time-of-flight distribution in our spectrometer. The trajectories of the particles are calculated by solving the classical motion equation of charged particles with a 4th-order Runge-Kutta algorithm \cite{NumericalRecipes}. Due to a large variety in orientation, geometry and size of the clusters in the beam, no alignment of the clusters is {\it a-priori} expected. Thus the initial condition is an isotropic distribution of particles emitted in space. The mother ion is defined by its lifetime $\tau_m$ and its initial kinetic energy distribution (KE$_1$). The number of mother ions decreases in time as: DelBlock(Argon_size_depedence.tex,112,1) -- N_\mathrm{d}(t)=N_0/\tau_m\exp(-t/\tau_m) AddBlock(Argon_size_depedence.tex,112,1) ++ N_\mathrm{d}(t)=N_0/\tau_m\exp(-t/\tau_m). DelBlock(Argon_size_depedence.tex,114,1) -- The daughter ion is assumed to be emitted with an isotropic distribution and we considered the case of variable release kinetic energy (KE$_2$) in the dissociation. One should notice that from momenta conservation, the kinetic energy of the daughter ion is expressed as: KE$_d=(m_m-m_d)/m_m$KE$_2$. The final time of flight is constructed with Monte-Carlo integration and we convolute the numerical peak shape with our experiment broadening. To understand the result of the simulation two cases ought to be considered. If the mother ion dissociate in the drift tube the daughter ion arrive at the time of flight of the mother ion (t$_m$). The peak is symmetric and the time spread is related to kinetic energy imparted to the daughter ion, the fields strength as well as the length of the drift tube. If the mother ion dissociation happens before the drift tube, the daughter ion arrive with a short time of flight (t$_d$). The peak is asymmetric and looks like an exponential decay which actually follows the dissociation rate eqn~(\ref{eqn:daughters}). The peak shape is in that case independent of the extraction condition as well as the kinetic energy KE$_1$ and KE$_2$ but depends on the ratio $m_d/m_m$. AddBlock(Argon_size_depedence.tex,114,1) ++ The daughter ion is assumed to be emitted with an isotropic distribution and we considered the case of variable kinetic energy released (KE$_2$) in the dissociation. One should notice that from momentum conservation, the kinetic energy of the daughter ion is expressed as: KE$_d=(m_m-m_d)/m_m$KE$_2$. The final time of flight is constructed with Monte-Carlo integration and we convolute the numerical peak shape with our experimental broadening. To understand the result of the simulation, two cases ought to be considered. If the mother ion dissociates in the drift tube the daughter ion arrives at the time of flight of the mother ion (t$_m$). The peak is symmetric and the time spread is related to kinetic energy imparted to the daughter ion, the field strength as well as the length of the drift tube. If the mother ion dissociation happens before the drift tube, the daughter ion arrive with a short time of flight (t$_d$). The peak is asymmetric and looks like an exponential decay which actually follows the dissociation rate eqn~(\ref{eqn:daughters}). The peak shape is in that case independent of the extraction condition as well as the kinetic energy KE$_1$ and KE$_2$ but depends on the ratio $m_d/m_m$. DelBlock(Argon_size_depedence.tex,116,1) -- We present in figure the characteristic peak shape obtained when the $\tau_m<<$t$_{acc}$, $\tau_m\sim $t$_{acc}$ and $\tau_m>>$t$_{acc}$ where t$_{acc}$ is the travel time of the mother ion from source point to the entrance of the drift tube. AddBlock(Argon_size_depedence.tex,116,1) ++ We present in figure the characteristic peak shapes obtained when the $\tau_m<<$t$_{acc}$, $\tau_m\sim $t$_{acc}$ and $\tau_m>>$t$_{acc}$ where t$_{acc}$ is the travel time of the mother ion from source point to the entrance of the drift tube. DelBlock(Argon_size_depedence.tex,128,1) -- In figure~\ref{Fig4}, mass spectra after ionization by 116~eV photons are shown for a series of clusters of average sizes $<$N$>$ = 10, 20, 100 and 1000. Since the cluster beam contains a large amount of uncondensed argon atoms, which produce atomic ions (even multiply charged) in the spectrum, we assume that most, but not all such ions, come from atoms in the sample. All heavier ions (time of flight $>$1400~ns) arise only from clusters. As we can see, the peak height of the ionic cluster fragments is almost constant between $<$N$>$=10 and 20 atoms, then decreases drastically for average cluster sizes above 20 atoms. This decrease in height is combined with a change in width. The peaks change from relatively narrow profile lines for $<$N$>$=10 and $<$N$>$=20, to broad features for larger clusters. In the $<$N$>$=100 and $<$N$>$=1000 spectra, all cluster peaks are affected, and the peak widths are broader for heavier fragments (see the insert Fig~\ref{Fig4}). Furthermore monomer and dimer peak shapes for large clusters becomes distinctly asymmetric while all other peaks stay mostly symmetric. One should notice that these observations are independent of the expansion conditions as it was checked with different set of nozzle, pressure and temperature. AddBlock(Argon_size_depedence.tex,128,1) ++ In figure~\ref{Fig4}, mass spectra after ionization by 116~eV photons are shown for a series of clusters of average sizes $<$N$>$ = 10, 20, 100 and 1000. Since the cluster beam contains a large amount of uncondensed argon atoms, which produce atomic ions (even multiply charged) in the spectrum, we assume that most, but not all such ions, come from atoms in the sample. All heavier ions (time of flight $>$1400~ns) arise only from clusters. As we can see, the peak height of the ionic cluster fragments is almost constant between $<$N$>$=10 and 20 atoms, then decreases drastically for average cluster sizes above 20 atoms. This decrease in height is combined with a change in width. The peaks change from relatively narrow profile lines for $<$N$>$=10 and $<$N$>$=20, to broad features for larger clusters. In the $<$N$>$=100 and $<$N$>$=1000 spectra, all cluster peaks are affected, and the peak widths are broader for heavier fragments (see the insert Fig~\ref{Fig4}). Furthermore monomer and dimer peak shapes for large clusters becomes distinctly asymmetric while all other peaks stay mostly symmetric. One should note that these observations are independent of the expansion conditions as it was checked with different set of nozzle, pressure and temperature. DelBlock(Argon_size_depedence.tex,131,1) -- The broadening of the peak in these series of spectra cannot be explained simply as the fragmentation of singly ionized clusters in the ground state. Indeed using the model developed by Haberland \cite{Haberland_book_1994,Haberland_book_1995}, cluster ionization is followed simply by neutral evaporation which tend to cool down the cluster. The typical energy released in this unimolecular fragmentation is typically 60-200~meV \cite{Ikegami_1993,Hrivnak_2001}. Although it is known that other dissociation mechanism are possible at this photon energy, for instance after inner-valence shell ionization \cite{Thissen_1998}, one can assume that the dominant decay channel observed is related to one vacancy in the outer shell. Hence large clusters fragment statistically: the excess energy is shared among all degrees of freedom and the kinetic energy of the fragment does not increase as a function of the cluster size. The observed fragmentation processes would imply a substantial amount of stored internal energy. AddBlock(Argon_size_depedence.tex,131,1) ++ The broadening of the peak in these series of spectra cannot be explained simply as the fragmentation of singly ionized clusters in the ground state. Indeed using the model developed by Haberland \cite{Haberland_book_1994,Haberland_book_1995}, cluster ionization is followed simply by neutral evaporation which tends to cool down the cluster. The typical energy released in this unimolecular fragmentation is typically 60-200~meV \cite{Ikegami_1993,Hrivnak_2001}. Although it is known that other dissociation mechanisms are possible at this photon energy, for instance after inner-valence shell ionization \cite{Thissen_1998}, one can assume that the dominant decay channel observed is related to one vacancy in the outer shell. Hence large clusters fragment statistically: the excess energy is shared among all degrees of freedom and the kinetic energy of the fragment does not increase as a function of the cluster size. The observed fragmentation processes would imply a substantial amount of stored internal energy. DelBlock(Argon_size_depedence.tex,133,1) -- Another hint which supports that our observation does not follow the classical picture of single ionization is that the neutral cluster size distribution (see fig~\ref{Fig2}) tell us that one should expect at least 3 orders of magnitude less signal between small and large clusters. In fact we observe not more than one order of magnitude difference when we integrate the signal over the whole peak. The origin of photo-cluster ions has to change from small to large cluster. AddBlock(Argon_size_depedence.tex,133,1) ++ Another hint which supports that our observation does not follow the classical picture of single ionization is that the neutral cluster size distribution (see fig~\ref{Fig2}) tells us that one should expect at least 3 orders of magnitude less signal between small and large clusters. In fact we observe not more than one order of magnitude difference when we integrate the signal over the whole peak. The origin of photo-cluster ions has to change from small to large clusters. DelBlock(Argon_size_depedence.tex,144,1) -- For the smallest clusters size ($<$N$>$=10, 20), the single ionization is strongly present but there is certain contribution of multiply charged species which corresponds to the wing broadening in the real mass spectra. For average cluster sizes $\geq$100 atoms, the real mass spectra mimic almost perfectly the time-of-flight distributions arising from multiple charged species. This means that these photo-ions are actually fragments arising from large multiply charged clusters. Multiply ionized clusters is expected to be stable when a critical size (N$_c$) is reached: for argon cluster, the first stable doubly charged species is at N$^{(2)}_c=$89 \cite{Gotts_1992} and the first triply stable charged species is at N$^{(3)}_c=$226 \cite{Scheier_87}. Thus, for the largest cluster sizes in our experiment, the most likely origin for the photo-ions is the fragmentation of unstable doubly/triply charged clusters which are always produced due to the broad neutral cluster size distributions. Assuming this one should expect a maximum production of unstable multiply charged species for a size $<$N$>$=100 since all clusters with a size below 89 or 226 undergo fragmentation if they are respectively doubly or triply charged. It is actually what is observed in the time-of-flight distributions of fragments measured in multiple-coincidence event. The count rate increase from $<$N$>$=10 to $<$N$>$=100, and decrease from $<$N$>$=100 to $<$N$>$=1000. AddBlock(Argon_size_depedence.tex,144,1) ++ For the smallest clusters size ($<$N$>$=10, 20), the single ionization dominates, but there is certainly a contribution from multiply-charged species which corresponds to the wing broadening in the real mass spectra. For average cluster sizes $\geq$100 atoms, the real mass spectra mimic almost perfectly the time-of-flight distributions arising from multiple charged species. This means that these photo-ions are actually fragments arising from large multiply charged clusters. Multiply ionized clusters are expected to be stable when a critical size (N$_\text{c}$) is reached: for argon clusters, the first stable doubly charged species is at N$^{(2)}_c=$89 \cite{Gotts_1992} and the first stable triply charged species is at N$^{(3)}_c=$226 \cite{Scheier_87}. Thus, for the largest cluster sizes in our experiment, the most likely origin for the photo-ions is the fragmentation of unstable doubly/triply charged clusters which are always produced due to the broad neutral cluster size distributions. Assuming this, one should expect a maximum production of unstable multiply charged species for a size $<$N$>$=100 since all clusters with a size below 89 or 226 undergo fragmentation if they are doubly or triply charged. It is actually what is observed in the time-of-flight distributions of fragments measured in multiple-coincidence event. The count rate increases from $<$N$>$=10 to $<$N$>$=100, and decreases from $<$N$>$=100 to $<$N$>$=1000. DelBlock(Argon_size_depedence.tex,146,1) -- This astounding importance of multiply charged species deserve further discussion. Although at this photon energy the photo double ionization cross section for free atoms is a minor channel, for clusters they are actually two more mechanisms that lead to the formation of multiply charged species. First, the double ionization continuum in 3p shell decreases from 43~eV in atoms to 32~eV in clusters of size N=101 \cite{Scheier_87}. Due to this lowering of the adiabatic ionization potentials, high ionic excited states (e.g. Ar$_m^{*+}$) auto-ionize into the double ionization continuum. For instance, a single charge exchange between atoms can occur, opening dissociation channels Ar$_p^+$ + Ar$_q^+$ located around $\sim$31~eV (depending on the cluster size). Secondly, ÒindirectÓ processes like scattering of a primary electron on another atom can also occur as it has been pointed out in studies on large clusters. In our case, direct photo-ionization can produce either one electron from the ($3p/3s$) shells, or two/three electrons from the 3p shell, thus the electron kinetic energies can range from 0-100~eV. This corresponds to an inelastic mean free path which can be smaller than the cluster size. Such mechanism would heat up the cluster, increase the overall degree of ionization and strengthen Coulomb repulsion forces. Inelastic scattering is expected to be mainly significant close to atomic ionization thresholds as it has been shown in Ne \cite{Hergenhahn_2002}, but this mechanism could be emphasized by the auto-ionization of high ionic excited states (e.g. Ar$_m^{*+}$) which would produced low kinetic energy electrons. AddBlock(Argon_size_depedence.tex,146,1) ++ This astounding importance of multiply charged species deserve further discussion. Although at this photon energy the double photo ionization cross section for free atoms is a minor channel, for clusters there are actually two more mechanisms that lead to the formation of multiply charged species. First, the double ionization continuum in 3p shell decreases from 43~eV in atoms to 32~eV in clusters of size N=101 \cite{Scheier_87}. Due to this lowering of the adiabatic ionization potentials, high ionic excited states (e.g. Ar$_m^{*+}$) auto-ionize into the double ionization continuum. For instance, a single charge exchange between atoms can occur, opening dissociation channels Ar$_p^+$ + Ar$_q^+$ located around $\sim$31~eV (depending on the cluster size). Secondly, ÒindirectÓ processes like scattering of a primary electron on another atom can also occur as it has been pointed out in studies on large clusters. In our case, direct photo-ionization can produce either one electron from the ($3p/3s$) shells, or two/three electrons from the 3p shell, thus the electron kinetic energies can range from 0-100~eV. This corresponds to an inelastic mean free path which can be smaller than the cluster size. Such mechanism would heat up the cluster, increase the overall degree of ionization and strengthen Coulomb repulsion forces. Inelastic scattering is expected to be mainly significant close to atomic ionization thresholds as it has been shown in Ne \cite{Hergenhahn_2002}, but this mechanism could be emphasized by the auto-ionization of high ionic excited states (e.g. Ar$_m^{*+}$) which would produced low kinetic energy electrons. DelBlock(Argon_size_depedence.tex,149,1) -- We are now interested to understand the fragmentation of the multiply charged cluster, we will in the following only treat the peaks arising form multi-coincidence events. Time dependent fragmentation dynamics of large multiply charged van-der-Walls clusters have been studied theoretically \cite{Casero_1988}. Asymmetric Coulomb fission of doubly charged clusters is expected below their critical size ($N_c$=89) to take place in the picosecond time scale, while above the critical size it occurs in a tenth of microsecond. This is in agreement with previous experimental results performed above the $L$-edges \cite{Ruhl_1994} and our own observation in PEPIPICO spectra. Thus we will assume that only meta-stable decays of clusters are the reasons for the peak shape since the fragmentation which happen in the ps time scale just introduce kinetic energy to the mother ion. Furthermore, with our present statistic, shapes in different fragmentation channels have the same behavior, thus we use a simple model to extrapolate a typical time scale for various process using numerical simulation. AddBlock(Argon_size_depedence.tex,149,1) ++ Our aim is to understand the fragmentation of the multiply charged clusters; we will in the following only treat the peaks arising from multi-coincidence events. Time dependent fragmentation dynamics of large multiply charged van-der-Walls clusters have been studied theoretically \cite{Casero_1988}. Asymmetric Coulomb fission of doubly charged clusters is expected below their critical size ($N_c$=89) to take place in the picosecond time scale, while above the critical size it occurs in a tenth of microsecond. This is in agreement with previous experimental results performed above the $L$-edges \cite{Ruhl_1994} and our own observation in PEPIPICO spectra. Thus we will assume that only meta-stable decays of clusters are the reasons for the peak shape since the fragmentation which happen in the ps time scale just introduce kinetic energy to the mother ion. Furthermore, with our present statistics, shapes in different fragmentation channels have the same behavior, thus we use a simple model to extrapolate a typical time scale for various process using numerical simulation. DelBlock(Argon_size_depedence.tex,174,1) -- sizes ($<$N$>$=10,20), exhibit a typical peak shape with "eiffel tower" signature of decay in the drift tube. For dimer channels, it corresponds to the degradation of Ar$^+_2\rightarrow$Ar$^+$+Ar. According to Whitaker~\textit{et al.} \cite{Whitaker_93} this process can arise from radiative decay from the electronic $\Pi$(1/2)$_u$ state of the ion to the I(1/2)$_g$. Such decay is reasonable in our experiment since there is no particular reason to produce dimer fragments arising from the fragmentation of multiply charge clusters only in its ground state. However, one should keep in mind that collision induced dissociation (CID) is very a likely reason for cluster-ion degradation for background pressure above 10$^{-7}$~mbar which was the case. Our experimental resolution is not good enough to quantify properly the importance of such process but we think that at least both processes can happen. For trimer, the gaussian like distribution is due to a more complex fragmentation mechanisms which can lead either to formation of monomer or dimer depending of the internal energy left in the trimer, blurring hence the "either-tower" distribution. We present in table I, the result of our simulation in order to give an estimation of the time scale associated the degradation of this species. Accurate values for the kinetic energy KE$_1$ and KE$_2$ is hard to extract since both parameters acts almost the same way, however one can estimate that they are in the order of 500~meV down to 100~meV. AddBlock(Argon_size_depedence.tex,174,1) ++ sizes ($<$N$>$=10,20), exhibit a typical peak shape with "eiffel tower" signature of decay in the drift tube. For dimer channels, it corresponds to the degradation of Ar$^+_2\rightarrow$Ar$^+$+Ar. According to Whitaker~\textit{et al.} \cite{Whitaker_93} this process can arise from radiative decay from the electronic $\Pi$(1/2)$_u$ state of the ion to the I(1/2)$_g$. Such decay is reasonable in our experiment since there is no particular reason to produce dimer fragments arising from the fragmentation of multiply charge clusters only in its ground state. However, one should keep in mind that collision induced dissociation (CID) is very a likely reason for cluster-ion degradation for background pressure above 10$^{-7}$~mbar which was the case. Our experimental resolution is not good enough to properly quantify the importance of such process but we think that at least both processes can happen. For the trimer, the gaussian like distribution is due to a more complex fragmentation mechanisms which can lead either to formation of monomer or dimer depending on the internal energy left in the trimer, blurring hence the "Eiffel-tower" distribution. We present in table I, the result of our simulation in order to give an estimation of the time scale associated the degradation of this species. Accurate values for the kinetic energy KE$_1$ and KE$_2$ are hard to extract since both parameters behave similarly, however one can estimate that they are in the order of 500~meV down to 100~meV. DelBlock(Argon_size_depedence.tex,176,1) -- In the case of large clusters (from 100 to 1000), these peaks are no longer sharp. The shape can be explained either considering that fragments carry away measurable kinetic energy upon fragmentation of multiply charged species or meta-stable decay leading to neutral evaporation. From the simulation, it is clear that the time scale or such process has to be in the order of time-of-flight until the drift tube (t$^{dimer/trimer}_{acc}$) to reproduce the roundish-shape. The typical kinetic energy KE$_1$ and KE$_2$ is in the order of 2~eV down to 300meV. Another peculiar feature is observed in the fragmentation of large clusters, the Ar$_2^+$ line profile exhibits an asymmetric wing (tail) extending towards longer time-of-flight while Ar$_3^+$ is symmetric. This tail is a clear signature of decay producing dimer in a time scale shorter then t$^{dimer}_{acc}$: Ar$^+_m\rightarrow$Ar$^+_2$+X. The fact that this tail occur in dimer channels may reflect that dimer ionic core is the most likely unit formed inside large argon clusters as it has been observed on xenon clusters \cite{Laarmann_2002}. We performed measurement at lower extraction field to increase the flight time for dimers in the extraction region from 150~ns to 320~ns and no change from the tail was observed, as it should be expected. (trimer peak change from roundish shape to square shape ?) Since different mother ions can lead to the formation of the dimer the determination of the life-time cannot be accurate but has to be in the order AddBlock(Argon_size_depedence.tex,176,2) ++ In the case of large clusters (from 100 to 1000), these peaks are no longer sharp. The shape can be explained either considering that fragments carry away measurable kinetic energy upon fragmentation of multiply charged species or meta-stable decay leading to neutral evaporation. From the simulation, it is clear that the time-scale of such process a has to be on the order of time-of-flight until the drift tube (t$^{dimer/trimer}_{acc}$) to reproduce the roundish-shape. The typical kinetic energy KE$_1$ and KE$_2$ is on the order of 2~eV down to 300~meV. Another peculiar feature is observed in the fragmentation of large clusters, the Ar$_2^+$ line profile exhibits an asymmetric wing (tail) extending towards longer time-of-flight while Ar$_3^+$ is symmetric. This tail is a clear signature of decay producing dimer in a time scale shorter then t$^{dimer}_{acc}$: Ar$^+_m\rightarrow$Ar$^+_2$+X. The fact that this tail occurs in dimer channels may reflect that dimer ionic core is the most likely unit formed inside large argon clusters as it has been observed on xenon clusters \cite{Laarmann_2002}. We performed measurement at a lower extraction field to increase the flight time for dimers in the extraction region from 150~ns to 320~ns and no change from the tail was observed, as it should be expected. %(trimer peak change from roundish shape to square shape ?) ++ Since different mother ions can lead to the formation of the dimer the determination of the life-time cannot be accurate but has to be in the order DelBlock(Argon_size_depedence.tex,179,1) -- of hundred ns. The times scale found for small cluster are typical for usual meta-stable unimolecular degradation of van-der-Waals clusters \cite{Stephan_1983, Lethbridge_1988}. In the case of large clusters, the time scale is relatively short and it shows that there are strong interactions within the cluster. One should point out that for clusters of $<$N$>$=100 and 1000 atoms, the similarity of the two time scale within the error bars implies that the fragmentation mechanism does not change drastically with cluster size. This corroborate that AddBlock(Argon_size_depedence.tex,179,1) ++ of hundred ns. The times-scale found for small cluster are typical for usual meta-stable unimolecular degradation of van-der-Waals clusters \cite{Stephan_1983, Lethbridge_1988}. In the case of large clusters, the time-scale is relatively short and it shows that there are strong interactions within the cluster. One should point out that for clusters of $<$N$>$=100 and 1000 atoms, the similarity of the two time-scales within the error bars implies that the fragmentation mechanism does not change drastically with cluster size. This corroborate that DelBlock(Argon_size_depedence.tex,183,1) -- It shows also that another dissociation mechanism is energetically possible when a certain size is reached. One should notice that there is a small contribution in the peak shape of slow meta-stable decay as we have seen for small clusters. AddBlock(Argon_size_depedence.tex,183,1) ++ It shows also that another dissociation mechanism is energetically possible when a certain size is reached. Note the small contribution from slow meta-stable decay as we have seen for small clusters. DelBlock(Argon_size_depedence.tex,193,1) -- After fission, the extra internal energy of the cluster is released in different ways. For small clusters, it is likely that neutral evaporation (neutral expulsion) impart most of the kinetic energy, while for large cluster this energy would be more dissipated among all the degree of freedom. For instance molecular-dynamic in a droplet liquid model\cite{Casero_1988} shows that only fission due to Coulomb repulsion AddBlock(Argon_size_depedence.tex,193,1) ++ After fission, the extra internal energy of the cluster is released in different ways. For small clusters, it is likely that neutral evaporation (neutral expulsion) imparts most of the kinetic energy, while for large cluster this energy would be more dissipated among all the degrees of freedom. For instance molecular-dynamics in a liquid droplet model\cite{Casero_1988} shows that only fission due to Coulomb repulsion DelBlock(Argon_size_depedence.tex,195,1) -- of triply ionized clusters could justify a delayed or thermal fragmentation. After ionization, the three charges would tend to form an equilateral triangle (minimum energy configuration), repelling simultaneously outwards, while the most favorable pathway to fission would preferably be that two of the charges approach each other while the other ones moves outwards. This effect would leave time to thermal excitation to spread all over the cluster. This is in agreement with our observation since the tails in dimer are observed in coincidence spectra up to the 3rd degree, although these channels are very weak. In multi-layer argon surfaces, the energy dissipation of high lying ionic states is known to be the dominant primary electronic process for photo-desorption \cite{Dujardin_1990}. One could speculate that the same behavior is present here with the expulsion of dimer, as it has been seen by A. Stace~\textit{et al.} \cite{Stace_1991} for large cluster. Although the time scale is not the same, it may be that the internal energy in our experiment is high enough to enhance this mechanism. To the best of our knowledge, there is no evidence of such a relaxation mechanism in Argon clusters but it has been found in He clusters \cite{Moller_99}. One should point out that the estimated typical time scale is long enough to localize a charged in the cluster followed by the formation of self-trapped atomic or molecular excitons. Radiative decays from a molecular exciton (excimer), via bound-to-free transition, are known to open dissociation channels: for example for a neutral excited cluster to Ar+ Ar limit. Studies on doubly charged clusters \cite{Ruhl_1993} have revealed the presence of a third continuum related to the decay from a dication excimer to Ar$^+$+ Ar$^+$ limit. To the best of our knowledge, decay from excited cation excimer has not been reported but a likely dissociation limit to Ar$^+$+ Ar can be inferred through atomic radiative transition \cite{Nist}. Lifetimes for these excitons can be estimated to vary from 300~ps to 200~ns which could be is in agreement with our measurement. AddBlock(Argon_size_depedence.tex,195,1) ++ of triply ionized clusters could justify a delayed or thermal fragmentation. After ionization, the three charges would tend to form an equilateral triangle (minimum energy configuration), repelling simultaneously outwards, while the most favorable pathway to fission would preferably be that two of the charges approach each other while the other ones move outwards. This effect would leave time for thermal excitation to spread all over the cluster. This is in agreement with our observation since the tails in dimer are observed in coincidence spectra up to the 3rd degree, although these channels are very weak. In multi-layer argon surfaces, the energy dissipation of high lying ionic states is known to be the dominant primary electronic process for photo-desorption \cite{Dujardin_1990}. One could speculate that the same behavior is present here with the expulsion of dimer, as it has been seen by A. Stace~\textit{et al.} \cite{Stace_1991} for large clusters. Although the time scale is not the same, it may be that the internal energy in our experiment is high enough to enhance this mechanism. To the best of our knowledge, there is no evidence of such a relaxation mechanism in argon clusters but it has been found in He clusters \cite{Moller_99}. One should point out that the estimated typical time scale is long enough to localize a charged in the cluster followed by the formation of self-trapped atomic or molecular excitons. Radiative decays from a molecular exciton (excimer), via bound-to-free transitions, are known to open dissociation channels: for example for a neutral excited cluster to Ar+ Ar limit. Studies on doubly charged clusters \cite{Ruhl_1993} have revealed the presence of a third continuum related to the decay from a dication excimer to Ar$^+$+ Ar$^+$ limit. To the best of our knowledge, decay from excited cation excimer has not been reported but a likely dissociation limit to Ar$^+$+ Ar can be inferred through atomic radiative transitions \cite{Nist}. Lifetimes for these excitons can be estimated to vary from 300~ps to 200~ns which could be is in agreement with our measurement. DelBlock(Argon_size_depedence.tex.bak,1,3) -- %\documentclass[aps,prl,preprint,nobibnotes,groupedaddress,showpacs]{revtex4} -- %\documentclass[aps,pra,preprint,superscriptaddress,nobibnotes,showpacs]{revtex4} -- \documentclass[aps,pra,twocolumn,superscriptaddress,nobibnotes,showpacs, preprintnumbers]{revtex4} AddBlock(Argon_size_depedence.tex.bak,1,2) ++ %\documentclass[preprint,superscriptaddress,showpacs,endfloats*]{revtex4} ++ \documentclass[aps,pra,twocolumn,superscriptaddress,nobibnotes,showpacs,preprintnumbers]{revtex4} DelBlock(Argon_size_depedence.tex.bak,20,2) -- 91405 Orsay, France} -- \affiliation{MAX-Lab, Lund University, Box 118, S-221 00 Lund, Sweden} AddBlock(Argon_size_depedence.tex.bak,20,2) ++ 91405 Orsay, France} ++ \affiliation{MAX-Lab, Lund University, Box 118, S-221 00 Lund, Sweden} DelBlock(Argon_size_depedence.tex.bak,32,1) -- \affiliation{MAX-Lab, Lund University, Box 118, S-221 00 Lund, Sweden} AddBlock(Argon_size_depedence.tex.bak,32,1) ++ \affiliation{MAX-Lab, Lund University, Box 118, S-221 00 Lund, Sweden} DelBlock(Argon_size_depedence.tex.bak,54,4) -- Photo-fragmentation of argon clusters with average size ranging from 10 up to 1000 atoms is reported at a photon energy of 116 eV using multi-coincidence technique with a mass spectrometer. A spectacular -- change in fragmentation pattern is observed when the cluster size increases -- %change "pointing out" -- revealing the different time scale of the dissociation mechanisms. For small clusters ($<$10$>$), after ionization a fast fragmentation with neutral emission imparting large amount of energy in the ps time scale occurs, then slow degradation of the photo-cluster ions is observed in the $\mu$s time scale. For larger clusters ($\geq <$100$>$) we believe that we observe the fragmentation pattern of large unstable multiply charged species in time scale which last a few hundred of ns. The reason for these apparent slow processes could be that the large amount of neutral atoms acts as an efficient cooling bath which tend to dissipate the excess of energy ("heat") among all degree of freedom. Degradation of the photo-cluster ions take place in the $\mu$s time scale as for small clusters. AddBlock(Argon_size_depedence.tex.bak,54,1) ++ Photo-fragmentation of argon clusters of average size ranging from 10 up to 1000 atoms is reported at a photon energy of 116 eV using multi-coincidence technique with a mass spectrometer. A spectacular change in fragmentation pattern is observed when the cluster size increases, arising from a change in the dissociation time-scale. For small clusters ($<$10$>$), after ionization a fast fragmentation with neutral emission imparting large amount of energy in the ps time scale occurs, then slow degradation of the photo-cluster ions is observed in the $\mu$s time scale. For larger clusters ($\geq <$100$>$) we believe that we observe the fragmentation pattern of large unstable multiply charged species in time scale which last a few hundred of ns. The reason for these apparent slow processes could be that the large amount of neutral atoms acts as an efficient cooling bath which tend to dissipate the excess of energy ("heat") among all degree of freedom. Degradation of the photo-cluster ions take place in the $\mu$s time scale as for small clusters. DelBlock(Argon_size_depedence.tex.bak,63,3) -- In a recent publication \cite{Gisselbrecht_2005} we presented the general fragmentation pattern of small argon clusters for resonant inner shell excitation and ionization. We did show that the inner shell photo-absorption prepared selectively ionic species below or above the vertical double ionization -- % Add maxim and marcus -- potential \cite{Maxim_2003, Lundwall_05}, respectively Ar$_m^{+*}$ and Ar$_m^{2+}$. In both case theses species undergo dissociation leading to two or more charged fragments pointing out the importance of the nuclear relaxation as well as the electronic relaxation. AddBlock(Argon_size_depedence.tex.bak,63,1) ++ In a recent publication \cite{Gisselbrecht_2005} we presented the general fragmentation pattern of small argon clusters for resonant inner shell excitation and ionization. We did show that the inner shell photo-absorption prepared selectively ionic species below or above the vertical double ionization potential \cite{Maxim_2003, Lundwall_05}, respectively Ar$_m^{+*}$ and Ar$_m^{2+}$. In both case theses species undergo dissociation leading to two or more charged fragments pointing out the importance of the nuclear relaxation as well as the electronic relaxation. DelBlock(Argon_size_depedence.tex.bak,65,3) -- In this study we focus on the cluster-size dependent fragmentation with a VUV photon of 116~eV. We perform a multicoincidence measurement Photo-Electron-n-Photo-Ions COincidence PE(PI)$_n$CO with a mass spectrometer. -- -- \begin{figure}[t] AddBlock(Argon_size_depedence.tex.bak,65,2) ++ This study focus on the cluster-size dependent fragmentation with a VUV photon of 116~eV. We perform a multicoincidence measurement Photo-Electron-n-Photo-Ions COincidence PE(PI)$_n$CO with a mass spectrometer. ++ \begin{figure}[t] DelBlock(Argon_size_depedence.tex.bak,69,1) -- \caption{\label{Fig1} Photo-ionization branching ratio for free argon atoms and schematic decay channels for clusters. } AddBlock(Argon_size_depedence.tex.bak,69,1) ++ \caption{\label{Fig1} Photo-ionization branching ratio for free argon atoms and schematic decay channels for clusters.} AddBlock(Argon_size_depedence.tex.bak,72,5) ++ The chosen photon energy implies that only the $3p$ valence and $3s$ inner valence shells can be ionized and Auger relaxation is energetically not possible. For free atoms, we are well above the double-ionization threshold 43.4~eV \cite{Nist}, the $3s$ Cooper minimum between 45-50~eV, and even exceeds the triple ionization threshold 84.3~eV\cite{Nist}. The branching ratios are known to be 83\% for single photo-ionization, 16\% for double photo-ionization, and less than 1\% for triple photo-ionization \cite{Holland_1979}. In the current picture of cluster ionization, so called Haberland's model \cite{Haberland_book_1995, Haberland_book_1994}, the system does not have time for nuclear rearrangement and states close to the dissociation limit are populated. Thus the cluster photo-ionization branching ratio should mimic the atomic one. However, in our experiment the time scale is long enough for nuclear relaxation to take place and adiabatic potentials to be relevant \cite{Ruhl_1992}. Hence, among the singly charge species a few of them ($\sim$15\%) prepared with two holes and one particle in the outer valence shell, should decay in the double ionization continuum as we have already eluded \cite{Gisselbrecht_2005}. Hence, one could speculate that the fragmentation depend on the cluster size. ++ %==== mathieu@g3 / andreas@work ++ %>The chosen photon energy implies that only the $3p$ valence and $3s$ inner valence shells can be ionized and Auger relaxation is energetically not possible. For free atoms, we are well above the double-ionization threshold 43.4~eV \cite{Nist}, the $3s$ Cooper minimum between 45-50~eV, and even exceeds the triple ionization threshold 84.3~eV. The branching ratios are known to be 83\% for single photo-ionization, 16\% for double photo-ionization, and less than 1\% for triple photo-ionization \cite{Holland_1979}. In the current picture of cluster ionization, so called Haberland's model \cite{Haberland_book_1995, Haberland_book_1994}, the system does not have time for nuclear rearrangement and states close to the dissociation limit are populated. Thus the cluster photo-ionization branching ratio should mimic the atomic one. However in our experiment the time scale is long enough for nuclear relaxation to take place and adiabatic potentials to be relevant \cite{Ruhl_1992}. Hence, among the singly charge species a few of them ($\sim$15\%) prepared with two holes and one particle in the outer valence shell, should decay in the double ionization continuum as we have already eluded \cite{Gisselbrecht_2005}. Hence, one could speculate that the fragmentation depend on the cluster size. ++ ++ In Fig.~\ref{Fig1} we present the photo-ionization branching ratio for free argon atoms and where the decay channel are expected for cluster. Our aim is to investigate the photo-fragmentation over a size range from a few up to thousands of atoms in order to know whether the fragmentation dynamics is a sensitive probe to the formation of stable multiply ionized clusters. DelBlock(Argon_size_depedence.tex.bak,78,13) -- >>>> CONFLICT >>>> ADD - ADD -- >The chosen photon energy implies that only the $3p$ valence and $3s$ inner valence shells can be ionized and Auger relaxation is energetically not possible. For free atoms, we are well above the double-ionization threshold 43.4~eV \cite{Nist}, the $3s$ Cooper minimum between 45-50~eV, and -- >% ref for triple ionization -- >even exceeds the triple ionization threshold 84.3~eV\cite{Nist}. The branching ratios are known to be 83\% for single photo-ionization, 16\% for double photo-ionization, and less than 1\% for triple photo-ionization \cite{Holland_1979}. In the current picture of cluster ionization, so called Haberland's model \cite{Haberland_book_1995, Haberland_book_1994}, the system does not have time for nuclear rearrangement and states close to the dissociation limit are populated. Thus the cluster photo-ionization branching ratio should mimic the atomic one. However in our experiment the time scale is long enough for nuclear relaxation to take place and adiabatic potentials to be relevant \cite{Ruhl_1992}. Hence, among the singly charge species a few of them ($\sim$15\%) prepared with two holes and one particle in the outer valence shell, should decay in the double ionization continuum as we have already eluded \cite{Gisselbrecht_2005}. Hence, one could speculate that the fragmentation depend on the cluster size.\\ -- ==== mathieu@g3 / andreas@work -- >The chosen photon energy implies that only the $3p$ valence and $3s$ inner valence shells can be ionized and Auger relaxation is energetically not possible. For free atoms, we are well above the double-ionization threshold 43.4~eV \cite{Nist}, the $3s$ Cooper minimum between 45-50~eV, and even exceeds the triple ionization threshold 84.3~eV. The branching ratios are known to be 83\% for single photo-ionization, 16\% for double photo-ionization, and less than 1\% for triple photo-ionization \cite{Holland_1979}. In the current picture of cluster ionization, so called Haberland's model \cite{Haberland_book_1995, Haberland_book_1994}, the system does not have time for nuclear rearrangement and states close to the dissociation limit are populated. Thus the cluster photo-ionization branching ratio should mimic the atomic one. However in our experiment the time scale is long enough for nuclear relaxation to take place and adiabatic potentials to be relevant \cite{Ruhl_1992}. Hence, among the singly charge species a few of them ($\sim$15\%) prepared with two holes and one particle in the outer valence shell, should decay in the double ionization continuum as we have already eluded \cite{Gisselbrecht_2005}. Hence, one could speculate that the fragmentation depend on the cluster size. -- > -- >We present figure~\ref{Fig1}, the photo-ionization branching ratio for free argon atoms (check again ?) and where the decay channel are expected for cluster. Our aim is to investigate the photo-fragmentation over a size range from a few up to thousands of atoms in order to know whether the fragmentation dynamics is a sensitive probe to the formation of stable multiply ionized clusters. -- <<<< CONFLICT <<<< -- -- -- -- DelBlock(Argon_size_depedence.tex.bak,92,4) -- electrons and the ions from this region. Electrons with kinetic energy up to 500~eV can be collected over a solid angle of 4$\pi$ steradian. In order to satisfy the so-called 'space-time focusing' \cite{Wiley_1955} criterion, ions were post-accelerated before they passed into a field free drift tube. The spectrometer was positioned perpendicular to the polarization plane of the light. Thus, the spatial extent of the source volume along the spectrometer axis is negligible since it is defined by the vertical size of the -- light spot ($\sim$0.4~mm) and is independent of the expansion conditions of the cluster source. A resolving power of $m/\delta m \sim 500$ was achieved. -- Electrons and ions, detected by micro channel plate (MCP) pairs in a chevron configuration, provide start and stop signals for the Time-to-Digital Converter (TDC) in the set-up. The time of flight of ions arising from single, up to quadruple ionization events, was recorded and treated in real time. For all measurements the ion count rate was essentially constant, less than 2~kHz, keeping theoretically the detection probability of a random ion (false coincidence) at about 1\% within our acquisition time -- window (5~$\mu$s). This probability is in practice degraded by the fact that the density of uncondensed atoms in the cluster source is 10 to 20 times higher than the density of clusters. Calibration on rare gases (argon, krypton, and xenon) has shown that the ion efficiency decreases for masses above $\sim$150 a.u. even though the photo-ions are accelerated up to 4~keV. This is due to the use of discriminators in the electronics scheme which cut-off a part of the pulse height distribution of the MCP signal for heavy particles \cite{Furuya_2002}. Thus the detection efficiencies of argon dimers and trimers are comparable, but heavier ions have lower detection efficiency. Calibration of the cluster source has shown that cluster sizes larger than 35 atoms can easily be observed with the present spectrometer. AddBlock(Argon_size_depedence.tex.bak,92,1) ++ electrons and the ions from this region. Electrons with kinetic energy up to 500~eV can be collected over a solid angle of 4$\pi$ steradian. In order to satisfy the so-called 'space-time focusing' \cite{Wiley_1955} criterion, ions were post-accelerated before they passed into a field free drift tube. The spectrometer was positioned perpendicular to the polarization plane of the light. Thus, the spatial extent of the source volume along the spectrometer axis is negligible since it is defined by the vertical size of the light spot ($\sim$0.4~mm) and is independent of the expansion conditions of the cluster source. A resolving power of $m/\delta m \sim 500$ was achieved. AddBlock(Argon_size_depedence.tex.bak,94,1) ++ Electrons and ions, detected by micro channel plate (MCP) pairs in a chevron configuration, provide start and stop signals for the Time-to-Digital Converter (TDC) in the set-up. The time of flight of ions arising from single, up to quadruple ionization events, was recorded and treated in real time. For all measurements the ion count rate was essentially constant, less than 2~kHz, keeping theoretically the detection probability of a random ion (false coincidence) at about 1\% within our acquisition time window (5~$\mu$s). This probability is in practice degraded by the fact that the density of uncondensed atoms in the cluster source is 10 to 20 times higher than the density of clusters. Calibration on rare gases (argon, krypton, and xenon) has shown that the ion efficiency decreases for masses above $\sim$150 a.u. even though the photo-ions are accelerated up to 4~keV. This is due to the use of discriminators in the electronics scheme which cut-off a part of the pulse height distribution of the MCP signal for heavy particles \cite{Furuya_2002}. Thus the detection efficiencies of argon dimers and trimers are comparable, but heavier ions have lower detection efficiency. Calibration of the cluster source has shown that cluster sizes larger than 35 atoms can easily be observed with the present spectrometer. AddBlock(Argon_size_depedence.tex.bak,96,1) ++ DelBlock(Argon_size_depedence.tex.bak,152,3) -- \caption{\label{table1} Typical time scale associated with the decay of dimers into monomer and mother ion into the dimer channel } -- \begin{tabular}{c|c|c} -- $<$N$>$ & Decay channel & Lifetime \\ AddBlock(Argon_size_depedence.tex.bak,152,4) ++ \caption{\label{table1} Typical time scale associated with the decay of dimers into monomer and mother ion into the dimer channel.} ++ \begin{ruledtabular} ++ \begin{tabular}{ccc} ++ $<$N$>$ & Decay channel & Lifetime, $\tau_m$ \\ DelBlock(Argon_size_depedence.tex.bak,157,4) -- 10 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ -- & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ -- 20 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ -- & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ AddBlock(Argon_size_depedence.tex.bak,157,4) ++ 10 & Ar$^+_2\rightarrow$Ar$^+$+Ar & 1.5$\pm$0.5 $\mu$s \\ ++ & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & 1.5$\pm$0.5 $\mu$s \\ ++ 20 & Ar$^+_2\rightarrow$Ar$^+$+Ar & 1.5$\pm$0.5 $\mu$s \\ ++ & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & 1.5$\pm$0.5 $\mu$s \\ DelBlock(Argon_size_depedence.tex.bak,162,6) -- 100 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$=300$\pm$50 ns \\ -- & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$=300$\pm$50 ns \\ -- & Ar$^+_m\rightarrow$Ar$^+_2$+X & $\tau_m$=100$\pm$ 50 ns \\ -- 1000 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$=300$\pm$50 ns \\ -- & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$=300$\pm$50 ns \\ -- & Ar$^+_m\rightarrow$Ar$^+_2$+X & $\tau_m$=100$\pm$30 ns \\ AddBlock(Argon_size_depedence.tex.bak,162,6) ++ 100 & Ar$^+_2\rightarrow$Ar$^+$+Ar & 300$\pm$50 ns \\ ++ & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & 300$\pm$50 ns \\ ++ & Ar$^+_m\rightarrow$Ar$^+_2$+X & 100$\pm$ 50 ns \\ ++ 1000 & Ar$^+_2\rightarrow$Ar$^+$+Ar & 300$\pm$50 ns \\ ++ & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & 300$\pm$50 ns \\ ++ & Ar$^+_m\rightarrow$Ar$^+_2$+X & 100$\pm$30 ns \\ AddBlock(Argon_size_depedence.tex.bak,169,1) ++ \end{ruledtabular} DelBlock(Argon_size_depedence.tex.bak,174,1) -- sizes ($<$N$>$=10,20), exhibit a typical peak shape with "eiffel tower" signature of decay in the drift tube. For dimer channels, it corresponds to the degradation of Ar$^+_2\rightarrow$Ar$^+$+Ar. According to Whitaker~\textit{et al.} \cite{Whitaker_93} this process can arise from radiative decay from the electronic $\Pi$(1/2)$_u$ state of the ion to the I(1/2)$_g$. Such decay is reasonable in our experiment since there is no particular reason to produce dimer fragments arising from the fragmentation of multiply charge clusters only in its ground state. However, one should keep in mind that collision induced dissociation (CID) is very a likely reason for cluster-ion degradation for background pressure above 10$^{-7}$~mbar which was the case. Our experimental resolution is not good enough to quantify properly the importance of such process but we think that at least both processes can happen. For trimer, the gaussian like distribution is due to a more complex fragmentation mechanisms which can lead either to formation of monomer or dimer depending of the internal energy left in the trimer, blurring hence the "either-tower" distribution. We present in table I, the result of our simulation in order to give an estimation of the time scale associated the degradation of this species. Accurate values for the kinetic energy KE$_1$ and KE$_2$ is hard to extract since both parameters acts almost the same way, however one can estimate that they are in the order of 500ÊmeV down to 100meV. AddBlock(Argon_size_depedence.tex.bak,174,1) ++ sizes ($<$N$>$=10,20), exhibit a typical peak shape with "eiffel tower" signature of decay in the drift tube. For dimer channels, it corresponds to the degradation of Ar$^+_2\rightarrow$Ar$^+$+Ar. According to Whitaker~\textit{et al.} \cite{Whitaker_93} this process can arise from radiative decay from the electronic $\Pi$(1/2)$_u$ state of the ion to the I(1/2)$_g$. Such decay is reasonable in our experiment since there is no particular reason to produce dimer fragments arising from the fragmentation of multiply charge clusters only in its ground state. However, one should keep in mind that collision induced dissociation (CID) is very a likely reason for cluster-ion degradation for background pressure above 10$^{-7}$~mbar which was the case. Our experimental resolution is not good enough to quantify properly the importance of such process but we think that at least both processes can happen. For trimer, the gaussian like distribution is due to a more complex fragmentation mechanisms which can lead either to formation of monomer or dimer depending of the internal energy left in the trimer, blurring hence the "either-tower" distribution. We present in table I, the result of our simulation in order to give an estimation of the time scale associated the degradation of this species. Accurate values for the kinetic energy KE$_1$ and KE$_2$ is hard to extract since both parameters acts almost the same way, however one can estimate that they are in the order of 500~meV down to 100~meV. DelBlock(Argon_size_depedence.tex.bak,190,1) -- In figure \ref{Fig6}, we present a summary of the possible mechanisms that we observe. At 116~eV photon energy, direct photo-ionization can produce about 15 \% of excited singly charged clusters Ar$_m^{+*}$ and about 16\% of doubly charged clusters Ar$_m^{2+}$ with or without additional energy. This species can relax into the double ionization continuum of the clusters. AddBlock(Argon_size_depedence.tex.bak,190,1) ++ In Fig.~\ref{Fig6}, we present a summary of the possible mechanisms that we observe. At 116~eV photon energy, direct photo-ionization can produce about 15 \% of excited singly charged clusters Ar$_m^{+*}$ and about 16\% of doubly charged clusters Ar$_m^{2+}$ with or without additional energy. This species can relax into the double ionization continuum of the clusters. AddBlock(Argon_size_depedence.tex.bak,208,3) ++ \printtables ++ \printfigures ++
Some small typs. Checked the conflict part and included a documentclass usable for submision.
AddBlock(Argon_size_depedence.aux,12,1) ++ \citation{Svensson_1996} DelBlock(Argon_size_depedence.aux,15,1) -- \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Photo-ionization branching ratio for free argon atoms and schematic decay channels for clusters. }}{1}{}} AddBlock(Argon_size_depedence.aux,15,1) ++ \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Photo-ionization branching ratio for free argon atoms and schematic decay channels for clusters.}}{1}{}} DelBlock(Argon_size_depedence.aux,17,1) -- \citation{Svensson_1996} DelBlock(Argon_size_depedence.aux,63,1) -- \@writefile{lot}{\contentsline {table}{\numberline {I}{\ignorespaces Typical time scale associated with the decay of dimers into monomer and mother ion into the dimer channel }}{5}{}} AddBlock(Argon_size_depedence.aux,63,1) ++ \@writefile{lot}{\contentsline {table}{\numberline {I}{\ignorespaces Typical time scale associated with the decay of dimers into monomer and mother ion into the dimer channel.}}{5}{}} DelBlock(Argon_size_depedence.aux,67,1) -- \@writefile{toc}{\contentsline {section}{\numberline {IV}Conclusion}{6}{}} AddBlock(Argon_size_depedence.aux,101,1) ++ \@writefile{toc}{\contentsline {section}{\numberline {IV}Conclusion}{7}{}} UpdateBinaryFile(Argon_size_depedence.dvi) AddBinaryFile(Argon_size_depedence.dvi#222) AddTxtFile(Argon_size_depedence.fgx) DelBlock(Argon_size_depedence.log,1,1) -- This is pdfeTeX, Version 3.141592-1.20a-2.2 (Web2C 7.5.3) (format=latex 2005.2.14) 27 AUG 2006 12:29 AddBlock(Argon_size_depedence.log,1,1) ++ This is e-TeX, Version 3.141592-2.1 (MiKTeX 2.4) (preloaded format=latex 2004.8.20) 27 AUG 2006 18:02 DelBlock(Argon_size_depedence.log,4,1) -- (./Argon_size_depedence.tex AddBlock(Argon_size_depedence.log,4,1) ++ (Argon_size_depedence.tex DelBlock(Argon_size_depedence.log,6,3) -- Babel <v3.8d> and hyphenation patterns for american, french, german, ngerman, d -- utch, italian, norsk, portuges, spanish, swedish, nohyphenation, loaded. -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/revtex4/revtex4.cls AddBlock(Argon_size_depedence.log,6,3) ++ Babel <v3.8a> and hyphenation patterns for english, french, german, ngerman, du ++ mylang, nohyphenation, loaded. ++ (C:\texmf\tex\latex\revtex4\revtex4.cls DelBlock(Argon_size_depedence.log,34,1) -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/url/url.sty AddBlock(Argon_size_depedence.log,34,1) ++ (C:\texmf\tex\latex\ltxmisc\url.sty DelBlock(Argon_size_depedence.log,50,2) -- -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/natbib/natbib.sty AddBlock(Argon_size_depedence.log,50,1) ++ (C:\texmf\tex\latex\natbib\natbib.sty DelBlock(Argon_size_depedence.log,60,1) -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/revtex4/revsymb.sty AddBlock(Argon_size_depedence.log,60,1) ++ (C:\texmf\tex\latex\revtex4\revsymb.sty DelBlock(Argon_size_depedence.log,64,2) -- )) -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/revtex4/aps.rtx AddBlock(Argon_size_depedence.log,64,1) ++ )) (C:\texmf\tex\latex\revtex4\aps.rtx DelBlock(Argon_size_depedence.log,68,1) -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/revtex4/10pt.rtx AddBlock(Argon_size_depedence.log,68,1) ++ (C:\texmf\tex\latex\revtex4\10pt.rtx DelBlock(Argon_size_depedence.log,71,2) -- ) -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/base/latexsym.sty AddBlock(Argon_size_depedence.log,71,1) ++ ) (C:\texmf\tex\latex\base\latexsym.sty DelBlock(Argon_size_depedence.log,77,1) -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/graphics/graphics.sty AddBlock(Argon_size_depedence.log,77,1) ++ (C:\texmf\tex\latex\graphics\graphics.sty DelBlock(Argon_size_depedence.log,79,2) -- -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/graphics/trig.sty AddBlock(Argon_size_depedence.log,79,1) ++ (C:\texmf\tex\latex\graphics\trig.sty AddBlock(Argon_size_depedence.log,81,2) ++ ) (C:\texmf\tex\latex\00miktex\graphics.cfg ++ File: graphics.cfg 2003/03/12 v1.1 MiKTeX 'graphics' configuration DelBlock(Argon_size_depedence.log,84,3) -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/graphics/graphics.cfg -- File: graphics.cfg 2005/02/03 v1.3 graphics configuration of teTeX/TeXLive -- ) DelBlock(Argon_size_depedence.log,86,1) -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/graphics/dvips.def AddBlock(Argon_size_depedence.log,86,1) ++ (C:\texmf\tex\latex\graphics\dvips.def DelBlock(Argon_size_depedence.log,89,1) -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsfonts/amsfonts.sty AddBlock(Argon_size_depedence.log,89,1) ++ (C:\texmf\tex\latex\amsfonts\amsfonts.sty DelBlock(Argon_size_depedence.log,99,1) -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsfonts/amssymb.sty AddBlock(Argon_size_depedence.log,99,1) ++ (C:\texmf\tex\latex\amsfonts\amssymb.sty DelBlock(Argon_size_depedence.log,102,1) -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsmath/amsmath.sty AddBlock(Argon_size_depedence.log,102,1) ++ (C:\texmf\tex\latex\amsmath\amsmath.sty DelBlock(Argon_size_depedence.log,107,1) -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsmath/amstext.sty AddBlock(Argon_size_depedence.log,107,1) ++ (C:\texmf\tex\latex\amsmath\amstext.sty DelBlock(Argon_size_depedence.log,109,2) -- -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsmath/amsgen.sty AddBlock(Argon_size_depedence.log,109,1) ++ (C:\texmf\tex\latex\amsmath\amsgen.sty DelBlock(Argon_size_depedence.log,113,2) -- )) -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsmath/amsbsy.sty AddBlock(Argon_size_depedence.log,113,1) ++ )) (C:\texmf\tex\latex\amsmath\amsbsy.sty DelBlock(Argon_size_depedence.log,117,1) -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsmath/amsopn.sty AddBlock(Argon_size_depedence.log,117,1) ++ (C:\texmf\tex\latex\amsmath\amsopn.sty DelBlock(Argon_size_depedence.log,157,3) -- ) -- (./Argon_size_depedence.aux) -- \openout1 = `Argon_size_depedence.aux'. AddBlock(Argon_size_depedence.log,157,17) ++ ) (Argon_size_depedence.aux) ++ LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 12. ++ LaTeX Font Info: ... okay on input line 12. ++ LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 12. ++ LaTeX Font Info: ... okay on input line 12. ++ LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 12. ++ LaTeX Font Info: ... okay on input line 12. ++ LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 12. ++ LaTeX Font Info: ... okay on input line 12. ++ LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 12. ++ LaTeX Font Info: ... okay on input line 12. ++ LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 12. ++ LaTeX Font Info: ... okay on input line 12. ++ Class revtex4 Info: Patching LaTeX tabular. on input line 12. ++ Class revtex4 Info: cite was not loaded (OK!) on input line 12. ++ Class revtex4 Info: multicol was not loaded (OK!) on input line 12. ++ LaTeX Font Info: Try loading font information for U+lasy on input line 55. DelBlock(Argon_size_depedence.log,175,18) -- LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 13. -- LaTeX Font Info: ... okay on input line 13. -- LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 13. -- LaTeX Font Info: ... okay on input line 13. -- LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 13. -- LaTeX Font Info: ... okay on input line 13. -- LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 13. -- LaTeX Font Info: ... okay on input line 13. -- LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 13. -- LaTeX Font Info: ... okay on input line 13. -- LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 13. -- LaTeX Font Info: ... okay on input line 13. -- Class revtex4 Info: Patching LaTeX tabular. on input line 13. -- Class revtex4 Info: cite was not loaded (OK!) on input line 13. -- Class revtex4 Info: multicol was not loaded (OK!) on input line 13. -- LaTeX Font Info: Try loading font information for U+lasy on input line 58. -- -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/base/ulasy.fd AddBlock(Argon_size_depedence.log,175,1) ++ (C:\texmf\tex\latex\base\ulasy.fd DelBlock(Argon_size_depedence.log,178,3) -- LaTeX Font Info: Try loading font information for U+msa on input line 58. -- -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsfonts/umsa.fd AddBlock(Argon_size_depedence.log,178,2) ++ LaTeX Font Info: Try loading font information for U+msa on input line 55. ++ (C:\texmf\tex\latex\amsfonts\umsa.fd DelBlock(Argon_size_depedence.log,182,1) -- LaTeX Font Info: Try loading font information for U+msb on input line 58. AddBlock(Argon_size_depedence.log,182,1) ++ LaTeX Font Info: Try loading font information for U+msb on input line 55. DelBlock(Argon_size_depedence.log,184,1) -- (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsfonts/umsb.fd AddBlock(Argon_size_depedence.log,184,1) ++ (C:\texmf\tex\latex\amsfonts\umsb.fd DelBlock(Argon_size_depedence.log,189,2) -- -- <figures/figure1.eps> [1] AddBlock(Argon_size_depedence.log,189,1) ++ <figures/figure1.eps> [1] DelBlock(Argon_size_depedence.log,191,1) -- <figures/figure2.eps> AddBlock(Argon_size_depedence.log,191,6) ++ ++ <figures/figure2.eps> ++ Underfull \hbox (badness 1622) in paragraph at lines 95--96 ++ \OT1/cmr/m/n/10 and stop sig-nals for the Time-to-Digital Con-verter ++ [] ++ DelBlock(Argon_size_depedence.log,198,1) -- <figures/figure3.eps> AddBlock(Argon_size_depedence.log,198,1) ++ <figures/figure3.eps> DelBlock(Argon_size_depedence.log,205,1) -- on input line 116. AddBlock(Argon_size_depedence.log,205,1) ++ on input line 109. DelBlock(Argon_size_depedence.log,209,2) -- Overfull \hbox (0.92249pt too wide) in paragraph at lines 130--131 -- [][] AddBlock(Argon_size_depedence.log,209,2) ++ Overfull \hbox (0.92249pt too wide) in paragraph at lines 121--122 ++ [][][] DelBlock(Argon_size_depedence.log,219,2) -- Underfull \hbox (badness 2521) in paragraph at lines 156--157 -- []\OT1/cmr/m/n/10 This as-tound-ing im-por-tance of mul-ti-ply charged AddBlock(Argon_size_depedence.log,219,2) ++ Underfull \hbox (badness 2521) in paragraph at lines 147--148 ++ [][]\OT1/cmr/m/n/10 This as-tound-ing im-por-tance of mul-ti-ply charged DelBlock(Argon_size_depedence.log,224,1) -- Missing character: There is no Ê in font cmr10! DelBlock(Argon_size_depedence.log,225,1) -- <figures/figure6.eps> [5] [6] (./Argon_size_depedence.bbl AddBlock(Argon_size_depedence.log,225,1) ++ <figures/figure6.eps> [5] [6] (Argon_size_depedence.bbl DelBlock(Argon_size_depedence.log,227,1) -- []\OT1/cmr/m/n/9 W.H. Press, S.A. Teukol-sky, W.T. Vet-ter-ling, and AddBlock(Argon_size_depedence.log,227,1) ++ [][]\OT1/cmr/m/n/9 W.H. Press, S.A. Teukol-sky, W.T. Vet-ter-ling, and DelBlock(Argon_size_depedence.log,230,1) -- ) [7] (./Argon_size_depedence.aux) ) AddBlock(Argon_size_depedence.log,230,1) ++ ) [7] (Argon_size_depedence.aux) ) DelBlock(Argon_size_depedence.log,232,10) -- 2920 strings out of 95204 -- 35350 string characters out of 1184352 -- 2090080 words of memory out of 4544915 -- 6016 multiletter control sequences out of 10000+50000 -- 12591 words of font info for 52 fonts, out of 2000000 for 2000 -- 58 hyphenation exceptions out of 1000 -- 29i,8n,22p,2163b,309s stack positions out of 1500i,500n,5000p,200000b,5000s -- 0 PDF objects out of 300000 -- 0 named destinations out of 131072 -- 1 words of extra memory for PDF output out of 65536 AddBlock(Argon_size_depedence.log,232,7) ++ 3058 strings out of 95898 ++ 34222 string characters out of 1195288 ++ 107756 words of memory out of 1094637 ++ 5943 multiletter control sequences out of 35000 ++ 12591 words of font info for 52 fonts, out of 500000 for 1000 ++ 14 hyphenation exceptions out of 607 ++ 29i,8n,22p,2163b,313s stack positions out of 1500i,500n,5000p,200000b,32768s DelBlock(Argon_size_depedence.log,240,1) -- Output written on Argon_size_depedence.dvi (7 pages, 49008 bytes). AddBlock(Argon_size_depedence.log,240,1) ++ Output written on Argon_size_depedence.dvi (7 pages, 49240 bytes). UpdateBinaryFile(Argon_size_depedence.pdf) AddTxtFile(Argon_size_depedence.pdf#288) AddTxtFile(Argon_size_depedence.tbx) DelBlock(Argon_size_depedence.tex,1,3) -- %\documentclass[aps,prl,preprint,nobibnotes,groupedaddress,showpacs]{revtex4} -- %\documentclass[aps,pra,preprint,superscriptaddress,nobibnotes,showpacs]{revtex4} -- \documentclass[aps,pra,twocolumn,superscriptaddress,nobibnotes,showpacs, preprintnumbers]{revtex4} AddBlock(Argon_size_depedence.tex,1,2) ++ %\documentclass[preprint,superscriptaddress,showpacs,endfloats*]{revtex4} ++ \documentclass[aps,pra,twocolumn,superscriptaddress,nobibnotes,showpacs,preprintnumbers]{revtex4} DelBlock(Argon_size_depedence.tex,20,2) -- 91405 Orsay, France} -- \affiliation{MAX-Lab, Lund University, Box 118, S-221 00 Lund, Sweden} AddBlock(Argon_size_depedence.tex,20,2) ++ 91405 Orsay, France} ++ \affiliation{MAX-Lab, Lund University, Box 118, S-221 00 Lund, Sweden} DelBlock(Argon_size_depedence.tex,32,1) -- \affiliation{MAX-Lab, Lund University, Box 118, S-221 00 Lund, Sweden} AddBlock(Argon_size_depedence.tex,32,1) ++ \affiliation{MAX-Lab, Lund University, Box 118, S-221 00 Lund, Sweden} DelBlock(Argon_size_depedence.tex,55,3) -- change in fragmentation pattern is observed when the cluster size increases -- %change "pointing out" -- revealing the different time scale of the dissociation mechanisms. For small clusters ($<$10$>$), after ionization a fast fragmentation with neutral emission imparting large amount of energy in the ps time scale occurs, then slow degradation of the photo-cluster ions is observed in the $\mu$s time scale. For larger clusters ($\geq <$100$>$) we believe that we observe the fragmentation pattern of large unstable multiply charged species in time scale which last a few hundred of ns. The reason for these apparent slow processes could be that the large amount of neutral atoms acts as an efficient cooling bath which tend to dissipate the excess of energy ("heat") among all degree of freedom. Degradation of the photo-cluster ions take place in the $\mu$s time scale as for small clusters. AddBlock(Argon_size_depedence.tex,55,1) ++ change in fragmentation pattern is observed when the cluster size increases revealing the different time scale of the dissociation mechanisms. For small clusters ($<$10$>$), after ionization a fast fragmentation with neutral emission imparting large amount of energy in the ps time scale occurs, then slow degradation of the photo-cluster ions is observed in the $\mu$s time scale. For larger clusters ($\geq <$100$>$) we believe that we observe the fragmentation pattern of large unstable multiply charged species in time scale which last a few hundred of ns. The reason for these apparent slow processes could be that the large amount of neutral atoms acts as an efficient cooling bath which tend to dissipate the excess of energy ("heat") among all degree of freedom. Degradation of the photo-cluster ions take place in the $\mu$s time scale as for small clusters. DelBlock(Argon_size_depedence.tex,64,3) -- In a recent publication \cite{Gisselbrecht_2005} we presented the general fragmentation pattern of small argon clusters for resonant inner shell excitation and ionization. We did show that the inner shell photo-absorption prepared selectively ionic species below or above the vertical double ionization -- % Add maxim and marcus -- potential \cite{Maxim_2003, Lundwall_05}, respectively Ar$_m^{+*}$ and Ar$_m^{2+}$. In both case theses species undergo dissociation leading to two or more charged fragments pointing out the importance of the nuclear relaxation as well as the electronic relaxation. AddBlock(Argon_size_depedence.tex,64,1) ++ In a recent publication \cite{Gisselbrecht_2005} we presented the general fragmentation pattern of small argon clusters for resonant inner shell excitation and ionization. We did show that the inner shell photo-absorption prepared selectively ionic species below or above the vertical double ionization potential \cite{Maxim_2003, Lundwall_05}, respectively Ar$_m^{+*}$ and Ar$_m^{2+}$. In both case theses species undergo dissociation leading to two or more charged fragments pointing out the importance of the nuclear relaxation as well as the electronic relaxation. DelBlock(Argon_size_depedence.tex,66,3) -- In this study we focus on the cluster-size dependent fragmentation with a VUV photon of 116~eV. We perform a multicoincidence measurement Photo-Electron-n-Photo-Ions COincidence PE(PI)$_n$CO with a mass spectrometer. -- -- \begin{figure}[t] AddBlock(Argon_size_depedence.tex,66,2) ++ This study focus on the cluster-size dependent fragmentation with a VUV photon of 116~eV. We perform a multicoincidence measurement Photo-Electron-n-Photo-Ions COincidence PE(PI)$_n$CO with a mass spectrometer. ++ \begin{figure}[t] DelBlock(Argon_size_depedence.tex,70,1) -- \caption{\label{Fig1} Photo-ionization branching ratio for free argon atoms and schematic decay channels for clusters. } AddBlock(Argon_size_depedence.tex,70,1) ++ \caption{\label{Fig1} Photo-ionization branching ratio for free argon atoms and schematic decay channels for clusters.} AddBlock(Argon_size_depedence.tex,73,5) ++ The chosen photon energy implies that only the $3p$ valence and $3s$ inner valence shells can be ionized and Auger relaxation is energetically not possible. For free atoms, we are well above the double-ionization threshold 43.4~eV \cite{Nist}, the $3s$ Cooper minimum between 45-50~eV, and even exceeds the triple ionization threshold 84.3~eV\cite{Nist}. The branching ratios are known to be 83\% for single photo-ionization, 16\% for double photo-ionization, and less than 1\% for triple photo-ionization \cite{Holland_1979}. In the current picture of cluster ionization, so called Haberland's model \cite{Haberland_book_1995, Haberland_book_1994}, the system does not have time for nuclear rearrangement and states close to the dissociation limit are populated. Thus the cluster photo-ionization branching ratio should mimic the atomic one. However, in our experiment the time scale is long enough for nuclear relaxation to take place and adiabatic potentials to be relevant \cite{Ruhl_1992}. Hence, among the singly charge species a few of them ($\sim$15\%) prepared with two holes and one particle in the outer valence shell, should decay in the double ionization continuum as we have already eluded \cite{Gisselbrecht_2005}. Hence, one could speculate that the fragmentation depend on the cluster size. ++ %==== mathieu@g3 / andreas@work ++ %>The chosen photon energy implies that only the $3p$ valence and $3s$ inner valence shells can be ionized and Auger relaxation is energetically not possible. For free atoms, we are well above the double-ionization threshold 43.4~eV \cite{Nist}, the $3s$ Cooper minimum between 45-50~eV, and even exceeds the triple ionization threshold 84.3~eV. The branching ratios are known to be 83\% for single photo-ionization, 16\% for double photo-ionization, and less than 1\% for triple photo-ionization \cite{Holland_1979}. In the current picture of cluster ionization, so called Haberland's model \cite{Haberland_book_1995, Haberland_book_1994}, the system does not have time for nuclear rearrangement and states close to the dissociation limit are populated. Thus the cluster photo-ionization branching ratio should mimic the atomic one. However in our experiment the time scale is long enough for nuclear relaxation to take place and adiabatic potentials to be relevant \cite{Ruhl_1992}. Hence, among the singly charge species a few of them ($\sim$15\%) prepared with two holes and one particle in the outer valence shell, should decay in the double ionization continuum as we have already eluded \cite{Gisselbrecht_2005}. Hence, one could speculate that the fragmentation depend on the cluster size. ++ ++ In Fig.~\ref{Fig1} we present the photo-ionization branching ratio for free argon atoms and where the decay channel are expected for cluster. Our aim is to investigate the photo-fragmentation over a size range from a few up to thousands of atoms in order to know whether the fragmentation dynamics is a sensitive probe to the formation of stable multiply ionized clusters. DelBlock(Argon_size_depedence.tex,79,8) -- The chosen photon energy implies that only the $3p$ valence and $3s$ inner valence shells can be ionized and Auger relaxation is energetically not possible. For free atoms, we are well above the double-ionization threshold 43.4~eV \cite{Nist}, the $3s$ Cooper minimum between 45-50~eV, and -- % ref for triple ionization -- even exceeds the triple ionization threshold 84.3~eV\cite{Nist}. The branching ratios are known to be 83\% for single photo-ionization, 16\% for double photo-ionization, and less than 1\% for triple photo-ionization \cite{Holland_1979}. In the current picture of cluster ionization, so called Haberland's model \cite{Haberland_book_1995, Haberland_book_1994}, the system does not have time for nuclear rearrangement and states close to the dissociation limit are populated. Thus the cluster photo-ionization branching ratio should mimic the atomic one. However in our experiment the time scale is long enough for nuclear relaxation to take place and adiabatic potentials to be relevant \cite{Ruhl_1992}. Hence, among the singly charge species a few of them ($\sim$15\%) prepared with two holes and one particle in the outer valence shell, should decay in the double ionization continuum as we have already eluded \cite{Gisselbrecht_2005}. Hence, one could speculate that the fragmentation depend on the cluster size.\\ -- We present figure~\ref{Fig1}, the photo-ionization branching ratio for free argon atoms (check again ?) and where the decay channel are expected for cluster. Our aim is to investigate the photo-fragmentation over a size range from a few up to thousands of atoms in order to know whether the fragmentation dynamics is a sensitive probe to the formation of stable multiply ionized clusters. -- -- -- -- DelBlock(Argon_size_depedence.tex,82,2) -- The experiment was carried out at the beam line I411 on the MAX II electron storage ring at the Swedish National Synchrotron Radiation Laboratory MAX-lab in Lund, Sweden \cite{Svensson_1996}. The undulator beamline was equipped with a modified SX-700 plane-grating monochromator, which allowed photon energy tuning from 61 to 1500~eV. A chamber with a 2-field electron-ion coincidence spectrometer was mounted on the beam line upstream of the permanent end station. -- Argon clusters were produced in a supersonic expansion with different experimental conditions (flat or conical nozzle at room or liquid nitrogen temperature). The beam consisted of a mixture of atoms and clusters, characterized by an average cluster size of $<$N$>$ atoms per cluster and the full-width at half-maximum (FWHM) of the size distribution is $N/2$. The average cluster size $<$N $>$ was estimated according to the $\Gamma^{\ast}$-formalism \cite{Karnbach_1993}. One should keep in mind that the uncertainty in the absolute size determintation can be of a factor of 2, depending on experimental parameter uncertainties and which of the published scaling law are used \cite{Karnbach_1993, Buck_1996}. We present Figure~\ref{Fig2} in log-log scale the theoretical intensity distribution of neutral clusters for different average sizes. It has been arbitrary normalized for $<$N$>$=10 for sake of clarity. The spectrum shows that between the smallest and the largest average size, the relative intensity of small clusters (e.g. dimers, trimers...) is a few order of magnitude more for smallest size. This means that in our experiment the physical origins of small photo-clusters changes gradually with the cluster size. For the smallest cluster size, the photo-clusters arise from direct photo-ionization and photo-fragmentation, while for largest cluster size photo-clusters arise exclusively from photo-fragmentation. The use of multi-coincidence technique allow us then to ensure that the measured photo-clusters are related to multiply charged mother clusters. AddBlock(Argon_size_depedence.tex,82,1) ++ The experiment was carried out at the beam line I411 on the MAX II electron storage ring at the Swedish National Synchrotron Radiation Laboratory MAX-lab in Lund, Sweden \cite{Svensson_1996}. The undulator beamline was equipped with a modified SX-700 plane-grating monochromator, which allowed photon energy tuning from 61 to 1500~eV. A chamber with a 2-field electron-ion coincidence spectrometer was mounted on the beam line upstream of the permanent end station. AddBlock(Argon_size_depedence.tex,84,2) ++ Argon clusters were produced in a supersonic expansion with different experimental conditions (flat or conical nozzle at room or liquid nitrogen temperature). The beam consisted of a mixture of atoms and clusters, characterized by an average cluster size of $<$N$>$ atoms per cluster and the full-width at half-maximum (FWHM) of the size distribution is $N/2$. The average cluster size $<$N$>$ was estimated according to the $\Gamma^{\ast}$-formalism \cite{Karnbach_1993}. One should keep in mind that the uncertainty in the absolute size determintation can be of a factor of 2, depending on experimental parameter uncertainties and which of the published scaling law are used \cite{Karnbach_1993, Buck_1996}. We present Figure~\ref{Fig2} in log-log scale the theoretical intensity distribution of neutral clusters for different average sizes. It has been arbitrary normalized for $<$N$>$=10 for sake of clarity. The spectrum shows that between the smallest and the largest average size, the relative intensity of small clusters (e.g. dimers, trimers...) is a few order of magnitude more for smallest size. This means that in our experiment the physical origins of small photo-clusters changes gradually with the cluster size. For the smallest cluster size, the photo-clusters arise from direct photo-ionization and photo-fragmentation, while for largest cluster size photo-clusters arise exclusively from photo-fragmentation. The use of multi-coincidence technique allow us then to ensure that the measured photo-clusters are related to multiply charged mother clusters. ++ DelBlock(Argon_size_depedence.tex,93,4) -- electrons and the ions from this region. Electrons with kinetic energy up to 500~eV can be collected over a solid angle of 4$\pi$ steradian. In order to satisfy the so-called 'space-time focusing' \cite{Wiley_1955} criterion, ions were post-accelerated before they passed into a field free drift tube. The spectrometer was positioned perpendicular to the polarization plane of the light. Thus, the spatial extent of the source volume along the spectrometer axis is negligible since it is defined by the vertical size of the -- light spot ($\sim$0.4~mm) and is independent of the expansion conditions of the cluster source. A resolving power of $m/\delta m \sim 500$ was achieved. -- Electrons and ions, detected by micro channel plate (MCP) pairs in a chevron configuration, provide start and stop signals for the Time-to-Digital Converter (TDC) in the set-up. The time of flight of ions arising from single, up to quadruple ionization events, was recorded and treated in real time. For all measurements the ion count rate was essentially constant, less than 2~kHz, keeping theoretically the detection probability of a random ion (false coincidence) at about 1\% within our acquisition time -- window (5~$\mu$s). This probability is in practice degraded by the fact that the density of uncondensed atoms in the cluster source is 10 to 20 times higher than the density of clusters. Calibration on rare gases (argon, krypton, and xenon) has shown that the ion efficiency decreases for masses above $\sim$150 a.u. even though the photo-ions are accelerated up to 4~keV. This is due to the use of discriminators in the electronics scheme which cut-off a part of the pulse height distribution of the MCP signal for heavy particles \cite{Furuya_2002}. Thus the detection efficiencies of argon dimers and trimers are comparable, but heavier ions have lower detection efficiency. Calibration of the cluster source has shown that cluster sizes larger than 35 atoms can easily be observed with the present spectrometer. AddBlock(Argon_size_depedence.tex,93,1) ++ electrons and the ions from this region. Electrons with kinetic energy up to 500~eV can be collected over a solid angle of 4$\pi$ steradian. In order to satisfy the so-called 'space-time focusing' \cite{Wiley_1955} criterion, ions were post-accelerated before they passed into a field free drift tube. The spectrometer was positioned perpendicular to the polarization plane of the light. Thus, the spatial extent of the source volume along the spectrometer axis is negligible since it is defined by the vertical size of the light spot ($\sim$0.4~mm) and is independent of the expansion conditions of the cluster source. A resolving power of $m/\delta m \sim 500$ was achieved. AddBlock(Argon_size_depedence.tex,95,1) ++ Electrons and ions, detected by micro channel plate (MCP) pairs in a chevron configuration, provide start and stop signals for the Time-to-Digital Converter (TDC) in the set-up. The time of flight of ions arising from single, up to quadruple ionization events, was recorded and treated in real time. For all measurements the ion count rate was essentially constant, less than 2~kHz, keeping theoretically the detection probability of a random ion (false coincidence) at about 1\% within our acquisition time window (5~$\mu$s). This probability is in practice degraded by the fact that the density of uncondensed atoms in the cluster source is 10 to 20 times higher than the density of clusters. Calibration on rare gases (argon, krypton, and xenon) has shown that the ion efficiency decreases for masses above $\sim$150 a.u. even though the photo-ions are accelerated up to 4~keV. This is due to the use of discriminators in the electronics scheme which cut-off a part of the pulse height distribution of the MCP signal for heavy particles \cite{Furuya_2002}. Thus the detection efficiencies of argon dimers and trimers are comparable, but heavier ions have lower detection efficiency. Calibration of the cluster source has shown that cluster sizes larger than 35 atoms can easily be observed with the present spectrometer. AddBlock(Argon_size_depedence.tex,97,1) ++ DelBlock(Argon_size_depedence.tex,153,3) -- \caption{\label{table1} Typical time scale associated with the decay of dimers into monomer and mother ion into the dimer channel } -- \begin{tabular}{c|c|c} -- $<$N$>$ & Decay channel & Lifetime \\ AddBlock(Argon_size_depedence.tex,153,4) ++ \caption{\label{table1} Typical time scale associated with the decay of dimers into monomer and mother ion into the dimer channel.} ++ \begin{ruledtabular} ++ \begin{tabular}{ccc} ++ $<$N$>$ & Decay channel & Lifetime, $\tau_m$ \\ DelBlock(Argon_size_depedence.tex,158,4) -- 10 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ -- & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ -- 20 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ -- & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ AddBlock(Argon_size_depedence.tex,158,4) ++ 10 & Ar$^+_2\rightarrow$Ar$^+$+Ar & 1.5$\pm$0.5 $\mu$s \\ ++ & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & 1.5$\pm$0.5 $\mu$s \\ ++ 20 & Ar$^+_2\rightarrow$Ar$^+$+Ar & 1.5$\pm$0.5 $\mu$s \\ ++ & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & 1.5$\pm$0.5 $\mu$s \\ DelBlock(Argon_size_depedence.tex,163,6) -- 100 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$=300$\pm$50 ns \\ -- & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$=300$\pm$50 ns \\ -- & Ar$^+_m\rightarrow$Ar$^+_2$+X & $\tau_m$=100$\pm$ 50 ns \\ -- 1000 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$=300$\pm$50 ns \\ -- & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$=300$\pm$50 ns \\ -- & Ar$^+_m\rightarrow$Ar$^+_2$+X & $\tau_m$=100$\pm$30 ns \\ AddBlock(Argon_size_depedence.tex,163,6) ++ 100 & Ar$^+_2\rightarrow$Ar$^+$+Ar & 300$\pm$50 ns \\ ++ & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & 300$\pm$50 ns \\ ++ & Ar$^+_m\rightarrow$Ar$^+_2$+X & 100$\pm$ 50 ns \\ ++ 1000 & Ar$^+_2\rightarrow$Ar$^+$+Ar & 300$\pm$50 ns \\ ++ & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & 300$\pm$50 ns \\ ++ & Ar$^+_m\rightarrow$Ar$^+_2$+X & 100$\pm$30 ns \\ AddBlock(Argon_size_depedence.tex,170,1) ++ \end{ruledtabular} DelBlock(Argon_size_depedence.tex,175,1) -- sizes ($<$N$>$=10,20), exhibit a typical peak shape with "eiffel tower" signature of decay in the drift tube. For dimer channels, it corresponds to the degradation of Ar$^+_2\rightarrow$Ar$^+$+Ar. According to Whitaker~\textit{et al.} \cite{Whitaker_93} this process can arise from radiative decay from the electronic $\Pi$(1/2)$_u$ state of the ion to the I(1/2)$_g$. Such decay is reasonable in our experiment since there is no particular reason to produce dimer fragments arising from the fragmentation of multiply charge clusters only in its ground state. However, one should keep in mind that collision induced dissociation (CID) is very a likely reason for cluster-ion degradation for background pressure above 10$^{-7}$~mbar which was the case. Our experimental resolution is not good enough to quantify properly the importance of such process but we think that at least both processes can happen. For trimer, the gaussian like distribution is due to a more complex fragmentation mechanisms which can lead either to formation of monomer or dimer depending of the internal energy left in the trimer, blurring hence the "either-tower" distribution. We present in table I, the result of our simulation in order to give an estimation of the time scale associated the degradation of this species. Accurate values for the kinetic energy KE$_1$ and KE$_2$ is hard to extract since both parameters acts almost the same way, however one can estimate that they are in the order of 500ÊmeV down to 100meV. AddBlock(Argon_size_depedence.tex,175,1) ++ sizes ($<$N$>$=10,20), exhibit a typical peak shape with "eiffel tower" signature of decay in the drift tube. For dimer channels, it corresponds to the degradation of Ar$^+_2\rightarrow$Ar$^+$+Ar. According to Whitaker~\textit{et al.} \cite{Whitaker_93} this process can arise from radiative decay from the electronic $\Pi$(1/2)$_u$ state of the ion to the I(1/2)$_g$. Such decay is reasonable in our experiment since there is no particular reason to produce dimer fragments arising from the fragmentation of multiply charge clusters only in its ground state. However, one should keep in mind that collision induced dissociation (CID) is very a likely reason for cluster-ion degradation for background pressure above 10$^{-7}$~mbar which was the case. Our experimental resolution is not good enough to quantify properly the importance of such process but we think that at least both processes can happen. For trimer, the gaussian like distribution is due to a more complex fragmentation mechanisms which can lead either to formation of monomer or dimer depending of the internal energy left in the trimer, blurring hence the "either-tower" distribution. We present in table I, the result of our simulation in order to give an estimation of the time scale associated the degradation of this species. Accurate values for the kinetic energy KE$_1$ and KE$_2$ is hard to extract since both parameters acts almost the same way, however one can estimate that they are in the order of 500~meV down to 100~meV. DelBlock(Argon_size_depedence.tex,191,1) -- In figure \ref{Fig6}, we present a summary of the possible mechanisms that we observe. At 116~eV photon energy, direct photo-ionization can produce about 15 \% of excited singly charged clusters Ar$_m^{+*}$ and about 16\% of doubly charged clusters Ar$_m^{2+}$ with or without additional energy. This species can relax into the double ionization continuum of the clusters. AddBlock(Argon_size_depedence.tex,191,1) ++ In Fig.~\ref{Fig6}, we present a summary of the possible mechanisms that we observe. At 116~eV photon energy, direct photo-ionization can produce about 15 \% of excited singly charged clusters Ar$_m^{+*}$ and about 16\% of doubly charged clusters Ar$_m^{2+}$ with or without additional energy. This species can relax into the double ionization continuum of the clusters. AddBlock(Argon_size_depedence.tex,209,3) ++ \printtables ++ \printfigures ++ AddTxtFile(Argon_size_depedence.tex.bak)
Small changes : reference, doubling words, eng. mistakes
AddBlock(Argon_size_depedence.aux,3,2) ++ \citation{Maxim_2003} ++ \citation{Lundwall_05} AddBlock(Argon_size_depedence.aux,6,1) ++ \citation{Nist} DelBlock(Argon_size_depedence.aux,14,1) -- \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Photo-ionisation branching ratio for free argon atoms and schematic decay channels for clusters. }}{1}{}} AddBlock(Argon_size_depedence.aux,14,1) ++ \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Photo-ionization branching ratio for free argon atoms and schematic decay channels for clusters. }}{1}{}} AddBlock(Argon_size_depedence.aux,42,1) ++ \@writefile{toc}{\contentsline {subsection}{\numberline {B}Peak shape}{3}{}} AddBlock(Argon_size_depedence.aux,47,2) ++ \citation{Casero_1988} ++ \citation{Ruhl_1994} DelBlock(Argon_size_depedence.aux,51,1) -- \@writefile{toc}{\contentsline {subsection}{\numberline {B}Peak shape}{4}{}} DelBlock(Argon_size_depedence.aux,52,2) -- \citation{Casero_1988} -- \citation{Ruhl_1994} AddBlock(Argon_size_depedence.aux,52,1) ++ \@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Analysis: influence of meta-stable decay}{4}{}} DelBlock(Argon_size_depedence.aux,57,3) -- \@writefile{lot}{\contentsline {table}{\numberline {I}{\ignorespaces Typical time scale associated with the decay of dimers into monomer and mother ion into the dimer channel }}{5}{}} -- \newlabel{table1}{{I}{5}{}{}{}} -- \@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Analysis: influence of meta-stable decay}{5}{}} AddBlock(Argon_size_depedence.aux,57,1) ++ \citation{Casero_1988} AddBlock(Argon_size_depedence.aux,63,2) ++ \@writefile{lot}{\contentsline {table}{\numberline {I}{\ignorespaces Typical time scale associated with the decay of dimers into monomer and mother ion into the dimer channel }}{5}{}} ++ \newlabel{table1}{{I}{5}{}{}{}} AddBlock(Argon_size_depedence.aux,67,1) ++ \@writefile{toc}{\contentsline {section}{\numberline {IV}Conclusion}{6}{}} DelBlock(Argon_size_depedence.aux,70,28) -- \bibcite{Nist}{{2}{}{{Nis}}{{}}} -- \bibcite{Holland_1979}{{3}{1979}{{{D. M. P. Holland} et~al.}}{{{D. M. P. Holland}, {K. Codling}, {J. B. West}, and {G. V. Marr}}}} -- \bibcite{Haberland_book_1995}{{4}{1995}{{Haberland}}{{}}} -- \bibcite{Haberland_book_1994}{{5}{1994}{{Haberland}}{{}}} -- \bibcite{Ruhl_1992}{{6}{1992}{{{E. R\"{u}hl} et~al.}}{{{E. R\"{u}hl}, {C. Schmale}, {H.C. Schmelz}, and {H. Baumg\"{a}rtel}}}} -- \bibcite{Svensson_1996}{{7}{1996}{{{S. Svensson} et~al.}}{{{S. Svensson}, {J. -O. Forsell}, {H. Siegbahn}, {A. Ausmees}, {G. Bray}, {S. S\"{o}dergren}, {S. Sundin}, {S.J. Osborne}, {S. Aksela}, {E. N\"{o}mmiste} et~al.}}} -- \bibcite{Karnbach_1993}{{8}{1993}{{{R. Karnbach} et~al.}}{{{R. Karnbach}, {M. Joppien}, {J. Stapelfeldt}, {J. W\"{o}rmer}, and {T. M\"{o}ller}}}} -- \bibcite{Buck_1996}{{9}{1996}{{{U. Buck} and {R. Krohne}}}{{}}} -- \bibcite{Wiley_1955}{{10}{1955}{{{W. C. Wiley} and {I. H. McLaren}}}{{}}} -- \bibcite{Furuya_2002}{{11}{2002}{{{K. Furuya} and {Y. Hatano}}}{{}}} -- \bibcite{Stephan_1983}{{12}{1983}{{{K. Stephan} et~al.}}{{{K. Stephan}, {A. Stamatovic}, and {T.D. M\"{a}rk}}}} -- \bibcite{Lethbridge_1988}{{13}{1988}{{{P.G. Lethbridge} and {A.J. Stace}}}{{}}} -- \bibcite{NumericalRecipes}{{14}{1992}{{{W.H. Press} et~al.}}{{{W.H. Press}, {S.A. Teukolsky}, {W.T. Vetterling}, and {B.P. Flannery}}}} -- \bibcite{Ikegami_1993}{{15}{1993}{{{T. Ikegami} and {T. Kondow}}}{{}}} -- \bibcite{Hrivnak_2001}{{16}{2001}{{{D. Hrivnak} and {R. Kalus}}}{{}}} -- \bibcite{Thissen_1998}{{17}{1998}{{{R. Thissen} et~al.}}{{{R. Thissen}, {P. Lablanquie}, {R.I. Hall}, {M. Ukai}, and {K. Ito}}}} -- \bibcite{Gotts_1992}{{18}{1992}{{{N.G. Gotts} et~al.}}{{{N.G. Gotts}, {P.G. Lethbridge}, and {A.J. Stace}}}} -- \bibcite{Scheier_87}{{19}{1987}{{{P. Scheier } and {T.D. M\"{a}rk}}}{{}}} -- \bibcite{Hergenhahn_2002}{{20}{2002}{{{U. Hergenhahn} et~al.}}{{{U. Hergenhahn}, {A. Kolmakov}, {M. Reidler}, {A.R.B de Castro}, {O. L\"{o}fen}, and {T. M\"{o}ller}}}} -- \bibcite{Casero_1988}{{21}{1988}{{{R. Casero} et~al.}}{{{R. Casero}, {J. J. S\'{a}enz}, and {J.M. Soler}}}} -- \bibcite{Ruhl_1994}{{22}{1994}{{{E. R\"{u}hl} et~al.}}{{{E. R\"{u}hl}, {C. Heinzel}, {H. Baumg\"{a}rtel}, {M. Lavoll\'{e}e}, and {P. Morin}}}} -- \bibcite{Whitaker_93}{{23}{1990}{{{B.J. Whitaker} et~al.}}{{{B.J. Whitaker}, {C.A. Woodward}, {P.J. Knowles}, and {A.J. Stace}}}} -- \bibcite{Laarmann_2002}{{24}{2002}{{{T. Laarmann} et~al.}}{{{T. Laarmann}, {A. Kanaev}, {K. von Haeften}, {W. Wabnitz}, {R. von Pietrowski}, and {T. M\"{o}ller}}}} -- \bibcite{Dujardin_1990}{{25}{1990}{{{G. Dujardin} et~al.}}{{{G. Dujardin}, {L. Hellner}, {M.J. Besnardramage}, and {R. Azria}}}} -- \bibcite{Stace_1991}{{26}{1991}{{{A. Stace} et~al.}}{{{A. Stace}, {C.A. Woodward}, and {B.J. whitaker}}}} -- \bibcite{Moller_99}{{27}{1999}{{{T. Moller} et~al.}}{{{T. Moller}, {K. von Haeften}, {T. Laarman}, and {R. von Pietrowski}}}} -- \bibcite{Ruhl_1993}{{28}{1993}{{{E. R\"{u}hl} et~al.}}{{{E. R\"{u}hl}, {C. Heinzel}, and {H. W. Jochims}}}} -- \global \chardef \firstnote@num28\relax AddBlock(Argon_size_depedence.aux,70,30) ++ \bibcite{Maxim_2003}{{2}{2003}{{{M. Tchaplyguine} et~al.}}{{{M. Tchaplyguine}, {R. Feifel}, {R.R.T. Marinho}, {M. Gisselbrecht}, {S.L. Sorensen}, {A. Naves de Brito}, {N. M\r artensson}, {S. Svensson}, and {O. Bj\"{o}rneholm}}}} ++ \bibcite{Lundwall_05}{{3}{2005}{{{M. Lundwall} et~al.}}{{{M. Lundwall}, {M. Tchaplyguine}, {G. \"{O}hrwall}, {A. Lindblad}, {S.Peredkov}, {T. Rander}, and {O. Bj\"{o}rneholm}}}} ++ \bibcite{Nist}{{4}{}{{Nis}}{{}}} ++ \bibcite{Holland_1979}{{5}{1979}{{{D. M. P. Holland} et~al.}}{{{D. M. P. Holland}, {K. Codling}, {J. B. West}, and {G. V. Marr}}}} ++ \bibcite{Haberland_book_1995}{{6}{1995}{{Haberland}}{{}}} ++ \bibcite{Haberland_book_1994}{{7}{1994}{{Haberland}}{{}}} ++ \bibcite{Ruhl_1992}{{8}{1992}{{{E. R\"{u}hl} et~al.}}{{{E. R\"{u}hl}, {C. Schmale}, {H.C. Schmelz}, and {H. Baumg\"{a}rtel}}}} ++ \bibcite{Svensson_1996}{{9}{1996}{{{S. Svensson} et~al.}}{{{S. Svensson}, {J. -O. Forsell}, {H. Siegbahn}, {A. Ausmees}, {G. Bray}, {S. S\"{o}dergren}, {S. Sundin}, {S.J. Osborne}, {S. Aksela}, {E. N\"{o}mmiste} et~al.}}} ++ \bibcite{Karnbach_1993}{{10}{1993}{{{R. Karnbach} et~al.}}{{{R. Karnbach}, {M. Joppien}, {J. Stapelfeldt}, {J. W\"{o}rmer}, and {T. M\"{o}ller}}}} ++ \bibcite{Buck_1996}{{11}{1996}{{{U. Buck} and {R. Krohne}}}{{}}} ++ \bibcite{Wiley_1955}{{12}{1955}{{{W. C. Wiley} and {I. H. McLaren}}}{{}}} ++ \bibcite{Furuya_2002}{{13}{2002}{{{K. Furuya} and {Y. Hatano}}}{{}}} ++ \bibcite{Stephan_1983}{{14}{1983}{{{K. Stephan} et~al.}}{{{K. Stephan}, {A. Stamatovic}, and {T.D. M\"{a}rk}}}} ++ \bibcite{Lethbridge_1988}{{15}{1988}{{{P.G. Lethbridge} and {A.J. Stace}}}{{}}} ++ \bibcite{NumericalRecipes}{{16}{1992}{{{W.H. Press} et~al.}}{{{W.H. Press}, {S.A. Teukolsky}, {W.T. Vetterling}, and {B.P. Flannery}}}} ++ \bibcite{Ikegami_1993}{{17}{1993}{{{T. Ikegami} and {T. Kondow}}}{{}}} ++ \bibcite{Hrivnak_2001}{{18}{2001}{{{D. Hrivnak} and {R. Kalus}}}{{}}} ++ \bibcite{Thissen_1998}{{19}{1998}{{{R. Thissen} et~al.}}{{{R. Thissen}, {P. Lablanquie}, {R.I. Hall}, {M. Ukai}, and {K. Ito}}}} ++ \bibcite{Gotts_1992}{{20}{1992}{{{N.G. Gotts} et~al.}}{{{N.G. Gotts}, {P.G. Lethbridge}, and {A.J. Stace}}}} ++ \bibcite{Scheier_87}{{21}{1987}{{{P. Scheier } and {T.D. M\"{a}rk}}}{{}}} ++ \bibcite{Hergenhahn_2002}{{22}{2002}{{{U. Hergenhahn} et~al.}}{{{U. Hergenhahn}, {A. Kolmakov}, {M. Reidler}, {A.R.B de Castro}, {O. L\"{o}fen}, and {T. M\"{o}ller}}}} ++ \bibcite{Casero_1988}{{23}{1988}{{{R. Casero} et~al.}}{{{R. Casero}, {J. J. S\'{a}enz}, and {J.M. Soler}}}} ++ \bibcite{Ruhl_1994}{{24}{1994}{{{E. R\"{u}hl} et~al.}}{{{E. R\"{u}hl}, {C. Heinzel}, {H. Baumg\"{a}rtel}, {M. Lavoll\'{e}e}, and {P. Morin}}}} ++ \bibcite{Whitaker_93}{{25}{1990}{{{B.J. Whitaker} et~al.}}{{{B.J. Whitaker}, {C.A. Woodward}, {P.J. Knowles}, and {A.J. Stace}}}} ++ \bibcite{Laarmann_2002}{{26}{2002}{{{T. Laarmann} et~al.}}{{{T. Laarmann}, {A. Kanaev}, {K. von Haeften}, {W. Wabnitz}, {R. von Pietrowski}, and {T. M\"{o}ller}}}} ++ \bibcite{Dujardin_1990}{{27}{1990}{{{G. Dujardin} et~al.}}{{{G. Dujardin}, {L. Hellner}, {M.J. Besnardramage}, and {R. Azria}}}} ++ \bibcite{Stace_1991}{{28}{1991}{{{A. Stace} et~al.}}{{{A. Stace}, {C.A. Woodward}, and {B.J. whitaker}}}} ++ \bibcite{Moller_99}{{29}{1999}{{{T. Moller} et~al.}}{{{T. Moller}, {K. von Haeften}, {T. Laarman}, and {R. von Pietrowski}}}} ++ \bibcite{Ruhl_1993}{{30}{1993}{{{E. R\"{u}hl} et~al.}}{{{E. R\"{u}hl}, {C. Heinzel}, and {H. W. Jochims}}}} ++ \global \chardef \firstnote@num30\relax DelBlock(Argon_size_depedence.aux,102,1) -- \@writefile{toc}{\contentsline {section}{\numberline {IV}Conclusion}{7}{}} DelBlock(Argon_size_depedence.aux,104,1) -- \newlabel{LastBibItem}{{28}{7}{}{}{}} AddBlock(Argon_size_depedence.aux,104,1) ++ \newlabel{LastBibItem}{{30}{7}{}{}{}} DelBlock(Argon_size_depedence.bbl,1,1) -- \begin{thebibliography}{28} AddBlock(Argon_size_depedence.bbl,1,1) ++ \begin{thebibliography}{30} AddBlock(Argon_size_depedence.bbl,32,29) ++ \bibitem[{\citenamefont{{M. Tchaplyguine} et~al.}(2003)\citenamefont{{M. ++ Tchaplyguine}, {R. Feifel}, {R.R.T. Marinho}, {M. Gisselbrecht}, {S.L. ++ Sorensen}, {A. Naves de Brito}, {N. M\aa rtensson}, {S. Svensson}, and {O. ++ Bj\"{o}rneholm}}}]{Maxim_2003} ++ \bibinfo{author}{\bibnamefont{{M. Tchaplyguine}}}, ++ \bibinfo{author}{\bibnamefont{{R. Feifel}}}, ++ \bibinfo{author}{\bibnamefont{{R.R.T. Marinho}}}, ++ \bibinfo{author}{\bibnamefont{{M. Gisselbrecht}}}, ++ \bibinfo{author}{\bibnamefont{{S.L. Sorensen}}}, ++ \bibinfo{author}{\bibnamefont{{A. Naves de Brito}}}, ++ \bibinfo{author}{\bibnamefont{{N. M\aa rtensson}}}, ++ \bibinfo{author}{\bibnamefont{{S. Svensson}}}, \bibnamefont{and} ++ \bibinfo{author}{\bibnamefont{{O. Bj\"{o}rneholm}}}, \bibinfo{journal}{Chem. ++ Phys.} \textbf{\bibinfo{volume}{289}}, \bibinfo{pages}{3} ++ (\bibinfo{year}{2003}). ++ ++ \bibitem[{\citenamefont{{M. Lundwall} et~al.}(2005)\citenamefont{{M. Lundwall}, ++ {M. Tchaplyguine}, {G. \"{O}hrwall}, {A. Lindblad}, {S.Peredkov}, {T. ++ Rander}, and {O. Bj\"{o}rneholm}}}]{Lundwall_05} ++ \bibinfo{author}{\bibnamefont{{M. Lundwall}}}, ++ \bibinfo{author}{\bibnamefont{{M. Tchaplyguine}}}, ++ \bibinfo{author}{\bibnamefont{{G. \"{O}hrwall}}}, ++ \bibinfo{author}{\bibnamefont{{A. Lindblad}}}, ++ \bibinfo{author}{\bibnamefont{{S.Peredkov}}}, ++ \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{{T. Rander}}}, ++ \bibnamefont{and} \bibinfo{author}{\bibnamefont{{O. Bj\"{o}rneholm}}}, ++ \bibinfo{journal}{Surf. Science} \textbf{\bibinfo{volume}{594}}, ++ \bibinfo{pages}{12} (\bibinfo{year}{2005}). ++ DelBlock(Argon_size_depedence.blg,1,1) -- This is BibTeX, Version 0.99cThe top-level auxiliary file: Argon_size_depedence.aux AddBlock(Argon_size_depedence.blg,1,2) ++ This is BibTeX, Version 0.99c (Web2C 7.5.3) ++ The top-level auxiliary file: Argon_size_depedence.aux AddBlock(Argon_size_depedence.blg,5,42) ++ Reallocated wiz_functions (elt_size=4) to 6000 items from 3000. ++ You've used 30 entries, ++ 3411 wiz_defined-function locations, ++ 1364 strings with 15634 characters, ++ and the built_in function-call counts, 22397 in all, are: ++ = -- 1232 ++ > -- 985 ++ < -- 14 ++ + -- 850 ++ - -- 240 ++ * -- 3046 ++ := -- 2432 ++ add.period$ -- 30 ++ call.type$ -- 30 ++ change.case$ -- 121 ++ chr.to.int$ -- 30 ++ cite$ -- 32 ++ duplicate$ -- 1907 ++ empty$ -- 1811 ++ format.name$ -- 577 ++ if$ -- 4185 ++ int.to.chr$ -- 1 ++ int.to.str$ -- 31 ++ missing$ -- 328 ++ newline$ -- 105 ++ num.names$ -- 89 ++ pop$ -- 556 ++ preamble$ -- 1 ++ purify$ -- 120 ++ quote$ -- 0 ++ skip$ -- 997 ++ stack$ -- 0 ++ substring$ -- 625 ++ swap$ -- 1447 ++ text.length$ -- 5 ++ text.prefix$ -- 0 ++ top$ -- 0 ++ type$ -- 174 ++ warning$ -- 0 ++ while$ -- 84 ++ width$ -- 0 ++ write$ -- 312 UpdateBinaryFile(Argon_size_depedence.dvi) DelBlock(Argon_size_depedence.log,1,1) -- This is e-TeX, Version 3.141592-2.1 (MiKTeX 2.4) (preloaded format=latex 2004.8.20) 26 AUG 2006 14:20 AddBlock(Argon_size_depedence.log,1,1) ++ This is pdfeTeX, Version 3.141592-1.20a-2.2 (Web2C 7.5.3) (format=latex 2005.2.14) 27 AUG 2006 12:29 DelBlock(Argon_size_depedence.log,4,1) -- (Argon_size_depedence.tex AddBlock(Argon_size_depedence.log,4,1) ++ (./Argon_size_depedence.tex DelBlock(Argon_size_depedence.log,6,3) -- Babel <v3.8a> and hyphenation patterns for english, french, german, ngerman, du -- mylang, nohyphenation, loaded. -- (C:\texmf\tex\latex\revtex4\revtex4.cls AddBlock(Argon_size_depedence.log,6,3) ++ Babel <v3.8d> and hyphenation patterns for american, french, german, ngerman, d ++ utch, italian, norsk, portuges, spanish, swedish, nohyphenation, loaded. ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/revtex4/revtex4.cls DelBlock(Argon_size_depedence.log,34,1) -- (C:\texmf\tex\latex\ltxmisc\url.sty AddBlock(Argon_size_depedence.log,34,1) ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/url/url.sty DelBlock(Argon_size_depedence.log,50,1) -- (C:\texmf\tex\latex\natbib\natbib.sty AddBlock(Argon_size_depedence.log,50,2) ++ ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/natbib/natbib.sty DelBlock(Argon_size_depedence.log,61,1) -- (C:\texmf\tex\latex\revtex4\revsymb.sty AddBlock(Argon_size_depedence.log,61,1) ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/revtex4/revsymb.sty DelBlock(Argon_size_depedence.log,65,1) -- )) (C:\texmf\tex\latex\revtex4\aps.rtx AddBlock(Argon_size_depedence.log,65,2) ++ )) ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/revtex4/aps.rtx DelBlock(Argon_size_depedence.log,70,1) -- (C:\texmf\tex\latex\revtex4\10pt.rtx AddBlock(Argon_size_depedence.log,70,1) ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/revtex4/10pt.rtx DelBlock(Argon_size_depedence.log,73,1) -- ) (C:\texmf\tex\latex\base\latexsym.sty AddBlock(Argon_size_depedence.log,73,2) ++ ) ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/base/latexsym.sty DelBlock(Argon_size_depedence.log,80,1) -- (C:\texmf\tex\latex\graphics\graphics.sty AddBlock(Argon_size_depedence.log,80,1) ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/graphics/graphics.sty DelBlock(Argon_size_depedence.log,82,1) -- (C:\texmf\tex\latex\graphics\trig.sty AddBlock(Argon_size_depedence.log,82,2) ++ ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/graphics/trig.sty DelBlock(Argon_size_depedence.log,85,2) -- ) (C:\texmf\tex\latex\00miktex\graphics.cfg -- File: graphics.cfg 2003/03/12 v1.1 MiKTeX 'graphics' configuration AddBlock(Argon_size_depedence.log,86,3) ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/graphics/graphics.cfg ++ File: graphics.cfg 2005/02/03 v1.3 graphics configuration of teTeX/TeXLive ++ ) DelBlock(Argon_size_depedence.log,91,1) -- (C:\texmf\tex\latex\graphics\dvips.def AddBlock(Argon_size_depedence.log,91,1) ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/graphics/dvips.def DelBlock(Argon_size_depedence.log,94,1) -- (C:\texmf\tex\latex\amsfonts\amsfonts.sty AddBlock(Argon_size_depedence.log,94,1) ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsfonts/amsfonts.sty DelBlock(Argon_size_depedence.log,104,1) -- (C:\texmf\tex\latex\amsfonts\amssymb.sty AddBlock(Argon_size_depedence.log,104,1) ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsfonts/amssymb.sty DelBlock(Argon_size_depedence.log,107,1) -- (C:\texmf\tex\latex\amsmath\amsmath.sty AddBlock(Argon_size_depedence.log,107,1) ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsmath/amsmath.sty DelBlock(Argon_size_depedence.log,112,1) -- (C:\texmf\tex\latex\amsmath\amstext.sty AddBlock(Argon_size_depedence.log,112,1) ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsmath/amstext.sty DelBlock(Argon_size_depedence.log,114,1) -- (C:\texmf\tex\latex\amsmath\amsgen.sty AddBlock(Argon_size_depedence.log,114,2) ++ ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsmath/amsgen.sty DelBlock(Argon_size_depedence.log,119,1) -- )) (C:\texmf\tex\latex\amsmath\amsbsy.sty AddBlock(Argon_size_depedence.log,119,2) ++ )) ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsmath/amsbsy.sty DelBlock(Argon_size_depedence.log,124,1) -- (C:\texmf\tex\latex\amsmath\amsopn.sty AddBlock(Argon_size_depedence.log,124,1) ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsmath/amsopn.sty DelBlock(Argon_size_depedence.log,164,1) -- ) (Argon_size_depedence.aux) AddBlock(Argon_size_depedence.log,164,4) ++ ) ++ (./Argon_size_depedence.aux) ++ \openout1 = `Argon_size_depedence.aux'. ++ DelBlock(Argon_size_depedence.log,185,1) -- (C:\texmf\tex\latex\base\ulasy.fd AddBlock(Argon_size_depedence.log,185,1) ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/base/ulasy.fd DelBlock(Argon_size_depedence.log,189,1) -- (C:\texmf\tex\latex\amsfonts\umsa.fd AddBlock(Argon_size_depedence.log,189,2) ++ ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsfonts/umsa.fd DelBlock(Argon_size_depedence.log,195,1) -- (C:\texmf\tex\latex\amsfonts\umsb.fd AddBlock(Argon_size_depedence.log,195,1) ++ (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsfonts/umsb.fd DelBlock(Argon_size_depedence.log,200,2) -- <figures/figure1.eps> [1] -- File: figures/figure2.eps Graphic file (type eps) DelBlock(Argon_size_depedence.log,201,1) -- <figures/figure2.eps> AddBlock(Argon_size_depedence.log,201,3) ++ <figures/figure1.eps> [1] ++ File: figures/figure2.eps Graphic file (type eps) ++ <figures/figure2.eps> DelBlock(Argon_size_depedence.log,212,1) -- on input line 112. AddBlock(Argon_size_depedence.log,212,1) ++ on input line 116. DelBlock(Argon_size_depedence.log,216,2) -- Overfull \hbox (0.92249pt too wide) in paragraph at lines 126--127 -- [][][] AddBlock(Argon_size_depedence.log,216,2) ++ Overfull \hbox (0.92249pt too wide) in paragraph at lines 130--131 ++ [][] DelBlock(Argon_size_depedence.log,226,2) -- Underfull \hbox (badness 2521) in paragraph at lines 152--153 -- [][]\OT1/cmr/m/n/10 This as-tound-ing im-por-tance of mul-ti-ply charged AddBlock(Argon_size_depedence.log,226,2) ++ Underfull \hbox (badness 2521) in paragraph at lines 156--157 ++ []\OT1/cmr/m/n/10 This as-tound-ing im-por-tance of mul-ti-ply charged DelBlock(Argon_size_depedence.log,233,3) -- <figures/figure6.eps> [5] [6] (Argon_size_depedence.bbl -- Underfull \hbox (badness 1436) in paragraph at lines 126--132 -- [][]\OT1/cmr/m/n/9 W.H. Press, S.A. Teukol-sky, W.T. Vet-ter-ling, and AddBlock(Argon_size_depedence.log,233,3) ++ <figures/figure6.eps> [5] [6] (./Argon_size_depedence.bbl ++ Underfull \hbox (badness 1436) in paragraph at lines 155--161 ++ []\OT1/cmr/m/n/9 W.H. Press, S.A. Teukol-sky, W.T. Vet-ter-ling, and DelBlock(Argon_size_depedence.log,238,1) -- ) [7] (Argon_size_depedence.aux) ) AddBlock(Argon_size_depedence.log,238,1) ++ ) [7] (./Argon_size_depedence.aux) ) DelBlock(Argon_size_depedence.log,240,7) -- 3055 strings out of 95898 -- 34189 string characters out of 1195288 -- 105045 words of memory out of 1093462 -- 5940 multiletter control sequences out of 35000 -- 12591 words of font info for 52 fonts, out of 500000 for 1000 -- 14 hyphenation exceptions out of 607 -- 29i,8n,22p,2565b,309s stack positions out of 1500i,500n,5000p,200000b,32768s AddBlock(Argon_size_depedence.log,240,10) ++ 2920 strings out of 95204 ++ 35350 string characters out of 1184352 ++ 2090080 words of memory out of 4544915 ++ 6016 multiletter control sequences out of 10000+50000 ++ 12591 words of font info for 52 fonts, out of 2000000 for 2000 ++ 58 hyphenation exceptions out of 1000 ++ 29i,8n,22p,2163b,309s stack positions out of 1500i,500n,5000p,200000b,5000s ++ 0 PDF objects out of 300000 ++ 0 named destinations out of 131072 ++ 1 words of extra memory for PDF output out of 65536 DelBlock(Argon_size_depedence.log,251,1) -- Output written on Argon_size_depedence.dvi (7 pages, 49220 bytes). AddBlock(Argon_size_depedence.log,251,1) ++ Output written on Argon_size_depedence.dvi (7 pages, 49008 bytes). UpdateBinaryFile(Argon_size_depedence.pdf) DelBlock(Argon_size_depedence.tex,41,3) -- \author{Ricardo R.T. Marinho} -- \affiliation{Laborat\'{o}rio Nacional de Luz S\'{\i}ncrotron (LNLS), Box 6192, 13084-971 Campinas SP, Brazil} -- DelBlock(Argon_size_depedence.tex,55,1) -- Photo-fragmentation of argon clusters with average size ranging from 10 up to 1000 atoms is reported at a photon energy of 116 eV using multi-coincidence technique with a mass spectrometer. A spectacular change in fragmentation pattern is observed when the cluster size increases pointing out the different time scale of the dissociation mechanisms. For small clusters ($<$10$>$), after ionization a fast fragmentation with neutral emission imparting large amount of energy in the ps time scale occurs, then slow degradation of the photo-cluster ions is observed in the $\mu$s time scale. For larger clusters ($\geq <$100$>$) we believe that we observe the fragmentation pattern of large unstable multiply charged species in time scale which last a few hundred of ns. The reason for these apparent slow processes could be that the large amount of neutral atoms acts as an efficient cooling bath which tend to dissipate the excess of energy ("heat") among all degree of freedom. Degradation of the photo-cluster ions take place in the $\mu$s time scale as for small clusters. AddBlock(Argon_size_depedence.tex,55,4) ++ Photo-fragmentation of argon clusters with average size ranging from 10 up to 1000 atoms is reported at a photon energy of 116 eV using multi-coincidence technique with a mass spectrometer. A spectacular ++ change in fragmentation pattern is observed when the cluster size increases ++ %change "pointing out" ++ revealing the different time scale of the dissociation mechanisms. For small clusters ($<$10$>$), after ionization a fast fragmentation with neutral emission imparting large amount of energy in the ps time scale occurs, then slow degradation of the photo-cluster ions is observed in the $\mu$s time scale. For larger clusters ($\geq <$100$>$) we believe that we observe the fragmentation pattern of large unstable multiply charged species in time scale which last a few hundred of ns. The reason for these apparent slow processes could be that the large amount of neutral atoms acts as an efficient cooling bath which tend to dissipate the excess of energy ("heat") among all degree of freedom. Degradation of the photo-cluster ions take place in the $\mu$s time scale as for small clusters. DelBlock(Argon_size_depedence.tex,67,1) -- In a recent publication \cite{Gisselbrecht_2005} we presented the general fragmentation pattern of small argon clusters for resonant inner shell excitation and ionization. We did show that the inner shell photo-absorption prepared selectively ionic species below or above the vertical double ionization potential, respectively Ar$_m^{+*}$ and Ar$_m^{2+}$. In both case theses species undergo dissociation leading to two or more charged fragments pointing out the importance of the nuclear relaxation as well as the electronic relaxation. AddBlock(Argon_size_depedence.tex,67,3) ++ In a recent publication \cite{Gisselbrecht_2005} we presented the general fragmentation pattern of small argon clusters for resonant inner shell excitation and ionization. We did show that the inner shell photo-absorption prepared selectively ionic species below or above the vertical double ionization ++ % Add maxim and marcus ++ potential \cite{Maxim_2003, Lundwall_05}, respectively Ar$_m^{+*}$ and Ar$_m^{2+}$. In both case theses species undergo dissociation leading to two or more charged fragments pointing out the importance of the nuclear relaxation as well as the electronic relaxation. DelBlock(Argon_size_depedence.tex,76,1) -- \caption{\label{Fig1} Photo-ionisation branching ratio for free argon atoms and schematic decay channels for clusters. } AddBlock(Argon_size_depedence.tex,76,1) ++ \caption{\label{Fig1} Photo-ionization branching ratio for free argon atoms and schematic decay channels for clusters. } DelBlock(Argon_size_depedence.tex,80,1) -- The chosen photon energy implies that only the $3p$ valence and $3s$ inner valence shells can be ionized and Auger relaxation is energetically not possible. For free atoms, we are well above the double-ionization threshold 43.4~eV \cite{Nist}, the $3s$ Cooper minimum between 45-50~eV, and even exceeds the triple ionization threshold 84.3~eV. The branching ratios are known to be 83\% for single photo-ionization, 16\% for double photo-ionization, and less than 1\% for triple photo-ionization \cite{Holland_1979}. In the current picture of cluster ionization, so called Haberland's model \cite{Haberland_book_1995, Haberland_book_1994}, the system does not have time for nuclear rearrangement and states close to the dissociation limit are populated. Thus the cluster photo-ionization branching ratio should mimic the atomic one. However in our experiment the time scale is long enough for nuclear relaxation to take place and adiabatic potentials to be relevant \cite{Ruhl_1992}. Hence, among the singly charge species a few of them ($\sim$15\%) prepared with two holes and one particle in the outer valence shell, should decay in the double ionization continuum as we have already eluded \cite{Gisselbrecht_2005}. Hence, one could speculate that the fragmentation depend on the cluster size.\\ AddBlock(Argon_size_depedence.tex,80,3) ++ The chosen photon energy implies that only the $3p$ valence and $3s$ inner valence shells can be ionized and Auger relaxation is energetically not possible. For free atoms, we are well above the double-ionization threshold 43.4~eV \cite{Nist}, the $3s$ Cooper minimum between 45-50~eV, and ++ % ref for triple ionization ++ even exceeds the triple ionization threshold 84.3~eV\cite{Nist}. The branching ratios are known to be 83\% for single photo-ionization, 16\% for double photo-ionization, and less than 1\% for triple photo-ionization \cite{Holland_1979}. In the current picture of cluster ionization, so called Haberland's model \cite{Haberland_book_1995, Haberland_book_1994}, the system does not have time for nuclear rearrangement and states close to the dissociation limit are populated. Thus the cluster photo-ionization branching ratio should mimic the atomic one. However in our experiment the time scale is long enough for nuclear relaxation to take place and adiabatic potentials to be relevant \cite{Ruhl_1992}. Hence, among the singly charge species a few of them ($\sim$15\%) prepared with two holes and one particle in the outer valence shell, should decay in the double ionization continuum as we have already eluded \cite{Gisselbrecht_2005}. Hence, one could speculate that the fragmentation depend on the cluster size.\\ DelBlock(Argon_size_depedence.tex,180,1) -- In figure \ref{Fig5}, the Ar$_2^+$ and Ar$_3^+$ peaks (dashed-line) arising from the smallest cluster sizes ($<$N$>$=10,20), exhibit a a typical peak shape with "eiffel tower" signature of decay in the drift tube. For dimer channels, it corresponds to the degradation of Ar$^+_2\rightarrow$Ar$^+$+Ar. According to Whitaker~\textit{et al.} \cite{Whitaker_93} this process can arise from radiative decay from the electronic $\Pi$(1/2)$_u$ state of the ion to the I(1/2)$_g$. Such decay is reasonable in our experiment since there is no particular reason to produce dimer fragments arising from the fragmentation of multiply charge clusters only in its ground state. However, one should keep in mind that collision induced dissociation (CID) is very a likely reason for cluster-ion degradation for background pressure above 10$^{-7}$~mbar which was the case. Our experimental resolution is not good enough to quantify properly the importance of such process but we think that at least both processes can happen. For trimer, the gaussian like distribution is due to a more complex fragmentation mechanisms which can lead either to formation of monomer or dimer depending of the internal energy left in the trimer, blurring hence the "either-tower" distribution. We present in table I, the result of our simulation in order to give an estimation of the time scale associated the degradation of this species. Accurate values for the kinetic energy KE$_1$ and KE$_2$ is hard to extract since both parameters acts almost the same way, however one can estimate that they are in the order of 500ÊmeV down to 100meV. AddBlock(Argon_size_depedence.tex,180,3) ++ In figure \ref{Fig5}, the Ar$_2^+$ and Ar$_3^+$ peaks (dashed-line) arising from the smallest cluster ++ % there was a double "a a typical peak shape ++ sizes ($<$N$>$=10,20), exhibit a typical peak shape with "eiffel tower" signature of decay in the drift tube. For dimer channels, it corresponds to the degradation of Ar$^+_2\rightarrow$Ar$^+$+Ar. According to Whitaker~\textit{et al.} \cite{Whitaker_93} this process can arise from radiative decay from the electronic $\Pi$(1/2)$_u$ state of the ion to the I(1/2)$_g$. Such decay is reasonable in our experiment since there is no particular reason to produce dimer fragments arising from the fragmentation of multiply charge clusters only in its ground state. However, one should keep in mind that collision induced dissociation (CID) is very a likely reason for cluster-ion degradation for background pressure above 10$^{-7}$~mbar which was the case. Our experimental resolution is not good enough to quantify properly the importance of such process but we think that at least both processes can happen. For trimer, the gaussian like distribution is due to a more complex fragmentation mechanisms which can lead either to formation of monomer or dimer depending of the internal energy left in the trimer, blurring hence the "either-tower" distribution. We present in table I, the result of our simulation in order to give an estimation of the time scale associated the degradation of this species. Accurate values for the kinetic energy KE$_1$ and KE$_2$ is hard to extract since both parameters acts almost the same way, however one can estimate that they are in the order of 500ÊmeV down to 100meV. DelBlock(Argon_size_depedence.tex,184,1) -- In the case of large clusters (from 100 to 1000), these peaks are no longer sharp. The shape can be explained either considering that fragments carry away measurable kinetic energy upon fragmentation of multiply charged species or meta-stable decay leading to neutral evaporation. From the simulation, it is clear that the time scale or such process has to be in the order of time-of-flight until the drift tube (t$^{dimer/trimer}_{acc}$) to reproduce the roundish-shape. The typical kinetic energy KE$_1$ and KE$_2$ is in the order of 2~eV down to 300meV. Another peculiar feature is observed in the fragmentation of large clusters, the Ar$_2^+$ line profile exhibits an asymmetric wing (tail) extending towards longer time-of-flight while Ar$_3^+$ is symmetric. This tail is a clear signature of decay producing dimer in a time scale shorter then t$^{dimer}_{acc}$: Ar$^+_m\rightarrow$Ar$^+_2$+X. The fact that this tail occur in dimer channels may reflect that dimer ionic core is the most likely unit formed inside large argon clusters as it has been observed on xenon clusters \cite{Laarmann_2002}. We performed measurement at lower extraction field to increase the flight time for dimers in the extraction region from 150~ns to 320~ns and no change from the tail was observed, as it should be expected. (trimer peak change from roundish shape to square shape ?) Since different mother ions can lead to the formation of the dimer the determination of the life-time cannot be accurate but has to be in the order a few hundred of ns. The times scale found for small cluster are typical for usual meta-stable unimolecular degradation of van-der-Waals clusters \cite{Stephan_1983, Lethbridge_1988}. In the case of large clusters, the time scale is relatively short and it shows that there are strong interactions within the cluster. One should point out that for clusters of $<$N$>$=100 and 1000 atoms, the similarity of the two time scale within the error bars implies that the fragmentation mechanism does not change drastically with cluster size. This corroborate that this observed mechanisms likely originates from the same species: unstable multiple charged clusters. This shows also that one another dissociation mechanism is energetically possible when a certain size is reached. One should notice that there is a small contribution in the peak shape of slow meta-stable decay as we have seen for small clusters. AddBlock(Argon_size_depedence.tex,184,7) ++ In the case of large clusters (from 100 to 1000), these peaks are no longer sharp. The shape can be explained either considering that fragments carry away measurable kinetic energy upon fragmentation of multiply charged species or meta-stable decay leading to neutral evaporation. From the simulation, it is clear that the time scale or such process has to be in the order of time-of-flight until the drift tube (t$^{dimer/trimer}_{acc}$) to reproduce the roundish-shape. The typical kinetic energy KE$_1$ and KE$_2$ is in the order of 2~eV down to 300meV. Another peculiar feature is observed in the fragmentation of large clusters, the Ar$_2^+$ line profile exhibits an asymmetric wing (tail) extending towards longer time-of-flight while Ar$_3^+$ is symmetric. This tail is a clear signature of decay producing dimer in a time scale shorter then t$^{dimer}_{acc}$: Ar$^+_m\rightarrow$Ar$^+_2$+X. The fact that this tail occur in dimer channels may reflect that dimer ionic core is the most likely unit formed inside large argon clusters as it has been observed on xenon clusters \cite{Laarmann_2002}. We performed measurement at lower extraction field to increase the flight time for dimers in the extraction region from 150~ns to 320~ns and no change from the tail was observed, as it should be expected. (trimer peak change from roundish shape to square shape ?) Since different mother ions can lead to the formation of the dimer the determination of the life-time cannot be accurate but has to be in the order ++ % remove "a few hundred" ++ of hundred ns. The times scale found for small cluster are typical for usual meta-stable unimolecular degradation of van-der-Waals clusters \cite{Stephan_1983, Lethbridge_1988}. In the case of large clusters, the time scale is relatively short and it shows that there are strong interactions within the cluster. One should point out that for clusters of $<$N$>$=100 and 1000 atoms, the similarity of the two time scale within the error bars implies that the fragmentation mechanism does not change drastically with cluster size. This corroborate that ++ %change: these observed mechanisms likely originates ++ the observed mechanisms originate from the same species: unstable multiple charged clusters. ++ % change "this shows also that one another" ++ It shows also that another dissociation mechanism is energetically possible when a certain size is reached. One should notice that there is a small contribution in the peak shape of slow meta-stable decay as we have seen for small clusters. DelBlock(Argon_size_depedence.tex,200,1) -- After fission, the extra internal energy of the cluster is released in different ways. For small clusters, it is likely that neutral evaporation (neutral expulsion) impart most of the kinetic energy, while for large cluster this energy would be more dissipated among all the degree of freedom. For instance molecular-dynamic in a droplet liquid model shows that only fission due to Coulomb repulsion of triply ionized clusters could justify a delayed or thermal fragmentation. After ionization, the three charges would tend to form an equilateral triangle (minimum energy configuration), repelling simultaneously outwards, while the most favorable pathway to fission would preferably be that two of the charges approach each other while the other ones moves outwards. This effect would leave time to thermal excitation to spread all over the cluster. This is in agreement with our observation since the tails in dimer are observed in coincidence spectra up to the 3rd degree, although these channels are very weak. In multi-layer argon surfaces, the energy dissipation of high lying ionic states is known to be the dominant primary electronic process for photo-desorption \cite{Dujardin_1990}. One could speculate that the same behavior is present here with the expulsion of dimer, as it has been seen by A. Stace~\textit{et al.} \cite{Stace_1991} for large cluster. Although the time scale is not the same, it may be that the internal energy in our experiment is high enough to enhance this mechanism. To the best of our knowledge, there is no evidence of such a relaxation mechanism in Argon clusters but it has been found in He clusters \cite{Moller_99}. One should point out that the estimated typical time scale is long enough to localize a charged in the cluster followed by the formation of self-trapped atomic or molecular excitons. Radiative decays from a molecular exciton (excimer), via bound-to-free transition, are known to open dissociation channels: for example for a neutral excited cluster to Ar+ Ar limit. Studies on doubly charged clusters \cite{Ruhl_1993} have revealed the presence of a third continuum related to the decay from a dication excimer to Ar$^+$+ Ar$^+$ limit. To the best of our knowledge, decay from excited cation excimer has not been reported but a likely dissociation limit to Ar$^+$+ Ar can be inferred through atomic radiative transition \cite{Nist}. Lifetimes for these excitons can be estimated to vary from 300~ps to 200~ns which could be is in agreement with our measurement. AddBlock(Argon_size_depedence.tex,200,3) ++ After fission, the extra internal energy of the cluster is released in different ways. For small clusters, it is likely that neutral evaporation (neutral expulsion) impart most of the kinetic energy, while for large cluster this energy would be more dissipated among all the degree of freedom. For instance molecular-dynamic in a droplet liquid model\cite{Casero_1988} shows that only fission due to Coulomb repulsion ++ % set the ref for the droplet liquid model\ ++ of triply ionized clusters could justify a delayed or thermal fragmentation. After ionization, the three charges would tend to form an equilateral triangle (minimum energy configuration), repelling simultaneously outwards, while the most favorable pathway to fission would preferably be that two of the charges approach each other while the other ones moves outwards. This effect would leave time to thermal excitation to spread all over the cluster. This is in agreement with our observation since the tails in dimer are observed in coincidence spectra up to the 3rd degree, although these channels are very weak. In multi-layer argon surfaces, the energy dissipation of high lying ionic states is known to be the dominant primary electronic process for photo-desorption \cite{Dujardin_1990}. One could speculate that the same behavior is present here with the expulsion of dimer, as it has been seen by A. Stace~\textit{et al.} \cite{Stace_1991} for large cluster. Although the time scale is not the same, it may be that the internal energy in our experiment is high enough to enhance this mechanism. To the best of our knowledge, there is no evidence of such a relaxation mechanism in Argon clusters but it has been found in He clusters \cite{Moller_99}. One should point out that the estimated typical time scale is long enough to localize a charged in the cluster followed by the formation of self-trapped atomic or molecular excitons. Radiative decays from a molecular exciton (excimer), via bound-to-free transition, are known to open dissociation channels: for example for a neutral excited cluster to Ar+ Ar limit. Studies on doubly charged clusters \cite{Ruhl_1993} have revealed the presence of a third continuum related to the decay from a dication excimer to Ar$^+$+ Ar$^+$ limit. To the best of our knowledge, decay from excited cation excimer has not been reported but a likely dissociation limit to Ar$^+$+ Ar can be inferred through atomic radiative transition \cite{Nist}. Lifetimes for these excitons can be estimated to vary from 300~ps to 200~ns which could be is in agreement with our measurement. DelBlock(argonbib.bib,310,4) -- @UNPUBLISHED{Lundwall, -- author = {{M. Lundwall {\it et al.}}}, -- note = {to be published}, -- owner = {Andreas}, AddBlock(argonbib.bib,310,12) ++ @ARTICLE{Lundwall_05, ++ author = {{M. Lundwall} and {M. Tchaplyguine} and {G. \"{O}hrwall} and {A. ++ Lindblad} and {S.Peredkov} and {T. Rander}, {S. Svensson} and {O. ++ Bj\"{o}rneholm}}, ++ title = {Enhanced surface sensitivity in AES relative to XPS observed in free ++ argon clusters}, ++ journal = {Surf. Science}, ++ year = {2005}, ++ volume = {594}, ++ pages = {12-14}, ++ owner = {mathieu}, ++ timestamp = {2006.08.27}, DelBlock(argonbib.bib.bak,310,4) -- @UNPUBLISHED{Lundwall, -- author = {{M. Lundwall {\it et al.}}}, -- note = {to be published}, -- owner = {Andreas}, AddBlock(argonbib.bib.bak,310,12) ++ @ARTICLE{, ++ author = {{M. Lundwall} and {M. Tchaplyguine} and {G. \"{O}hrwall} and {A. ++ Lindblad} and {S.Peredkov} and {T. Rander}, {S. Svensson} and {O. ++ Bj\"{o}rneholm}}, ++ title = {Enhanced surface sensitivity in AES relative to XPS observed in free ++ argon clusters}, ++ journal = {Surf. Science}, ++ year = {2005}, ++ volume = {594}, ++ pages = {12-14}, ++ owner = {mathieu}, ++ timestamp = {2006.08.27}, AddBlock(argonbib.bib.bak,407,13) ++ @ARTICLE{Scheier_87, ++ author = {{P. Scheier } and {T.D. M\"{a}rk}}, ++ title = {TRIPLY CHARGED ARGON CLUSTERS ++ ++ PRODUCTION AND STARXLITY (APPEARANCE ENERGY AND APPEARANCE SIZE)}, ++ journal = {Chem. Phys. Lett}, ++ year = {1987}, ++ volume = {136}, ++ pages = {423-426}, ++ owner = {mathieu}, ++ timestamp = {2006.08.25}, ++ } ++ DelBlock(argonbib.bib.bak,513,13) -- @ARTICLE{Scheier_87, -- author = {{Scheier P.} and {M\"{a}rk T.D.}}, -- title = {TRIPLY CHARGED ARGON CLUSTERS -- -- PRODUCTION AND STARXLITY (APPEARANCE ENERGY AND APPEARANCE SIZE)}, -- journal = {Chem. Phys. Lett}, -- year = {1987}, -- volume = {136}, -- pages = {423-426}, -- owner = {mathieu}, -- timestamp = {2006.08.25}, -- } -- Remove(Argon_size_depedence.tex.bak)
UpdateBinaryFile(Argon_size_depedence.dvi) DelBlock(Argon_size_depedence.log,1,1) -- This is e-TeX, Version 3.141592-2.1 (MiKTeX 2.4) (preloaded format=latex 2004.8.20) 26 AUG 2006 14:10 AddBlock(Argon_size_depedence.log,1,1) ++ This is e-TeX, Version 3.141592-2.1 (MiKTeX 2.4) (preloaded format=latex 2004.8.20) 26 AUG 2006 14:20
AddTxtFile(Argon_size_depedence.aux) AddTxtFile(Argon_size_depedence.blg) UpdateBinaryFile(Argon_size_depedence.dvi) AddTxtFile(Argon_size_depedence.log) UpdateBinaryFile(Argon_size_depedence.pdf) DelBlock(Argon_size_depedence.tex,27,1) -- DelBlock(Argon_size_depedence.tex,67,3) -- In a recent publication \cite{Gisselbrecht_2005} we presented the general fragmentation pattern of small argon clusters for resonant inner shell excitation and ionization. We did show that the inner shell photo-absorption prepared selectively ionic species below or above the vertical double ionization potential, respectively Ar$_m^{+*}$ and Ar$_m^{2+}$. In both case theses species undergo dissociation leading to two or more charged fragments pointing out the importance of the nuclear relaxation as well as the electronic relaxation.\\ -- In this study we focus on the cluster-size dependent fragmentation with a VUV photon of 116 eV. We perform a multicoincidence measurement Photo-Electron-n-Photo-Ions COincidence PE(PI)$_n$CO with a mass spectrometer. -- AddBlock(Argon_size_depedence.tex,67,4) ++ In a recent publication \cite{Gisselbrecht_2005} we presented the general fragmentation pattern of small argon clusters for resonant inner shell excitation and ionization. We did show that the inner shell photo-absorption prepared selectively ionic species below or above the vertical double ionization potential, respectively Ar$_m^{+*}$ and Ar$_m^{2+}$. In both case theses species undergo dissociation leading to two or more charged fragments pointing out the importance of the nuclear relaxation as well as the electronic relaxation. ++ ++ In this study we focus on the cluster-size dependent fragmentation with a VUV photon of 116~eV. We perform a multicoincidence measurement Photo-Electron-n-Photo-Ions COincidence PE(PI)$_n$CO with a mass spectrometer. ++ DelBlock(Argon_size_depedence.tex,78,3) -- The chosen photon energy implies that only the 3p valence and 3s inner valence shells can be ionized and Auger relaxation is energetically not possible. For free atoms, we are well above the double-ionization threshold 43.4 eV\cite{Nist}, the 3s Cooper minimum between 45-50 eV, and even exceeds the triple ionization threshold 84.3~eV. The branching ratios are known to be 83\% for single photo-ionization, 16\% for double photo-ionization, and less than 1\% for triple photo-ionization \cite{Holland_1979}. In the current picture of cluster ionization, so called Haberland's model\cite{Haberland_book_1995, Haberland_book_1994}, the system does not have time for nuclear rearrangement and states close to the dissociation limit are populated. Thus the cluster photo-ionisation branching ratio should mimic the atomic one. However in our experiment the time scale is long enough for nuclear relaxation to take place and adiabatic potentials to be relevant\cite{Ruhl_1992}. Hence, among the singly charge species a few of them ($\sim$15\%) prepared with two holes and one particle in the outer valence shell, should decay in the double ionization continuum as we have already eluded \cite{Gisselbrecht_2005}. Hence, one could speculate that the fragmentation depend on the cluster size.\\ -- We present figure \ref{Fig1}, the photo-ionisation branching ratio for free argon atoms (check again ?) and where the decay channel are expected for cluster. Our aim is to investigate the photo-fragmentation over a size range from a few up to thousands of atoms in order to know whether the fragmentation dynamics is a sensitive probe to the formation of stable multiply ionized clusters. -- AddBlock(Argon_size_depedence.tex,78,3) ++ The chosen photon energy implies that only the $3p$ valence and $3s$ inner valence shells can be ionized and Auger relaxation is energetically not possible. For free atoms, we are well above the double-ionization threshold 43.4~eV \cite{Nist}, the $3s$ Cooper minimum between 45-50~eV, and even exceeds the triple ionization threshold 84.3~eV. The branching ratios are known to be 83\% for single photo-ionization, 16\% for double photo-ionization, and less than 1\% for triple photo-ionization \cite{Holland_1979}. In the current picture of cluster ionization, so called Haberland's model \cite{Haberland_book_1995, Haberland_book_1994}, the system does not have time for nuclear rearrangement and states close to the dissociation limit are populated. Thus the cluster photo-ionization branching ratio should mimic the atomic one. However in our experiment the time scale is long enough for nuclear relaxation to take place and adiabatic potentials to be relevant \cite{Ruhl_1992}. Hence, among the singly charge species a few of them ($\sim$15\%) prepared with two holes and one particle in the outer valence shell, should decay in the double ionization continuum as we have already eluded \cite{Gisselbrecht_2005}. Hence, one could speculate that the fragmentation depend on the cluster size.\\ ++ We present figure~\ref{Fig1}, the photo-ionization branching ratio for free argon atoms (check again ?) and where the decay channel are expected for cluster. Our aim is to investigate the photo-fragmentation over a size range from a few up to thousands of atoms in order to know whether the fragmentation dynamics is a sensitive probe to the formation of stable multiply ionized clusters. ++ DelBlock(Argon_size_depedence.tex,86,3) -- \subsection{Experimental equipement} -- The experiment was carried out at the beam line I411 on the MAX II electron storage ring at the Swedish National Synchrotron Radiation Laboratory MAX-lab in Lund, Sweden \cite{Svensson_1996}. The undulator beamline was equipped with a modified SX-700 plane-grating monochromator, which allowed photon energy tuning from 61 to 1500 eV. A chamber with a 2-field electron-ion coincidence spectrometer was mounted on the beam line upstream of the permanent end station. -- Argon clusters were produced in a supersonic expansion with different experimental conditions (flat or conical nozzle at room or liquid nitrogen temperature). The beam consisted of a mixture of atoms and clusters, characterized by an average cluster size of $<$N$>$ atoms per cluster and the full-width at half-maximum (FWHM) of the size distribution is $N/2$. The average cluster size $<$N $>$ was estimated according to the $\Gamma^{\ast}$-formalism \cite{Karnbach_1993}. One should keep in mind that the uncertainty in the absolute size determintation can be of a factor of 2, depending on experimental parameter uncertainties and which of the published scaling law are used \cite{Karnbach_1993, Buck_1996}. We present Figure \ref{Fig2} in log-log scale the theoretical intensity distribution of neutral clusters for different average sizes. It has been arbitrary normalized for $<$N$>$=10 for sake of clarity. The spectrum shows that between the smallest and the largest average size, the relative intensity of small clusters (e.g. dimers, trimers...) is a few order of magnitude more for smallest size. This means that in our experiment the physical origins of small photo-clusters changes gradually with the cluster size. For the smallest cluster size, the photo-clusters arise from direct photo-ionization and photo-fragmentation, while for largest cluster size photo-clusters arise exclusively from photo-fragmentation. The use of multi-coincidence technique allow us then to ensure that the measured photo-clusters are related to multiply charged mother clusters. \\ AddBlock(Argon_size_depedence.tex,86,3) ++ \subsection{Experimental equipment} ++ The experiment was carried out at the beam line I411 on the MAX II electron storage ring at the Swedish National Synchrotron Radiation Laboratory MAX-lab in Lund, Sweden \cite{Svensson_1996}. The undulator beamline was equipped with a modified SX-700 plane-grating monochromator, which allowed photon energy tuning from 61 to 1500~eV. A chamber with a 2-field electron-ion coincidence spectrometer was mounted on the beam line upstream of the permanent end station. ++ Argon clusters were produced in a supersonic expansion with different experimental conditions (flat or conical nozzle at room or liquid nitrogen temperature). The beam consisted of a mixture of atoms and clusters, characterized by an average cluster size of $<$N$>$ atoms per cluster and the full-width at half-maximum (FWHM) of the size distribution is $N/2$. The average cluster size $<$N $>$ was estimated according to the $\Gamma^{\ast}$-formalism \cite{Karnbach_1993}. One should keep in mind that the uncertainty in the absolute size determintation can be of a factor of 2, depending on experimental parameter uncertainties and which of the published scaling law are used \cite{Karnbach_1993, Buck_1996}. We present Figure~\ref{Fig2} in log-log scale the theoretical intensity distribution of neutral clusters for different average sizes. It has been arbitrary normalized for $<$N$>$=10 for sake of clarity. The spectrum shows that between the smallest and the largest average size, the relative intensity of small clusters (e.g. dimers, trimers...) is a few order of magnitude more for smallest size. This means that in our experiment the physical origins of small photo-clusters changes gradually with the cluster size. For the smallest cluster size, the photo-clusters arise from direct photo-ionization and photo-fragmentation, while for largest cluster size photo-clusters arise exclusively from photo-fragmentation. The use of multi-coincidence technique allow us then to ensure that the measured photo-clusters are related to multiply charged mother clusters. DelBlock(Argon_size_depedence.tex,96,5) -- Monochromatic synchrotron light crossed the cluster jet at right angles in the center of the source region of the spectrometer. A continuous field (U$_\mathrm{ext}$=1666 V/cm) extracts the -- electrons and the ions from this region. Electrons with kinetic energy up to 500 eV can be collected over a solid angle of 4$\pi$ steradian. In order to satisfy the so-called 'space-time focusing' \cite{Wiley_1955} criterion, ions were post-accelerated before they passed into a field free drift tube. The spectrometer was positioned perpendicular to the polarization plane of the light. Thus, the spatial extent of the source volume along the spectrometer axis is negligible since it is defined by the vertical size of the -- light spot ($\sim$0.4 mm) and is independent of the expansion conditions of the cluster source. A resolving power of $m/\delta m \sim 500$ was achieved. -- Electrons and ions, detected by micro channel plate (MCP) pairs in a chevron configuration, provide start and stop signals for the Time-to-Digital Converter (TDC) in the set-up. The time of flight of ions arising from single, up to quadruple ionization events, was recorded and treated in real time. For all measurements the ion count rate was essentially constant, less than 2 kHz, keeping theoretically the detection probability of a random ion (false coincidence) at about 1 \% within our acquisition time -- window (5 $\mu$s). This probability is in practice degraded by the fact that the density of uncondensed atoms in the cluster source is 10 to 20 times higher than the density of clusters. Calibration on rare gases (argon, krypton, and xenon) has shown that the ion efficiency decreases for masses above $\sim$150 a.u. even though the photo-ions are accelerated up to 4 keV. This is due to the use of discriminators in the electronics scheme which cut-off a part of the pulse height distribution of the MCP signal for heavy particles \cite{Furuya_2002}. Thus the detection efficiencies of argon dimers and trimers are comparable, but heavier ions have lower detection efficiency. Calibration of the cluster source has shown that cluster sizes larger than 35 atoms can easily be observed with the present spectrometer.\\ AddBlock(Argon_size_depedence.tex,96,5) ++ Monochromatic synchrotron light crossed the cluster jet at right angles in the center of the source region of the spectrometer. A continuous field (U$_\mathrm{ext}$=1666~V/cm) extracts the ++ electrons and the ions from this region. Electrons with kinetic energy up to 500~eV can be collected over a solid angle of 4$\pi$ steradian. In order to satisfy the so-called 'space-time focusing' \cite{Wiley_1955} criterion, ions were post-accelerated before they passed into a field free drift tube. The spectrometer was positioned perpendicular to the polarization plane of the light. Thus, the spatial extent of the source volume along the spectrometer axis is negligible since it is defined by the vertical size of the ++ light spot ($\sim$0.4~mm) and is independent of the expansion conditions of the cluster source. A resolving power of $m/\delta m \sim 500$ was achieved. ++ Electrons and ions, detected by micro channel plate (MCP) pairs in a chevron configuration, provide start and stop signals for the Time-to-Digital Converter (TDC) in the set-up. The time of flight of ions arising from single, up to quadruple ionization events, was recorded and treated in real time. For all measurements the ion count rate was essentially constant, less than 2~kHz, keeping theoretically the detection probability of a random ion (false coincidence) at about 1\% within our acquisition time ++ window (5~$\mu$s). This probability is in practice degraded by the fact that the density of uncondensed atoms in the cluster source is 10 to 20 times higher than the density of clusters. Calibration on rare gases (argon, krypton, and xenon) has shown that the ion efficiency decreases for masses above $\sim$150 a.u. even though the photo-ions are accelerated up to 4~keV. This is due to the use of discriminators in the electronics scheme which cut-off a part of the pulse height distribution of the MCP signal for heavy particles \cite{Furuya_2002}. Thus the detection efficiencies of argon dimers and trimers are comparable, but heavier ions have lower detection efficiency. Calibration of the cluster source has shown that cluster sizes larger than 35 atoms can easily be observed with the present spectrometer. DelBlock(Argon_size_depedence.tex,106,1) -- \caption{\label{Fig3} Time of flight distribution for daughter ion for different lifetime of the mother ion. t$_m$ and t$_d$ represent respectively the mother and daughter time-of flight if these ions where produced at the source point without kinetic energy. The scaling factor is given to compare the absolute peak height. For this simulation the t$_{acc}=$350 ns, $\tau_{m}=$50, 300, 3600 ns and $m_d/m_m$=1/2 } AddBlock(Argon_size_depedence.tex,106,1) ++ \caption{\label{Fig3} Time of flight distribution for daughter ion for different lifetime of the mother ion. t$_m$ and t$_d$ represent respectively the mother and daughter time-of flight if these ions where produced at the source point without kinetic energy. The scaling factor is given to compare the absolute peak height. For this simulation the t$_{acc}=$350~ns, $\tau_{m}=$50, 300, 3600~ns and $m_d/m_m$=1/2 } DelBlock(Argon_size_depedence.tex,111,1) -- From studies on cluster ion dynamic\cite{Stephan_1983, Lethbridge_1988}, the peak shape at this photon energy is the best described by meta-stable decay of the photo-clusters and photo-fragments within our time scale of observation. Therefore we developed a full numerical calculation of the time-of-flight distribution in our spectrometer. The trajectories of the particles are calculated by solving the classical motion equation of charged particles with a 4rth order Runge-Kutta algorithm\cite{NumericalRecipes}. Due to a large variety in orientation, geometry and size of the clusters in the beam, no alignment of the clusters is {\it a-priori} expected. Thus we used as initial condition an isotropic distribution of particles emitted in space. The mother ion is defined by its lifetime $\tau_m$ and its initial kinetic energy distribution (KE$_1$). The number of mother ions decreases in time as: AddBlock(Argon_size_depedence.tex,111,1) ++ From studies on cluster ion dynamic \cite{Stephan_1983, Lethbridge_1988}, the peak shape at this photon energy is the best described by meta-stable decay of the photo-clusters and photo-fragments within our time scale of observation. Therefore we developed a full numerical calculation of the time-of-flight distribution in our spectrometer. The trajectories of the particles are calculated by solving the classical motion equation of charged particles with a 4rth order Runge-Kutta algorithm \cite{NumericalRecipes}. Due to a large variety in orientation, geometry and size of the clusters in the beam, no alignment of the clusters is {\it a-priori} expected. Thus we used as initial condition an isotropic distribution of particles emitted in space. The mother ion is defined by its lifetime $\tau_m$ and its initial kinetic energy distribution (KE$_1$). The number of mother ions decreases in time as: AddBlock(Argon_size_depedence.tex,117,1) ++ \label{eqn:daughters} DelBlock(Argon_size_depedence.tex,120,1) -- The daughter ion is assumed to be emitted with an isotropic distribution and we considered the case of variable release kinetic energy (KE$_2$) in the dissociation. One should notice that from momenta conservation, the kinetic energy of the daughter ion is expressed as: KE$_d=(m_m-m_d)/m_m$KE$_2$. The final time of flight is constructed with Monte-Carlo integration and we convolute the numerical peak shape with our experiment broadening. To understand the result of the simulation two cases ought to be considered. If the mother ion dissociate in the drift tube the daughter ion arrive at the time of flight of the mother ion (t$_m$). The peak is symmetric and the time spread is related to kinetic energy imparted to the daughter ion, the fields strength as well as the length of the drift tube. If the mother ion dissociation happens before the drift tube, the daughter ion arrive with a short time of flight (t$_d$). The peak is asymmetric and looks like an exponential decay which actually follows the dissociation rate [eq.2]. The peak shape is in that case independent of the extraction condition as well as the kinetic energy KE$_1$ and KE$_2$ but depends on the ratio $m_d/m_m$. \\ AddBlock(Argon_size_depedence.tex,120,2) ++ The daughter ion is assumed to be emitted with an isotropic distribution and we considered the case of variable release kinetic energy (KE$_2$) in the dissociation. One should notice that from momenta conservation, the kinetic energy of the daughter ion is expressed as: KE$_d=(m_m-m_d)/m_m$KE$_2$. The final time of flight is constructed with Monte-Carlo integration and we convolute the numerical peak shape with our experiment broadening. To understand the result of the simulation two cases ought to be considered. If the mother ion dissociate in the drift tube the daughter ion arrive at the time of flight of the mother ion (t$_m$). The peak is symmetric and the time spread is related to kinetic energy imparted to the daughter ion, the fields strength as well as the length of the drift tube. If the mother ion dissociation happens before the drift tube, the daughter ion arrive with a short time of flight (t$_d$). The peak is asymmetric and looks like an exponential decay which actually follows the dissociation rate eqn~(\ref{eqn:daughters}). The peak shape is in that case independent of the extraction condition as well as the kinetic energy KE$_1$ and KE$_2$ but depends on the ratio $m_d/m_m$. ++ DelBlock(Argon_size_depedence.tex,127,1) -- \caption{\label{Fig4} Mass spectra for cluster with 10 up to 1000 atoms at 116 eV. The spectra are normalized with respect to the total number of electrons (starts) and to the acquisition time, so the intensity of each peak reflects the partial cross section of each photo-ions multiplied with its detection probability} AddBlock(Argon_size_depedence.tex,127,1) ++ \caption{\label{Fig4} Mass spectra for cluster with 10 up to 1000 atoms at 116~eV. The spectra are normalized with respect to the total number of electrons (starts) and to the acquisition time, so the intensity of each peak reflects the partial cross section of each photo-ions multiplied with its detection probability} DelBlock(Argon_size_depedence.tex,130,2) -- -- DelBlock(Argon_size_depedence.tex,134,1) -- In figure \ref{Fig4}, mass spectra after ionization by 116 eV photons are shown for a series of clusters of average sizes $<$N$>$ = 10, 20, 100 and 1000. Since the cluster beam contains a large amount of uncondensed argon atoms, which produce atomic ions (even multiply charged) in the spectrum, we assume that most, but not all such ions, come from atoms in the sample. All heavier ions (time of flight $>$1400 ns) arise only from clusters. As we can see, the peak height of the ionic cluster fragments is almost constant between $<$N$>$=10 and 20 atoms, then decreases drastically for average cluster sizes above 20 atoms. This decrease in height is combined with a change in width. The peaks change from relatively narrow profile lines for $<$N$>$=10 and $<$N$>$=20, to broad features for larger clusters. In the $<$N$>$=100 and $<$N$>$=1000 spectra, all cluster peaks are affected, and the peak widths are broader for heavier fragments (see the insert Fig \ref{Fig4}). Furthermore monomer and dimer peak shapes for large clusters becomes distinctly asymmetric while all other peaks stay mostly symmetric. One should notice that these observations are independent of the expansion conditions as it was checked with different set of nozzle, pressure and temperature. \\ AddBlock(Argon_size_depedence.tex,134,1) ++ In figure~\ref{Fig4}, mass spectra after ionization by 116~eV photons are shown for a series of clusters of average sizes $<$N$>$ = 10, 20, 100 and 1000. Since the cluster beam contains a large amount of uncondensed argon atoms, which produce atomic ions (even multiply charged) in the spectrum, we assume that most, but not all such ions, come from atoms in the sample. All heavier ions (time of flight $>$1400~ns) arise only from clusters. As we can see, the peak height of the ionic cluster fragments is almost constant between $<$N$>$=10 and 20 atoms, then decreases drastically for average cluster sizes above 20 atoms. This decrease in height is combined with a change in width. The peaks change from relatively narrow profile lines for $<$N$>$=10 and $<$N$>$=20, to broad features for larger clusters. In the $<$N$>$=100 and $<$N$>$=1000 spectra, all cluster peaks are affected, and the peak widths are broader for heavier fragments (see the insert Fig~\ref{Fig4}). Furthermore monomer and dimer peak shapes for large clusters becomes distinctly asymmetric while all other peaks stay mostly symmetric. One should notice that these observations are independent of the expansion conditions as it was checked with different set of nozzle, pressure and temperature. DelBlock(Argon_size_depedence.tex,136,3) -- \subsection{Peak shape} -- The broadening of the peak in these series of spectra cannot be explained simply as the fragmentation of singly ionized clusters in the ground state. Indeed using the model developed by Haberland\cite{Haberland_book_1994,Haberland_book_1995}, cluster ionization is followed simply by neutral evaporation which tend to cool down the cluster. The typical energy released in this unimolecular fragmentation is typically 60-200 meV \cite{Ikegami_1993,Hrivnak_2001}. Although it is known that other dissociation mechanism are possible at this photon energy, for instance after inner-valence shell ionization \cite{Thissen_1998}, one can assume that the dominant decay channel observed is related to one vacancy in the outer shell. Hence large clusters fragment statistically: the excess energy is shared among all degrees of freedom and the kinetic energy of the fragment does not increase as a function of the cluster size. The observed fragmentation processes would imply a substantial amount of stored internal energy. -- Another hint which supports that our observation does not follow the classical picture of single ionization is that the neutral cluster size distribution (see fig \ref{Fig2}) tell us that one should expect at least 3 orders of magnitude less signal between small and large clusters. In fact we observe not more than one order of magnitude difference when we integrate the signal over the whole peak. The origin of photo-cluster ions has to change from small to large cluster. AddBlock(Argon_size_depedence.tex,136,2) ++ \subsection{Peak shape} ++ The broadening of the peak in these series of spectra cannot be explained simply as the fragmentation of singly ionized clusters in the ground state. Indeed using the model developed by Haberland \cite{Haberland_book_1994,Haberland_book_1995}, cluster ionization is followed simply by neutral evaporation which tend to cool down the cluster. The typical energy released in this unimolecular fragmentation is typically 60-200~meV \cite{Ikegami_1993,Hrivnak_2001}. Although it is known that other dissociation mechanism are possible at this photon energy, for instance after inner-valence shell ionization \cite{Thissen_1998}, one can assume that the dominant decay channel observed is related to one vacancy in the outer shell. Hence large clusters fragment statistically: the excess energy is shared among all degrees of freedom and the kinetic energy of the fragment does not increase as a function of the cluster size. The observed fragmentation processes would imply a substantial amount of stored internal energy. AddBlock(Argon_size_depedence.tex,139,2) ++ Another hint which supports that our observation does not follow the classical picture of single ionization is that the neutral cluster size distribution (see fig~\ref{Fig2}) tell us that one should expect at least 3 orders of magnitude less signal between small and large clusters. In fact we observe not more than one order of magnitude difference when we integrate the signal over the whole peak. The origin of photo-cluster ions has to change from small to large cluster. ++ DelBlock(Argon_size_depedence.tex,144,1) -- \caption{\label{Fig5} The Ar$_2^+$ and Ar$_3^+$ photoion peaks Fig \ref{Fig4} are shown using a solid line. The dashed line represents the line shape for the same ion measures in a double, triple and quadruple ion-coincidence event. } AddBlock(Argon_size_depedence.tex,144,1) ++ \caption{\label{Fig5} The Ar$_2^+$ and Ar$_3^+$ photo-ion peaks Fig~\ref{Fig4} are shown using a solid line. The dashed line represents the line shape for the same ion measures in a double, triple and quadruple ion-coincidence event. } DelBlock(Argon_size_depedence.tex,147,8) -- \subsubsection{Origin} -- In figure \ref{Fig5}, a detailed view of the dimer (Ar$_2^+$) and trimer (Ar$_3^+$) fragments is presented for the same average sizes as in figure \ref{Fig4}. Ar$_2^+$ and Ar$_3^+$ fragments are selected because they nicely illustrate our observations. The dashed lines shown in each plot are the sum of time-of-flight distributions of the same fragment measured in multiple-coincidence event, where several photo-ions are detected together [sum of projected PE(PI)$_n$CO spectra n$>$1]. The peak shape in these spectra is unambiguously related to fragmentation of multiply charged clusters.\\ -- For the smallest clusters size ($<$N$>$=10, 20), the single ionization is strongly present but there is certain contribution of multiply charged species which corresponds to the wing broadening in the real mass spectra. For average cluster sizes $\geq$100 atoms, the real mass spectra mimic almost perfectly the time-of-flight distributions arising from multiple charged species. This means that these photo-ions are actually fragments arising from large multiply charged clusters. Multiply ionized clusters is expected to be stable when a critical size (N$_c$) is reached: for argon cluster, the first stable doubly charged species is at N$^{(2)}_c=$89\cite{Gotts_1992} and the first triply stable charged species is at N$^{(3)}_c=$226\cite{Scheier_87}. Thus, for the largest cluster sizes in our experiment, the most likely origin for the photo-ions is the fragmentation of unstable doubly/triply charged clusters which are always produced due to the broad neutral cluster size distributions. Assuming this one should expect a maximum production of unstable multiply charged species for a size $<$N$>$=100 since all clusters with a size below 89 or 226 undergo fragmentation if they are respectively doubly or triply charged. It is actually what is observed in the time-of-flight distributions of fragments measured in multiple-coincidence event. The count rate increase from $<$N$>$=10 to $<$N$>$=100, and decrease from $<$N$>$=100 to $<$N$>$=1000.\\ -- -- This astounding importance of multiply charged species deserve further discussion. Although at this photon energy the photo double ionization cross section for free atoms is a minor channel, for clusters they are actually two more mechanisms that lead to the formation of multiply charged species. First, the double ionization continuum in 3p shell decreases from 43 eV in atoms to 32 eV in clusters of size N=101\cite{Scheier_87}. Due to this lowering of the adiabatic ionization potentials, high ionic excited states (e.g. Ar$_m^{*+}$) auto-ionize into the double ionization continuum. For instance, a single charge exchange between atoms can occur, opening dissociation channels Ar$_p^+$ + Ar$_q^+$ located around $\sim$31 eV (depending on the cluster size). Secondly, ÒindirectÓ processes like scattering of a primary electron on another atom can also occur as it has been pointed out in studies on large clusters. In our case, direct photo-ionization can produce either one electron from the (3p/3s) shells, or two/three electrons from the 3p shell, thus the electron kinetic energies can range from 0-100 eV. This corresponds to an inelastic mean free path which can be smaller than the cluster size. Such mechanism would heat up the cluster, increase the overall degree of ionization and strengthen Coulomb repulsion forces. Inelastic scattering is expected to be mainly significant close to atomic ionization thresholds as it has been shown in Ne\cite{Hergenhahn_2002}, but this mechanism could be emphasized by the auto-ionization of high ionic excited states (e.g. Ar$_m^{*+}$) which would produced low kinetic energy electrons. -- -- \subsubsection{Analysis: influence of meta-stable decay} -- We are now interested to understand the fragmentation of the multiply charged cluster, we will in the following only treat the peaks arising form multi-coincidence events. Time dependent fragmentation dynamics of large multiply charged van-der-Walls clusters have been studied theoretically \cite{Casero_1988}. Asymmetric Coulomb fission of doubly charged clusters is expected below their critical size ($N_c$=89) to take place in the picosecond time scale, while above the critical size it occurs in a tenth of microsecond. This is in agreement with previous experimental results performed above the L-edges\cite{Ruhl_1994} and our own observation in PEPIPICO spectra. Thus we will assume that only meta-stable decays of clusters are the reasons for the peak shape since the fragmentation which happen in the ps time scale just introduce kinetic energy to the mother ion. Furthemore, with our present statistic, shapes in different fragmentation channels have the same behavior, thus we use a simple model to extrapolate a typical time scale for various process using numerical simulation.\\ AddBlock(Argon_size_depedence.tex,147,10) ++ \subsubsection{Origin} ++ In figure \ref{Fig5}, a detailed view of the dimer (Ar$_2^+$) and trimer (Ar$_3^+$) fragments is presented for the same average sizes as in figure~\ref{Fig4}. Ar$_2^+$ and Ar$_3^+$ fragments are selected because they nicely illustrate our observations. The dashed lines shown in each plot are the sum of time-of-flight distributions of the same fragment measured in multiple-coincidence event, where several photo-ions are detected together [sum of projected PE(PI)$_n$CO spectra n$>$1]. The peak shape in these spectra is unambiguously related to fragmentation of multiply charged clusters. ++ ++ For the smallest clusters size ($<$N$>$=10, 20), the single ionization is strongly present but there is certain contribution of multiply charged species which corresponds to the wing broadening in the real mass spectra. For average cluster sizes $\geq$100 atoms, the real mass spectra mimic almost perfectly the time-of-flight distributions arising from multiple charged species. This means that these photo-ions are actually fragments arising from large multiply charged clusters. Multiply ionized clusters is expected to be stable when a critical size (N$_c$) is reached: for argon cluster, the first stable doubly charged species is at N$^{(2)}_c=$89 \cite{Gotts_1992} and the first triply stable charged species is at N$^{(3)}_c=$226 \cite{Scheier_87}. Thus, for the largest cluster sizes in our experiment, the most likely origin for the photo-ions is the fragmentation of unstable doubly/triply charged clusters which are always produced due to the broad neutral cluster size distributions. Assuming this one should expect a maximum production of unstable multiply charged species for a size $<$N$>$=100 since all clusters with a size below 89 or 226 undergo fragmentation if they are respectively doubly or triply charged. It is actually what is observed in the time-of-flight distributions of fragments measured in multiple-coincidence event. The count rate increase from $<$N$>$=10 to $<$N$>$=100, and decrease from $<$N$>$=100 to $<$N$>$=1000. ++ ++ This astounding importance of multiply charged species deserve further discussion. Although at this photon energy the photo double ionization cross section for free atoms is a minor channel, for clusters they are actually two more mechanisms that lead to the formation of multiply charged species. First, the double ionization continuum in 3p shell decreases from 43~eV in atoms to 32~eV in clusters of size N=101 \cite{Scheier_87}. Due to this lowering of the adiabatic ionization potentials, high ionic excited states (e.g. Ar$_m^{*+}$) auto-ionize into the double ionization continuum. For instance, a single charge exchange between atoms can occur, opening dissociation channels Ar$_p^+$ + Ar$_q^+$ located around $\sim$31~eV (depending on the cluster size). Secondly, ÒindirectÓ processes like scattering of a primary electron on another atom can also occur as it has been pointed out in studies on large clusters. In our case, direct photo-ionization can produce either one electron from the ($3p/3s$) shells, or two/three electrons from the 3p shell, thus the electron kinetic energies can range from 0-100~eV. This corresponds to an inelastic mean free path which can be smaller than the cluster size. Such mechanism would heat up the cluster, increase the overall degree of ionization and strengthen Coulomb repulsion forces. Inelastic scattering is expected to be mainly significant close to atomic ionization thresholds as it has been shown in Ne \cite{Hergenhahn_2002}, but this mechanism could be emphasized by the auto-ionization of high ionic excited states (e.g. Ar$_m^{*+}$) which would produced low kinetic energy electrons. ++ ++ \subsubsection{Analysis: influence of meta-stable decay} ++ We are now interested to understand the fragmentation of the multiply charged cluster, we will in the following only treat the peaks arising form multi-coincidence events. Time dependent fragmentation dynamics of large multiply charged van-der-Walls clusters have been studied theoretically \cite{Casero_1988}. Asymmetric Coulomb fission of doubly charged clusters is expected below their critical size ($N_c$=89) to take place in the picosecond time scale, while above the critical size it occurs in a tenth of microsecond. This is in agreement with previous experimental results performed above the $L$-edges \cite{Ruhl_1994} and our own observation in PEPIPICO spectra. Thus we will assume that only meta-stable decays of clusters are the reasons for the peak shape since the fragmentation which happen in the ps time scale just introduce kinetic energy to the mother ion. Furthermore, with our present statistic, shapes in different fragmentation channels have the same behavior, thus we use a simple model to extrapolate a typical time scale for various process using numerical simulation. ++ DelBlock(Argon_size_depedence.tex,160,1) -- $<$N$>$ & Decay channel & Lifetime \\ AddBlock(Argon_size_depedence.tex,160,1) ++ $<$N$>$ & Decay channel & Lifetime \\ DelBlock(Argon_size_depedence.tex,162,11) -- 10 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ -- & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ -- 20 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ -- & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ -- \hline -- 100 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$=300$\pm$50 ns \\ -- & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$=300$\pm$50 ns \\ -- & Ar$^+_m\rightarrow$Ar$^+_2$+X & $\tau_m$=100$\pm$ 50 ns \\ -- 1000 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$=300$\pm$50 ns \\ -- & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$=300$\pm$50 ns \\ -- & Ar$^+_m\rightarrow$Ar$^+_2$+X & $\tau_m$=100$\pm$30 ns \\ AddBlock(Argon_size_depedence.tex,162,11) ++ 10 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ ++ & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ ++ 20 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ ++ & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ ++ \hline ++ 100 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$=300$\pm$50 ns \\ ++ & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$=300$\pm$50 ns \\ ++ & Ar$^+_m\rightarrow$Ar$^+_2$+X & $\tau_m$=100$\pm$ 50 ns \\ ++ 1000 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$=300$\pm$50 ns \\ ++ & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$=300$\pm$50 ns \\ ++ & Ar$^+_m\rightarrow$Ar$^+_2$+X & $\tau_m$=100$\pm$30 ns \\ DelBlock(Argon_size_depedence.tex,175,2) -- In figure \ref{Fig5}, the Ar$_2^+$ and Ar$_3^+$ peaks (dashed-line) arising from the smallest cluster sizes ($<$N$>$=10,20) , exhibit a a typical peak shape with "eiffel tower" signature of decay in the drift tube. For dimer channels, it corresponds to the degradation of Ar$^+_2\rightarrow$Ar$^+$+Ar. According to Withaker et al\cite{Whitaker_93} this process can arise from radiative decay from the electronic $\Pi$(1/2)$_u$ state of the ion to the I(1/2)$_g$. Such decay is reasonable in our experiment since there is no particular reason to produce dimer fragments arising from the fragmentation of multiply charge clusters only in its ground state. However, one should keep in mind that collision induced dissociation (CID) is very a likely reason for cluster-ion degradation for background pressure above 10$^{-7}$ mbar which was the case. Our experimental resolution is not good enough to quantify properly the importance of such process but we think that at least both processes can happen. For trimer, the gaussian like distribution is due to a more complex fragmentation mechanisms which can lead either to formation of monomer or dimer depending of the internal energy left in the trimer, blurring hence the "either-tower" distribution. We present in table I, the result of our simulation in order to give an estimation of the time scale associated the degradation of this species. Accurate values for the kinetic energy KE$_1$ and KE$_2$ is hard to extract since both parameters acts almost the same way, however one can estimate that they are in the order of 500ÊmeV down to 100meV. \\ -- In the case of large clusters (from 100 to 1000), these peaks are no longer sharp. The shape can be explained either considering that fragments carry away measurable kinetic energy upon fragmentation of multiply charged species or meta-stable decay leading to neutral evaporation. From the simulation, it is clear that the time scale or such process has to be in the order of time-of-flight until the drift tube (t$^{dimer/trimer}_{acc}$) to reproduce the roundish-shape. The typical kinetic energy KE$_1$ and KE$_2$ is in the order of 2 eV down to 300meV. Another peculiar feature is observed in the fragmentation of large clusters, the Ar$_2^+$ line profile exhibits an asymmetric wing (ÒtailÓ) extending towards longer time-of-flight while Ar$_3^+$ is symmetric. This tail is a clear signature of decay producing dimer in a time scale shorter then t$^{dimer}_{acc}$: Ar$^+_m\rightarrow$Ar$^+_2$+X. The fact that this tail occur in dimer channels may reflect that dimer ionic core is the most likely unit formed inside large argon clusters as it has been observed on xenon clusters \cite{Laarmann_2002}. We performed measurement at lower extraction field to increase the flight time for dimers in the extraction region from 150 ns to 320 ns and no change from the tail was observed, as it should be expected. (trimer peak change from roundish shape to square shape ?) Since different mother ions can lead to the formation of the dimer the determination of the life-time cannot be accurate but has to be in the order a few hundred of ns. The times scale found for small cluster are typical for usual meta-stable unimolecular degradation of van-der-Waals clusters\cite{Stephan_1983, Lethbridge_1988}. In the case of large clusters, the time scale is relatively short and it shows that there are strong interactions within the cluster. One should point out that for clusters of $<$N$>$=100 and 1000 atoms, the similarity of the two time scale within the error bars implies that the fragmentation mechanism does not change drastically with cluster size. This corroborate that this observed mechanisms likely originates from the same species: unstable multiple charged clusters. This shows also that one another dissociation mechanism is energetically possible when a certain size is reached. One should notice that there is a small contribution in the peak shape of slow meta-stable decay as we have seen for small clusters. AddBlock(Argon_size_depedence.tex,176,4) ++ In figure \ref{Fig5}, the Ar$_2^+$ and Ar$_3^+$ peaks (dashed-line) arising from the smallest cluster sizes ($<$N$>$=10,20), exhibit a a typical peak shape with "eiffel tower" signature of decay in the drift tube. For dimer channels, it corresponds to the degradation of Ar$^+_2\rightarrow$Ar$^+$+Ar. According to Whitaker~\textit{et al.} \cite{Whitaker_93} this process can arise from radiative decay from the electronic $\Pi$(1/2)$_u$ state of the ion to the I(1/2)$_g$. Such decay is reasonable in our experiment since there is no particular reason to produce dimer fragments arising from the fragmentation of multiply charge clusters only in its ground state. However, one should keep in mind that collision induced dissociation (CID) is very a likely reason for cluster-ion degradation for background pressure above 10$^{-7}$~mbar which was the case. Our experimental resolution is not good enough to quantify properly the importance of such process but we think that at least both processes can happen. For trimer, the gaussian like distribution is due to a more complex fragmentation mechanisms which can lead either to formation of monomer or dimer depending of the internal energy left in the trimer, blurring hence the "either-tower" distribution. We present in table I, the result of our simulation in order to give an estimation of the time scale associated the degradation of this species. Accurate values for the kinetic energy KE$_1$ and KE$_2$ is hard to extract since both parameters acts almost the same way, however one can estimate that they are in the order of 500ÊmeV down to 100meV. ++ ++ In the case of large clusters (from 100 to 1000), these peaks are no longer sharp. The shape can be explained either considering that fragments carry away measurable kinetic energy upon fragmentation of multiply charged species or meta-stable decay leading to neutral evaporation. From the simulation, it is clear that the time scale or such process has to be in the order of time-of-flight until the drift tube (t$^{dimer/trimer}_{acc}$) to reproduce the roundish-shape. The typical kinetic energy KE$_1$ and KE$_2$ is in the order of 2~eV down to 300meV. Another peculiar feature is observed in the fragmentation of large clusters, the Ar$_2^+$ line profile exhibits an asymmetric wing (tail) extending towards longer time-of-flight while Ar$_3^+$ is symmetric. This tail is a clear signature of decay producing dimer in a time scale shorter then t$^{dimer}_{acc}$: Ar$^+_m\rightarrow$Ar$^+_2$+X. The fact that this tail occur in dimer channels may reflect that dimer ionic core is the most likely unit formed inside large argon clusters as it has been observed on xenon clusters \cite{Laarmann_2002}. We performed measurement at lower extraction field to increase the flight time for dimers in the extraction region from 150~ns to 320~ns and no change from the tail was observed, as it should be expected. (trimer peak change from roundish shape to square shape ?) Since different mother ions can lead to the formation of the dimer the determination of the life-time cannot be accurate but has to be in the order a few hundred of ns. The times scale found for small cluster are typical for usual meta-stable unimolecular degradation of van-der-Waals clusters \cite{Stephan_1983, Lethbridge_1988}. In the case of large clusters, the time scale is relatively short and it shows that there are strong interactions within the cluster. One should point out that for clusters of $<$N$>$=100 and 1000 atoms, the similarity of the two time scale within the error bars implies that the fragmentation mechanism does not change drastically with cluster size. This corroborate that this observed mechanisms likely originates from the same species: unstable multiple charged clusters. This shows also that one another dissociation mechanism is energetically possible when a certain size is reached. One should notice that there is a small contribution in the peak shape of slow meta-stable decay as we have seen for small clusters. ++ DelBlock(Argon_size_depedence.tex,183,1) -- \caption{\label{Fig6} Schematic diagram of the photo-ionization at 116 eV. Only the channels producing unstable multiply charged species are considered. See text for details } AddBlock(Argon_size_depedence.tex,183,1) ++ \caption{\label{Fig6} Schematic diagram of the photo-ionization at 116~eV. Only the channels producing unstable multiply charged species are considered. See text for details } DelBlock(Argon_size_depedence.tex,185,3) -- -- In figure \ref{Fig6}, we present a summary of the possible mechanisms that we observe. At 116 eV photon energy, direct photo-ionization can produce about 15 \% of excited singly charged clusters Ar$_m^{+*}$ and about 16\% of doubly charged clusters Ar$_m^{2+}$ with or without additional energy. This species can relax into the double ionization continuum of the clusters. \\ -- After fission, the extra internal energy of the cluster is released in different ways. For small clusters, it is likely that neutral evaporation (neutral expulsion) impart most of the kinetic energy, while for large cluster this energy would be more dissipated among all the degree of freedom. For instance molecular-dynamic in a droplet liquid model shows that only fission due to Coulomb repulsion of triply ionized clusters could justify a ÒdelayedÓ or ÒthermalÓ fragmentation. After ionization, the three charges would tend to form an equilateral triangle (minimum energy configuration), repelling simultaneously outwards, while the most favorable pathway to fission would preferably be that two of the charges approach each other while the other ones moves outwards. This effect would leave time to thermal excitation to spread all over the cluster. This is in agreement with our observation since the tails in dimer are observed in coincidence spectra up to the 3rd degree, although these channels are very weak. In multi-layer argon surfaces, the energy dissipation of high lying ionic states is known to be the dominant primary electronic process for photo-desorption\cite{Dujardin_1990}. One could speculate that the same behavior is present here with the expulsion of dimer, as it has been seen by A. Stace et al\cite{Stace_1991} for large cluster. Although the time scale is not the same, it may be that the internal energy in our experiment is high enough to enhance this mechanism. To the best of our knowledge, there is no evidence of such a relaxation mechanism in Argon clusters but it has been found in He clusters\cite{Moller_99}. One should point out that the estimated typical time scale is long enough to localize a charged in the cluster followed by the formation of self-trapped atomic or molecular excitons. Radiative decays from a molecular exciton (excimer), via bound-to-free transition, are known to open dissociation channels: for example for a neutral excited cluster to Ar+ Ar limit. Studies on doubly charged clusters\cite{Ruhl_1993} have revealed the presence of a Òthird continuumÓ related to the decay from a dication excimer to Ar$^+$+ Ar$^+$ limit. To the best of our knowledge, decay from excited cation excimer has not been reported but a likely dissociation limit to Ar$^+$+ Ar can be inferred through atomic radiative transition\cite{Nist}. Lifetimes for these excitons can be estimated to vary from 300 ps to 200 ns which could be is in agreement with our measurement.\\ AddBlock(Argon_size_depedence.tex,185,5) ++ ++ In figure \ref{Fig6}, we present a summary of the possible mechanisms that we observe. At 116~eV photon energy, direct photo-ionization can produce about 15 \% of excited singly charged clusters Ar$_m^{+*}$ and about 16\% of doubly charged clusters Ar$_m^{2+}$ with or without additional energy. This species can relax into the double ionization continuum of the clusters. ++ ++ After fission, the extra internal energy of the cluster is released in different ways. For small clusters, it is likely that neutral evaporation (neutral expulsion) impart most of the kinetic energy, while for large cluster this energy would be more dissipated among all the degree of freedom. For instance molecular-dynamic in a droplet liquid model shows that only fission due to Coulomb repulsion of triply ionized clusters could justify a delayed or thermal fragmentation. After ionization, the three charges would tend to form an equilateral triangle (minimum energy configuration), repelling simultaneously outwards, while the most favorable pathway to fission would preferably be that two of the charges approach each other while the other ones moves outwards. This effect would leave time to thermal excitation to spread all over the cluster. This is in agreement with our observation since the tails in dimer are observed in coincidence spectra up to the 3rd degree, although these channels are very weak. In multi-layer argon surfaces, the energy dissipation of high lying ionic states is known to be the dominant primary electronic process for photo-desorption \cite{Dujardin_1990}. One could speculate that the same behavior is present here with the expulsion of dimer, as it has been seen by A. Stace~\textit{et al.} \cite{Stace_1991} for large cluster. Although the time scale is not the same, it may be that the internal energy in our experiment is high enough to enhance this mechanism. To the best of our knowledge, there is no evidence of such a relaxation mechanism in Argon clusters but it has been found in He clusters \cite{Moller_99}. One should point out that the estimated typical time scale is long enough to localize a charged in the cluster followed by the formation of self-trapped atomic or molecular excitons. Radiative decays from a molecular exciton (excimer), via bound-to-free transition, are known to open dissociation channels: for example for a neutral excited cluster to Ar+ Ar limit. Studies on doubly charged clusters \cite{Ruhl_1993} have revealed the presence of a third continuum related to the decay from a dication excimer to Ar$^+$+ Ar$^+$ limit. To the best of our knowledge, decay from excited cation excimer has not been reported but a likely dissociation limit to Ar$^+$+ Ar can be inferred through atomic radiative transition \cite{Nist}. Lifetimes for these excitons can be estimated to vary from 300~ps to 200~ns which could be is in agreement with our measurement. ++ DelBlock(Argon_size_depedence.tex.bak,137,1) -- The broadening of the peak in these series of spectra cannot be explained simply as the fragmentation of singly ionized clusters in the ground state. Indeed using the model developed by Haberland[], cluster ionization is followed simply by neutral evaporation which tend to cool down the cluster. The typical energy released in this unimolecular fragmentation is typically 60-200 meV \cite{Ikegami_1993,Hrivnak_2001}. Although it is known that other dissociation mechanism are possible at this photon energy, for instance after inner-valence shell ionization \cite{Thissen_1998}, one can assume that the dominant decay channel observed is related to one vacancy in the outer shell. Hence large clusters fragment statistically: the excess energy is shared among all degrees of freedom and the kinetic energy of the fragment does not increase as a function of the cluster size. The observed fragmentation processes would imply a substantial amount of stored internal energy. AddBlock(Argon_size_depedence.tex.bak,137,1) ++ The broadening of the peak in these series of spectra cannot be explained simply as the fragmentation of singly ionized clusters in the ground state. Indeed using the model developed by Haberland\cite{Haberland_book_1994,Haberland_book_1995}, cluster ionization is followed simply by neutral evaporation which tend to cool down the cluster. The typical energy released in this unimolecular fragmentation is typically 60-200 meV \cite{Ikegami_1993,Hrivnak_2001}. Although it is known that other dissociation mechanism are possible at this photon energy, for instance after inner-valence shell ionization \cite{Thissen_1998}, one can assume that the dominant decay channel observed is related to one vacancy in the outer shell. Hence large clusters fragment statistically: the excess energy is shared among all degrees of freedom and the kinetic energy of the fragment does not increase as a function of the cluster size. The observed fragmentation processes would imply a substantial amount of stored internal energy. DelBlock(Argon_size_depedence.tex.bak,148,1) -- For the smallest clusters size ($<$N$>$=10, 20), the single ionization is strongly present but there is certain contribution of multiply charged species which corresponds to the wing broadening in the real mass spectra. For average cluster sizes $\geq$100 atoms, the real mass spectra mimic almost perfectly the time-of-flight distributions arising from multiple charged species. This means that these photo-ions are actually fragments arising from large multiply charged clusters. Multiply ionized clusters is expected to be stable when a critical size (N$_c$) is reached: for argon cluster, the first stable doubly charged species is at N$^{(2)}_c=$89\cite{Gotts_1992} and the first triply stable charged species is at N$^{(3)}_c=$226[]. Thus, for the largest cluster sizes in our experiment, the most likely origin for the photo-ions is the fragmentation of unstable doubly/triply charged clusters which are always produced due to the broad neutral cluster size distributions. Assuming this one should expect a maximum production of unstable multiply charged species for a size $<$N$>$=100 since all clusters with a size below 89 or 226 undergo fragmentation if they are respectively doubly or triply charged. It is actually what is observed in the time-of-flight distributions of fragments measured in multiple-coincidence event. The count rate increase from $<$N$>$=10 to $<$N$>$=100, and decrease from $<$N$>$=100 to $<$N$>$=1000.\\ AddBlock(Argon_size_depedence.tex.bak,148,1) ++ For the smallest clusters size ($<$N$>$=10, 20), the single ionization is strongly present but there is certain contribution of multiply charged species which corresponds to the wing broadening in the real mass spectra. For average cluster sizes $\geq$100 atoms, the real mass spectra mimic almost perfectly the time-of-flight distributions arising from multiple charged species. This means that these photo-ions are actually fragments arising from large multiply charged clusters. Multiply ionized clusters is expected to be stable when a critical size (N$_c$) is reached: for argon cluster, the first stable doubly charged species is at N$^{(2)}_c=$89\cite{Gotts_1992} and the first triply stable charged species is at N$^{(3)}_c=$226\cite{Scheier_87}. Thus, for the largest cluster sizes in our experiment, the most likely origin for the photo-ions is the fragmentation of unstable doubly/triply charged clusters which are always produced due to the broad neutral cluster size distributions. Assuming this one should expect a maximum production of unstable multiply charged species for a size $<$N$>$=100 since all clusters with a size below 89 or 226 undergo fragmentation if they are respectively doubly or triply charged. It is actually what is observed in the time-of-flight distributions of fragments measured in multiple-coincidence event. The count rate increase from $<$N$>$=10 to $<$N$>$=100, and decrease from $<$N$>$=100 to $<$N$>$=1000.\\ DelBlock(Argon_size_depedence.tex.bak,150,1) -- This astounding importance of multiply charged species deserve further discussion. Although at this photon energy the photo double ionization cross section for free atoms is a minor channel, for clusters they are actually two more mechanisms that lead to the formation of multiply charged species. First, the double ionization continuum in 3p shell decreases from 43 eV in atoms to 32 eV in clusters of size N=101[]. Due to this lowering of the adiabatic ionization potentials, high ionic excited states (e.g. Ar$_m^{*+}$) auto-ionize into the double ionization continuum. For instance, a single charge exchange between atoms can occur, opening dissociation channels Ar$_p^+$ + Ar$_q^+$ located around $\sim$31 eV (depending on the cluster size). Secondly, ÒindirectÓ processes like scattering of a primary electron on another atom can also occur as it has been pointed out in studies on large clusters[]. In our case, direct photo-ionization can produce either one electron from the (3p/3s) shells, or two/three electrons from the 3p shell, thus the electron kinetic energies can range from 0-100 eV. This corresponds to an inelastic mean free path which can be smaller than the cluster size[]. Such mechanism would heat up the cluster, increase the overall degree of ionization and strengthen Coulomb repulsion forces. Inelastic scattering is expected to be mainly significant close to atomic ionization thresholds as it has been shown in Ne\cite{Hergenhahn_2002}, but this mechanism could be emphasized by the auto-ionization of high ionic excited states (e.g. Ar$_m^{*+}$) which would produced low kinetic energy electrons. AddBlock(Argon_size_depedence.tex.bak,150,1) ++ This astounding importance of multiply charged species deserve further discussion. Although at this photon energy the photo double ionization cross section for free atoms is a minor channel, for clusters they are actually two more mechanisms that lead to the formation of multiply charged species. First, the double ionization continuum in 3p shell decreases from 43 eV in atoms to 32 eV in clusters of size N=101\cite{Scheier_87}. Due to this lowering of the adiabatic ionization potentials, high ionic excited states (e.g. Ar$_m^{*+}$) auto-ionize into the double ionization continuum. For instance, a single charge exchange between atoms can occur, opening dissociation channels Ar$_p^+$ + Ar$_q^+$ located around $\sim$31 eV (depending on the cluster size). Secondly, ÒindirectÓ processes like scattering of a primary electron on another atom can also occur as it has been pointed out in studies on large clusters. In our case, direct photo-ionization can produce either one electron from the (3p/3s) shells, or two/three electrons from the 3p shell, thus the electron kinetic energies can range from 0-100 eV. This corresponds to an inelastic mean free path which can be smaller than the cluster size. Such mechanism would heat up the cluster, increase the overall degree of ionization and strengthen Coulomb repulsion forces. Inelastic scattering is expected to be mainly significant close to atomic ionization thresholds as it has been shown in Ne\cite{Hergenhahn_2002}, but this mechanism could be emphasized by the auto-ionization of high ionic excited states (e.g. Ar$_m^{*+}$) which would produced low kinetic energy electrons. DelBlock(Argon_size_depedence.tex.bak,186,1) -- Fragmentation of clusters with coincidence mass spectroscopy techniques revealed an unexpected size dependence. The observed changes are actually related to the fragmentation dynamics of unstable multiplies charges. The overall relaxation dynamics takes longer time when the cluster gets bigger. This let us interpret this mechanism as an effect of the large amount of neutral atoms which acts as an efficient cooling bath and tends to dissipate the excess of energy ("heat") among all degree of freedom. AddBlock(Argon_size_depedence.tex.bak,186,1) ++ Fragmentation of clusters with coincidence mass spectroscopy techniques has revealed an unexpected size dependence. The observed changes are actually related to the fragmentation dynamics of unstable multiply charged clusters. The overall relaxation dynamics take in longer time scale when the cluster gets larger. This let us interpret this mechanism as an effect of the large amount of neutral atoms which acts as an efficient cooling bath and tends to dissipate the excess of energy ("heat") among all degree of freedom.
DelBlock(Argon_size_depedence.bbl,1,1) -- \begin{thebibliography}{27} AddBlock(Argon_size_depedence.bbl,1,1) ++ \begin{thebibliography}{28} AddBlock(Argon_size_depedence.bbl,160,6) ++ \bibitem[{\citenamefont{{P. Scheier } and {T.D. M\"{a}rk}}(1987)}]{Scheier_87} ++ \bibinfo{author}{\bibnamefont{{P. Scheier }}} \bibnamefont{and} ++ \bibinfo{author}{\bibnamefont{{T.D. M\"{a}rk}}}, \bibinfo{journal}{Chem. ++ Phys. Lett} \textbf{\bibinfo{volume}{136}}, \bibinfo{pages}{423} ++ (\bibinfo{year}{1987}). ++ UpdateBinaryFile(Argon_size_depedence.dvi) UpdateBinaryFile(Argon_size_depedence.pdf) DelBlock(Argon_size_depedence.tex,74,1) -- \caption{\label{Fig1} Photo-ionization branching ratio for free argon atoms and schematic decay channels for clusters. } AddBlock(Argon_size_depedence.tex,74,1) ++ \caption{\label{Fig1} Photo-ionisation branching ratio for free argon atoms and schematic decay channels for clusters. } DelBlock(Argon_size_depedence.tex,137,1) -- The broadening of the peak in these series of spectra cannot be explained simply as the fragmentation of singly ionized clusters in the ground state. Indeed using the model developed by Haberland[], cluster ionization is followed simply by neutral evaporation which tend to cool down the cluster. The typical energy released in this unimolecular fragmentation is typically 60-200 meV \cite{Ikegami_1993,Hrivnak_2001}. Although it is known that other dissociation mechanism are possible at this photon energy, for instance after inner-valence shell ionization \cite{Thissen_1998}, one can assume that the dominant decay channel observed is related to one vacancy in the outer shell. Hence large clusters fragment statistically: the excess energy is shared among all degrees of freedom and the kinetic energy of the fragment does not increase as a function of the cluster size. The observed fragmentation processes would imply a substantial amount of stored internal energy. AddBlock(Argon_size_depedence.tex,137,1) ++ The broadening of the peak in these series of spectra cannot be explained simply as the fragmentation of singly ionized clusters in the ground state. Indeed using the model developed by Haberland\cite{Haberland_book_1994,Haberland_book_1995}, cluster ionization is followed simply by neutral evaporation which tend to cool down the cluster. The typical energy released in this unimolecular fragmentation is typically 60-200 meV \cite{Ikegami_1993,Hrivnak_2001}. Although it is known that other dissociation mechanism are possible at this photon energy, for instance after inner-valence shell ionization \cite{Thissen_1998}, one can assume that the dominant decay channel observed is related to one vacancy in the outer shell. Hence large clusters fragment statistically: the excess energy is shared among all degrees of freedom and the kinetic energy of the fragment does not increase as a function of the cluster size. The observed fragmentation processes would imply a substantial amount of stored internal energy. DelBlock(Argon_size_depedence.tex,148,1) -- For the smallest clusters size ($<$N$>$=10, 20), the single ionization is strongly present but there is certain contribution of multiply charged species which corresponds to the wing broadening in the real mass spectra. For average cluster sizes $\geq$100 atoms, the real mass spectra mimic almost perfectly the time-of-flight distributions arising from multiple charged species. This means that these photo-ions are actually fragments arising from large multiply charged clusters. Multiply ionized clusters is expected to be stable when a critical size (N$_c$) is reached: for argon cluster, the first stable doubly charged species is at N$^{(2)}_c=$89\cite{Gotts_1992} and the first triply stable charged species is at N$^{(3)}_c=$226[]. Thus, for the largest cluster sizes in our experiment, the most likely origin for the photo-ions is the fragmentation of unstable doubly/triply charged clusters which are always produced due to the broad neutral cluster size distributions. Assuming this one should expect a maximum production of unstable multiply charged species for a size $<$N$>$=100 since all clusters with a size below 89 or 226 undergo fragmentation if they are respectively doubly or triply charged. It is actually what is observed in the time-of-flight distributions of fragments measured in multiple-coincidence event. The count rate increase from $<$N$>$=10 to $<$N$>$=100, and decrease from $<$N$>$=100 to $<$N$>$=1000.\\ AddBlock(Argon_size_depedence.tex,148,1) ++ For the smallest clusters size ($<$N$>$=10, 20), the single ionization is strongly present but there is certain contribution of multiply charged species which corresponds to the wing broadening in the real mass spectra. For average cluster sizes $\geq$100 atoms, the real mass spectra mimic almost perfectly the time-of-flight distributions arising from multiple charged species. This means that these photo-ions are actually fragments arising from large multiply charged clusters. Multiply ionized clusters is expected to be stable when a critical size (N$_c$) is reached: for argon cluster, the first stable doubly charged species is at N$^{(2)}_c=$89\cite{Gotts_1992} and the first triply stable charged species is at N$^{(3)}_c=$226\cite{Scheier_87}. Thus, for the largest cluster sizes in our experiment, the most likely origin for the photo-ions is the fragmentation of unstable doubly/triply charged clusters which are always produced due to the broad neutral cluster size distributions. Assuming this one should expect a maximum production of unstable multiply charged species for a size $<$N$>$=100 since all clusters with a size below 89 or 226 undergo fragmentation if they are respectively doubly or triply charged. It is actually what is observed in the time-of-flight distributions of fragments measured in multiple-coincidence event. The count rate increase from $<$N$>$=10 to $<$N$>$=100, and decrease from $<$N$>$=100 to $<$N$>$=1000.\\ DelBlock(Argon_size_depedence.tex,150,1) -- This astounding importance of multiply charged species deserve further discussion. Although at this photon energy the photo double ionization cross section for free atoms is a minor channel, for clusters they are actually two more mechanisms that lead to the formation of multiply charged species. First, the double ionization continuum in 3p shell decreases from 43 eV in atoms to 32 eV in clusters of size N=101[]. Due to this lowering of the adiabatic ionization potentials, high ionic excited states (e.g. Ar$_m^{*+}$) auto-ionize into the double ionization continuum. For instance, a single charge exchange between atoms can occur, opening dissociation channels Ar$_p^+$ + Ar$_q^+$ located around $\sim$31 eV (depending on the cluster size). Secondly, ÒindirectÓ processes like scattering of a primary electron on another atom can also occur as it has been pointed out in studies on large clusters[]. In our case, direct photo-ionization can produce either one electron from the (3p/3s) shells, or two/three electrons from the 3p shell, thus the electron kinetic energies can range from 0-100 eV. This corresponds to an inelastic mean free path which can be smaller than the cluster size[]. Such mechanism would heat up the cluster, increase the overall degree of ionization and strengthen Coulomb repulsion forces. Inelastic scattering is expected to be mainly significant close to atomic ionization thresholds as it has been shown in Ne\cite{Hergenhahn_2002}, but this mechanism could be emphasized by the auto-ionization of high ionic excited states (e.g. Ar$_m^{*+}$) which would produced low kinetic energy electrons. AddBlock(Argon_size_depedence.tex,150,1) ++ This astounding importance of multiply charged species deserve further discussion. Although at this photon energy the photo double ionization cross section for free atoms is a minor channel, for clusters they are actually two more mechanisms that lead to the formation of multiply charged species. First, the double ionization continuum in 3p shell decreases from 43 eV in atoms to 32 eV in clusters of size N=101\cite{Scheier_87}. Due to this lowering of the adiabatic ionization potentials, high ionic excited states (e.g. Ar$_m^{*+}$) auto-ionize into the double ionization continuum. For instance, a single charge exchange between atoms can occur, opening dissociation channels Ar$_p^+$ + Ar$_q^+$ located around $\sim$31 eV (depending on the cluster size). Secondly, ÒindirectÓ processes like scattering of a primary electron on another atom can also occur as it has been pointed out in studies on large clusters. In our case, direct photo-ionization can produce either one electron from the (3p/3s) shells, or two/three electrons from the 3p shell, thus the electron kinetic energies can range from 0-100 eV. This corresponds to an inelastic mean free path which can be smaller than the cluster size. Such mechanism would heat up the cluster, increase the overall degree of ionization and strengthen Coulomb repulsion forces. Inelastic scattering is expected to be mainly significant close to atomic ionization thresholds as it has been shown in Ne\cite{Hergenhahn_2002}, but this mechanism could be emphasized by the auto-ionization of high ionic excited states (e.g. Ar$_m^{*+}$) which would produced low kinetic energy electrons. AddBlock(argonbib.bib,399,13) ++ @ARTICLE{Scheier_87, ++ author = {{P. Scheier } and {T.D. M\"{a}rk}}, ++ title = {TRIPLY CHARGED ARGON CLUSTERS ++ ++ PRODUCTION AND STARXLITY (APPEARANCE ENERGY AND APPEARANCE SIZE)}, ++ journal = {Chem. Phys. Lett}, ++ year = {1987}, ++ volume = {136}, ++ pages = {423-426}, ++ owner = {mathieu}, ++ timestamp = {2006.08.25}, ++ } ++ AddBlock(argonbib.bib.bak,492,13) ++ @ARTICLE{Scheier_87, ++ author = {{Scheier P.} and {M\"{a}rk T.D.}}, ++ title = {TRIPLY CHARGED ARGON CLUSTERS ++ ++ PRODUCTION AND STARXLITY (APPEARANCE ENERGY AND APPEARANCE SIZE)}, ++ journal = {Chem. Phys. Lett}, ++ year = {1987}, ++ volume = {136}, ++ pages = {423-426}, ++ owner = {mathieu}, ++ timestamp = {2006.08.25}, ++ } ++ DelBlock(argonbib.bib.bak,638,1) -- editor = {Cambridge University Press}, Remove(Argon_size_depedence.log) Remove(Argon_size_depedence.blg) Remove(Argon_size_depedence.aux)
DelBlock(Argon_size_depedence.tex,74,1) -- \caption{\label{Fig1} Photo-ionisation branching ratio for free argon atoms and schematic decay channels for clusters. } AddBlock(Argon_size_depedence.tex,74,1) ++ \caption{\label{Fig1} Photo-ionization branching ratio for free argon atoms and schematic decay channels for clusters. }
AddBlock(Argon_size_depedence.tex,42,3) ++ \author{Ricardo R.T. Marinho} ++ \affiliation{Laborat\'{o}rio Nacional de Luz S\'{\i}ncrotron (LNLS), Box 6192, 13084-971 Campinas SP, Brazil} ++ DelBlock(Argon_size_depedence.tex,68,3) -- In a recent publication \cite{Gisselbrecht_2005} we presented the general fragmentation pattern of small argon clusters for resonant inner shell excitation and ionization. We did show that the inner shell photo-absorption prepared selectively ionic species below or above the vertical double ionization potential, respectively Ar$_m^{+*}$ and Ar$_m^{2+}$. In both case theses species undergo dissociation leading to two or more charged fragments pointing out the importance of the nuclear relaxation as well as the electronic relaxation.\\ -- In this study we focus on the cluster-size dependent fragmentation with a VUV photon of 116 eV. We perform a multicoincidence measurement Photo-Electron-n-Photo-Ions COincidence PE(PI)$_n$CO with a mass spectrometer. -- AddBlock(Argon_size_depedence.tex,68,3) ++ In a recent publication \cite{Gisselbrecht_2005} we presented the general fragmentation pattern of small argon clusters for resonant inner shell excitation and ionization. We did show that the inner shell photo-absorption prepared selectively ionic species below or above the vertical double ionization potential, respectively Ar$_m^{+*}$ and Ar$_m^{2+}$. In both case theses species undergo dissociation leading to two or more charged fragments pointing out the importance of the nuclear relaxation as well as the electronic relaxation.\\ ++ In this study we focus on the cluster-size dependent fragmentation with a VUV photon of 116 eV. We perform a multicoincidence measurement Photo-Electron-n-Photo-Ions COincidence PE(PI)$_n$CO with a mass spectrometer. ++ DelBlock(Argon_size_depedence.tex,78,3) -- The chosen photon energy implies that only the 3p valence and 3s inner valence shells can be ionized and Auger relaxation is energetically not possible. For free atoms, we are well above the double-ionization threshold 43.4 eV\cite{Nist}, the 3s Cooper minimum between 45-50 eV, and even exceeds the triple ionization threshold 84.3~eV. The branching ratios are known to be 83\% for single photo-ionization, 16\% for double photo-ionization, and less than 1\% for triple photo-ionization \cite{Holland_1979}. In the current picture of cluster ionization, so called Haberland's model\cite{Haberland_book_1995, Haberland_book_1994}, the system does not have time for nuclear rearrangement and states close to the dissociation limit are populated. Thus the cluster photo-ionisation branching ratio should mimic the atomic one. However in our experiment the time scale is long enough for nuclear relaxation to take place and adiabatic potentials to be relevant\cite{Ruhl_1992}. Hence, among the singly charge species a few of them ($\sim$15\%) prepared with two holes and one particle in the outer valence shell, should decay in the double ionization continuum as we have already eluded \cite{Gisselbrecht_2005}. Hence, one could speculate that the fragmentation depend on the cluster size.\\ -- We present figure \ref{Fig1}, the photo-ionisation branching ratio for free argon atoms (check again ?) and where the decay channel are expected for cluster. Our aim is to investigate the photo-fragmentation over a size range from a few up to thousands of atoms in order to know whether the fragmentation dynamics is a sensitive probe to the formation of stable multiply ionized clusters. -- AddBlock(Argon_size_depedence.tex,78,3) ++ The chosen photon energy implies that only the 3p valence and 3s inner valence shells can be ionized and Auger relaxation is energetically not possible. For free atoms, we are well above the double-ionization threshold 43.4 eV\cite{Nist}, the 3s Cooper minimum between 45-50 eV, and even exceeds the triple ionization threshold 84.3~eV. The branching ratios are known to be 83\% for single photo-ionization, 16\% for double photo-ionization, and less than 1\% for triple photo-ionization \cite{Holland_1979}. In the current picture of cluster ionization, so called Haberland's model\cite{Haberland_book_1995, Haberland_book_1994}, the system does not have time for nuclear rearrangement and states close to the dissociation limit are populated. Thus the cluster photo-ionisation branching ratio should mimic the atomic one. However in our experiment the time scale is long enough for nuclear relaxation to take place and adiabatic potentials to be relevant\cite{Ruhl_1992}. Hence, among the singly charge species a few of them ($\sim$15\%) prepared with two holes and one particle in the outer valence shell, should decay in the double ionization continuum as we have already eluded \cite{Gisselbrecht_2005}. Hence, one could speculate that the fragmentation depend on the cluster size.\\ ++ We present figure \ref{Fig1}, the photo-ionisation branching ratio for free argon atoms (check again ?) and where the decay channel are expected for cluster. Our aim is to investigate the photo-fragmentation over a size range from a few up to thousands of atoms in order to know whether the fragmentation dynamics is a sensitive probe to the formation of stable multiply ionized clusters. ++ DelBlock(Argon_size_depedence.tex,147,5) -- In figure \ref{Fig5}, a detailed view of the dimer (Ar$_2^+$) and trimer (Ar$_3^+$) fragments is presented for the same average sizes as in figure \ref{Fig4}. Ar$_2^+$ and Ar$_3^+$ fragments are selected because they nicely illustrate our observations. The dashed lines shown in each plot are the sum of time-of-flight distributions of the same fragment measured in multiple-coincidence event, where several photo-ions are detected together [sum of projected PE(PI)$_n$CO spectra n$>$1]. The peak shape in these spectra is unambiguously related to fragmentation of multiply charged clusters.\\ -- For the smallest clusters size ($<$N$>$=10, 20), the single ionization is strongly present but there is certain contribution of multiply charged species which corresponds to the wing broadening in the real mass spectra. For average cluster sizes $\geq$100 atoms, the real mass spectra mimic almost perfectly the time-of-flight distributions arising from multiple charged species. This means that these photo-ions are actually fragments arising from large multiply charged clusters. Multiply ionized clusters is expected to be stable when a critical size (N$_c$) is reached: for argon cluster, the first stable doubly charged species is at N$^{(2)}_c=$89\cite{Gotts_1992} and the first triply stable charged species is at N$^{(3)}_c=$226[]. Thus, for the largest cluster sizes in our experiment, the most likely origin for the photo-ions is the fragmentation of unstable doubly/triply charged clusters which are always produced due to the broad neutral cluster size distributions. Assuming this one should expect a maximum production of unstable multiply charged species for a size $<$N$>$=100 since all clusters with a size below 89 or 226 undergo fragmentation if they are respectively doubly or triply charged. It is actually what is observed in the time-of-flight distributions of fragments measured in multiple-coincidence event. The count rate increase from $<$N$>$=10 to $<$N$>$=100, and decrease from $<$N$>$=100 to $<$N$>$=1000.\\ -- -- This astounding importance of multiply charged species deserve further discussion. Although at this photon energy the photo double ionization cross section for free atoms is a minor channel, for clusters they are actually two more mechanisms that lead to the formation of multiply charged species. First, the double ionization continuum in 3p shell decreases from 43 eV in atoms to 32 eV in clusters of size N=101[]. Due to this lowering of the adiabatic ionization potentials, high ionic excited states (e.g. Ar$_m^{*+}$) auto-ionize into the double ionization continuum. For instance, a single charge exchange between atoms can occur, opening dissociation channels Ar$_p^+$ + Ar$_q^+$ located around $\sim$31 eV (depending on the cluster size). Secondly, ÒindirectÓ processes like scattering of a primary electron on another atom can also occur as it has been pointed out in studies on large clusters[]. In our case, direct photo-ionization can produce either one electron from the (3p/3s) shells, or two/three electrons from the 3p shell, thus the electron kinetic energies can range from 0-100 eV. This corresponds to an inelastic mean free path which can be smaller than the cluster size[]. Such mechanism would heat up the cluster, increase the overall degree of ionization and strengthen Coulomb repulsion forces. Inelastic scattering is expected to be mainly significant close to atomic ionization thresholds as it has been shown in Ne\cite{Hergenhahn_2002}, but this mechanism could be emphasized by the auto-ionization of high ionic excited states (e.g. Ar$_m^{*+}$) which would produced low kinetic energy electrons. -- AddBlock(Argon_size_depedence.tex,147,5) ++ In figure \ref{Fig5}, a detailed view of the dimer (Ar$_2^+$) and trimer (Ar$_3^+$) fragments is presented for the same average sizes as in figure \ref{Fig4}. Ar$_2^+$ and Ar$_3^+$ fragments are selected because they nicely illustrate our observations. The dashed lines shown in each plot are the sum of time-of-flight distributions of the same fragment measured in multiple-coincidence event, where several photo-ions are detected together [sum of projected PE(PI)$_n$CO spectra n$>$1]. The peak shape in these spectra is unambiguously related to fragmentation of multiply charged clusters.\\ ++ For the smallest clusters size ($<$N$>$=10, 20), the single ionization is strongly present but there is certain contribution of multiply charged species which corresponds to the wing broadening in the real mass spectra. For average cluster sizes $\geq$100 atoms, the real mass spectra mimic almost perfectly the time-of-flight distributions arising from multiple charged species. This means that these photo-ions are actually fragments arising from large multiply charged clusters. Multiply ionized clusters is expected to be stable when a critical size (N$_c$) is reached: for argon cluster, the first stable doubly charged species is at N$^{(2)}_c=$89\cite{Gotts_1992} and the first triply stable charged species is at N$^{(3)}_c=$226[]. Thus, for the largest cluster sizes in our experiment, the most likely origin for the photo-ions is the fragmentation of unstable doubly/triply charged clusters which are always produced due to the broad neutral cluster size distributions. Assuming this one should expect a maximum production of unstable multiply charged species for a size $<$N$>$=100 since all clusters with a size below 89 or 226 undergo fragmentation if they are respectively doubly or triply charged. It is actually what is observed in the time-of-flight distributions of fragments measured in multiple-coincidence event. The count rate increase from $<$N$>$=10 to $<$N$>$=100, and decrease from $<$N$>$=100 to $<$N$>$=1000.\\ ++ ++ This astounding importance of multiply charged species deserve further discussion. Although at this photon energy the photo double ionization cross section for free atoms is a minor channel, for clusters they are actually two more mechanisms that lead to the formation of multiply charged species. First, the double ionization continuum in 3p shell decreases from 43 eV in atoms to 32 eV in clusters of size N=101[]. Due to this lowering of the adiabatic ionization potentials, high ionic excited states (e.g. Ar$_m^{*+}$) auto-ionize into the double ionization continuum. For instance, a single charge exchange between atoms can occur, opening dissociation channels Ar$_p^+$ + Ar$_q^+$ located around $\sim$31 eV (depending on the cluster size). Secondly, ÒindirectÓ processes like scattering of a primary electron on another atom can also occur as it has been pointed out in studies on large clusters[]. In our case, direct photo-ionization can produce either one electron from the (3p/3s) shells, or two/three electrons from the 3p shell, thus the electron kinetic energies can range from 0-100 eV. This corresponds to an inelastic mean free path which can be smaller than the cluster size[]. Such mechanism would heat up the cluster, increase the overall degree of ionization and strengthen Coulomb repulsion forces. Inelastic scattering is expected to be mainly significant close to atomic ionization thresholds as it has been shown in Ne\cite{Hergenhahn_2002}, but this mechanism could be emphasized by the auto-ionization of high ionic excited states (e.g. Ar$_m^{*+}$) which would produced low kinetic energy electrons. ++ DelBlock(Argon_size_depedence.tex,153,1) -- We are now interested to understand the fragmentation of the multiply charged cluster, we will in the following only treat the peaks arising form multi-coincidence events. Time dependent fragmentation dynamics of large multiply charged van-der-Walls clusters have been studied theoretically \cite{Casero_1988}. Asymmetric Coulomb fission of doubly charged clusters is expected below their critical size ($N_c$=89) to take place in the picosecond time scale, while above the critical size it occurs in a tenth of microsecond. This is in agreement with previous experimental results performed above the L-edges\cite{Ruhl_1994} and our own observation in PEPIPICO spectra. Thus we will assume that only meta-stable decays of clusters are the reasons for the peak shape since the fragmentation which happen in the ps time scale just introduce kinetic energy to the mother ion. Furthemore, with our present statistic, shapes in different fragmentation channels have the same behavior, thus we use a simple model to extrapolate a typical time scale for various process using numerical simulation.\\ AddBlock(Argon_size_depedence.tex,153,1) ++ We are now interested to understand the fragmentation of the multiply charged cluster, we will in the following only treat the peaks arising form multi-coincidence events. Time dependent fragmentation dynamics of large multiply charged van-der-Walls clusters have been studied theoretically \cite{Casero_1988}. Asymmetric Coulomb fission of doubly charged clusters is expected below their critical size ($N_c$=89) to take place in the picosecond time scale, while above the critical size it occurs in a tenth of microsecond. This is in agreement with previous experimental results performed above the L-edges\cite{Ruhl_1994} and our own observation in PEPIPICO spectra. Thus we will assume that only meta-stable decays of clusters are the reasons for the peak shape since the fragmentation which happen in the ps time scale just introduce kinetic energy to the mother ion. Furthemore, with our present statistic, shapes in different fragmentation channels have the same behavior, thus we use a simple model to extrapolate a typical time scale for various process using numerical simulation.\\ DelBlock(Argon_size_depedence.tex,157,1) -- $<$N$>$ & Decay channel & Lifetime \\ AddBlock(Argon_size_depedence.tex,157,1) ++ $<$N$>$ & Decay channel & Lifetime \\ DelBlock(Argon_size_depedence.tex,159,11) -- 10 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ -- & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ -- 20 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ -- & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ -- \hline -- 100 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$=300$\pm$50 ns \\ -- & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$=300$\pm$50 ns \\ -- & Ar$^+_m\rightarrow$Ar$^+_2$+X & $\tau_m$=100$\pm$ 50 ns \\ -- 1000 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$=300$\pm$50 ns \\ -- & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$=300$\pm$50 ns \\ -- & Ar$^+_m\rightarrow$Ar$^+_2$+X & $\tau_m$=100$\pm$30 ns \\ AddBlock(Argon_size_depedence.tex,159,11) ++ 10 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ ++ & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ ++ 20 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ ++ & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$= 1.5$\pm$0.5 $\mu$s \\ ++ \hline ++ 100 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$=300$\pm$50 ns \\ ++ & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$=300$\pm$50 ns \\ ++ & Ar$^+_m\rightarrow$Ar$^+_2$+X & $\tau_m$=100$\pm$ 50 ns \\ ++ 1000 & Ar$^+_2\rightarrow$Ar$^+$+Ar & $\tau_m$=300$\pm$50 ns \\ ++ & Ar$^+_3\rightarrow$Ar$_2^+$/Ar$^+$+Ar/2Ar & $\tau_m$=300$\pm$50 ns \\ ++ & Ar$^+_m\rightarrow$Ar$^+_2$+X & $\tau_m$=100$\pm$30 ns \\ DelBlock(Argon_size_depedence.tex,172,2) -- In figure \ref{Fig5}, the Ar$_2^+$ and Ar$_3^+$ peaks (dashed-line) arising from the smallest cluster sizes ($<$N$>$=10,20) , exhibit a a typical peak shape with "eiffel tower" signature of decay in the drift tube. For dimer channels, it corresponds to the degradation of Ar$^+_2\rightarrow$Ar$^+$+Ar. According to Withaker et al\cite{Whitaker_93} this process can arise from radiative decay from the electronic $\Pi$(1/2)$_u$ state of the ion to the I(1/2)$_g$. Such decay is reasonable in our experiment since there is no particular reason to produce dimer fragments arising from the fragmentation of multiply charge clusters only in its ground state. However, one should keep in mind that collision induced dissociation (CID) is very a likely reason for cluster-ion degradation for background pressure above 10$^{-7}$ mbar which was the case. Our experimental resolution is not good enough to quantify properly the importance of such process but we think that at least both processes can happen. For trimer, the gaussian like distribution is due to a more complex fragmentation mechanisms which can lead either to formation of monomer or dimer depending of the internal energy left in the trimer, blurring hence the "either-tower" distribution. We present in table I, the result of our simulation in order to give an estimation of the time scale associated the degradation of this species. Accurate values for the kinetic energy KE$_1$ and KE$_2$ is hard to extract since both parameters acts almost the same way, however one can estimate that they are in the order of 500ÊmeV down to 100meV. \\ -- In the case of large clusters (from 100 to 1000), these peaks are no longer sharp. The shape can be explained either considering that fragments carry away measurable kinetic energy upon fragmentation of multiply charged species or meta-stable decay leading to neutral evaporation. From the simulation, it is clear that the time scale or such process has to be in the order of time-of-flight until the drift tube (t$^{dimer/trimer}_{acc}$) to reproduce the roundish-shape. The typical kinetic energy KE$_1$ and KE$_2$ is in the order of 2 eV down to 300meV. Another peculiar feature is observed in the fragmentation of large clusters, the Ar$_2^+$ line profile exhibits an asymmetric wing (ÒtailÓ) extending towards longer time-of-flight while Ar$_3^+$ is symmetric. This tail is a clear signature of decay producing dimer in a time scale shorter then t$^{dimer}_{acc}$: Ar$^+_m\rightarrow$Ar$^+_2$+X. The fact that this tail occur in dimer channels may reflect that dimer ionic core is the most likely unit formed inside large argon clusters as it has been observed on xenon clusters \cite{Laarmann_2002}. We performed measurement at lower extraction field to increase the flight time for dimers in the extraction region from 150 ns to 320 ns and no change from the tail was observed, as it should be expected. (trimer peak change from roundish shape to square shape ?) Since different mother ions can lead to the formation of the dimer the determination of the life-time cannot be accurate but has to be in the order a few hundred of ns. The times scale found for small cluster are typical for usual meta-stable unimolecular degradation of van-der-Waals clusters\cite{Stephan_1983, Lethbridge_1988}. In the case of large clusters, the time scale is relatively short and it shows that there are strong interactions within the cluster. One should point out that for clusters of $<$N$>$=100 and 1000 atoms, the similarity of the two time scale within the error bars implies that the fragmentation mechanism does not change drastically with cluster size. This corroborate that this observed mechanisms likely originates from the same species: unstable multiple charged clusters. This shows also that one another dissociation mechanism is energetically possible when a certain size is reached. One should notice that there is a small contribution in the peak shape of slow meta-stable decay as we have seen for small clusters. AddBlock(Argon_size_depedence.tex,172,2) ++ In figure \ref{Fig5}, the Ar$_2^+$ and Ar$_3^+$ peaks (dashed-line) arising from the smallest cluster sizes ($<$N$>$=10,20) , exhibit a a typical peak shape with "eiffel tower" signature of decay in the drift tube. For dimer channels, it corresponds to the degradation of Ar$^+_2\rightarrow$Ar$^+$+Ar. According to Withaker et al\cite{Whitaker_93} this process can arise from radiative decay from the electronic $\Pi$(1/2)$_u$ state of the ion to the I(1/2)$_g$. Such decay is reasonable in our experiment since there is no particular reason to produce dimer fragments arising from the fragmentation of multiply charge clusters only in its ground state. However, one should keep in mind that collision induced dissociation (CID) is very a likely reason for cluster-ion degradation for background pressure above 10$^{-7}$ mbar which was the case. Our experimental resolution is not good enough to quantify properly the importance of such process but we think that at least both processes can happen. For trimer, the gaussian like distribution is due to a more complex fragmentation mechanisms which can lead either to formation of monomer or dimer depending of the internal energy left in the trimer, blurring hence the "either-tower" distribution. We present in table I, the result of our simulation in order to give an estimation of the time scale associated the degradation of this species. Accurate values for the kinetic energy KE$_1$ and KE$_2$ is hard to extract since both parameters acts almost the same way, however one can estimate that they are in the order of 500ÊmeV down to 100meV. \\ ++ In the case of large clusters (from 100 to 1000), these peaks are no longer sharp. The shape can be explained either considering that fragments carry away measurable kinetic energy upon fragmentation of multiply charged species or meta-stable decay leading to neutral evaporation. From the simulation, it is clear that the time scale or such process has to be in the order of time-of-flight until the drift tube (t$^{dimer/trimer}_{acc}$) to reproduce the roundish-shape. The typical kinetic energy KE$_1$ and KE$_2$ is in the order of 2 eV down to 300meV. Another peculiar feature is observed in the fragmentation of large clusters, the Ar$_2^+$ line profile exhibits an asymmetric wing (ÒtailÓ) extending towards longer time-of-flight while Ar$_3^+$ is symmetric. This tail is a clear signature of decay producing dimer in a time scale shorter then t$^{dimer}_{acc}$: Ar$^+_m\rightarrow$Ar$^+_2$+X. The fact that this tail occur in dimer channels may reflect that dimer ionic core is the most likely unit formed inside large argon clusters as it has been observed on xenon clusters \cite{Laarmann_2002}. We performed measurement at lower extraction field to increase the flight time for dimers in the extraction region from 150 ns to 320 ns and no change from the tail was observed, as it should be expected. (trimer peak change from roundish shape to square shape ?) Since different mother ions can lead to the formation of the dimer the determination of the life-time cannot be accurate but has to be in the order a few hundred of ns. The times scale found for small cluster are typical for usual meta-stable unimolecular degradation of van-der-Waals clusters\cite{Stephan_1983, Lethbridge_1988}. In the case of large clusters, the time scale is relatively short and it shows that there are strong interactions within the cluster. One should point out that for clusters of $<$N$>$=100 and 1000 atoms, the similarity of the two time scale within the error bars implies that the fragmentation mechanism does not change drastically with cluster size. This corroborate that this observed mechanisms likely originates from the same species: unstable multiple charged clusters. This shows also that one another dissociation mechanism is energetically possible when a certain size is reached. One should notice that there is a small contribution in the peak shape of slow meta-stable decay as we have seen for small clusters. DelBlock(Argon_size_depedence.tex,180,3) -- -- In figure \ref{Fig6}, we present a summary of the possible mechanisms that we observe. At 116 eV photon energy, direct photo-ionization can produce about 15 \% of excited singly charged clusters Ar$_m^{+*}$ and about 16\% of doubly charged clusters Ar$_m^{2+}$ with or without additional energy. This species can relax into the double ionization continuum of the clusters. \\ -- After fission, the extra internal energy of the cluster is released in different ways. For small clusters, it is likely that neutral evaporation (neutral expulsion) impart most of the kinetic energy, while for large cluster this energy would be more dissipated among all the degree of freedom. For instance molecular-dynamic in a droplet liquid model shows that only fission due to Coulomb repulsion of triply ionized clusters could justify a ÒdelayedÓ or ÒthermalÓ fragmentation. After ionization, the three charges would tend to form an equilateral triangle (minimum energy configuration), repelling simultaneously outwards, while the most favorable pathway to fission would preferably be that two of the charges approach each other while the other ones moves outwards. This effect would leave time to thermal excitation to spread all over the cluster. This is in agreement with our observation since the tails in dimer are observed in coincidence spectra up to the 3rd degree, although these channels are very weak. In multi-layer argon surfaces, the energy dissipation of high lying ionic states is known to be the dominant primary electronic process for photo-desorption\cite{Dujardin_1990}. One could speculate that the same behavior is present here with the expulsion of dimer, as it has been seen by A. Stace et al\cite{Stace_1991} for large cluster. Although the time scale is not the same, it may be that the internal energy in our experiment is high enough to enhance this mechanism. To the best of our knowledge, there is no evidence of such a relaxation mechanism in Argon clusters but it has been found in He clusters\cite{Moller_99}. One should point out that the estimated typical time scale is long enough to localize a charged in the cluster followed by the formation of self-trapped atomic or molecular excitons. Radiative decays from a molecular exciton (excimer), via bound-to-free transition, are known to open dissociation channels: for example for a neutral excited cluster to Ar+ Ar limit. Studies on doubly charged clusters\cite{Ruhl_1993} have revealed the presence of a Òthird continuumÓ related to the decay from a dication excimer to Ar$^+$+ Ar$^+$ limit. To the best of our knowledge, decay from excited cation excimer has not been reported but a likely dissociation limit to Ar$^+$+ Ar can be inferred through atomic radiative transition\cite{Nist}. Lifetimes for these excitons can be estimated to vary from 300 ps to 200 ns which could be is in agreement with our measurement.\\ AddBlock(Argon_size_depedence.tex,180,3) ++ ++ In figure \ref{Fig6}, we present a summary of the possible mechanisms that we observe. At 116 eV photon energy, direct photo-ionization can produce about 15 \% of excited singly charged clusters Ar$_m^{+*}$ and about 16\% of doubly charged clusters Ar$_m^{2+}$ with or without additional energy. This species can relax into the double ionization continuum of the clusters. \\ ++ After fission, the extra internal energy of the cluster is released in different ways. For small clusters, it is likely that neutral evaporation (neutral expulsion) impart most of the kinetic energy, while for large cluster this energy would be more dissipated among all the degree of freedom. For instance molecular-dynamic in a droplet liquid model shows that only fission due to Coulomb repulsion of triply ionized clusters could justify a ÒdelayedÓ or ÒthermalÓ fragmentation. After ionization, the three charges would tend to form an equilateral triangle (minimum energy configuration), repelling simultaneously outwards, while the most favorable pathway to fission would preferably be that two of the charges approach each other while the other ones moves outwards. This effect would leave time to thermal excitation to spread all over the cluster. This is in agreement with our observation since the tails in dimer are observed in coincidence spectra up to the 3rd degree, although these channels are very weak. In multi-layer argon surfaces, the energy dissipation of high lying ionic states is known to be the dominant primary electronic process for photo-desorption\cite{Dujardin_1990}. One could speculate that the same behavior is present here with the expulsion of dimer, as it has been seen by A. Stace et al\cite{Stace_1991} for large cluster. Although the time scale is not the same, it may be that the internal energy in our experiment is high enough to enhance this mechanism. To the best of our knowledge, there is no evidence of such a relaxation mechanism in Argon clusters but it has been found in He clusters\cite{Moller_99}. One should point out that the estimated typical time scale is long enough to localize a charged in the cluster followed by the formation of self-trapped atomic or molecular excitons. Radiative decays from a molecular exciton (excimer), via bound-to-free transition, are known to open dissociation channels: for example for a neutral excited cluster to Ar+ Ar limit. Studies on doubly charged clusters\cite{Ruhl_1993} have revealed the presence of a Òthird continuumÓ related to the decay from a dication excimer to Ar$^+$+ Ar$^+$ limit. To the best of our knowledge, decay from excited cation excimer has not been reported but a likely dissociation limit to Ar$^+$+ Ar can be inferred through atomic radiative transition\cite{Nist}. Lifetimes for these excitons can be estimated to vary from 300 ps to 200 ns which could be is in agreement with our measurement.\\ DelBlock(Argon_size_depedence.tex,186,1) -- Fragmentation of clusters with coincidence mass spectroscopy techniques revealed an unexpected size dependence. The observed changes are actually related to the fragmentation dynamics of unstable multiplies charges. The overall relaxation dynamics takes longer time when the cluster gets bigger. This let us interpret this mechanism as an effect of the large amount of neutral atoms which acts as an efficient cooling bath and tends to dissipate the excess of energy ("heat") among all degree of freedom. AddBlock(Argon_size_depedence.tex,186,1) ++ Fragmentation of clusters with coincidence mass spectroscopy techniques has revealed an unexpected size dependence. The observed changes are actually related to the fragmentation dynamics of unstable multiply charged clusters. The overall relaxation dynamics take in longer time scale when the cluster gets larger. This let us interpret this mechanism as an effect of the large amount of neutral atoms which acts as an efficient cooling bath and tends to dissipate the excess of energy ("heat") among all degree of freedom.