Artenum Innovative Solutions - The Journal Of Chemical Physics 128, 044317 (2008)

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  ++ \author{Ricardo R.T. Marinho}
  ++ \affiliation{Laborat\'{o}rio Nacional de Luz S\'{\i}ncrotron (LNLS), Box 6192, 13084-971 Campinas SP, Brazil}
  ++ 


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  --     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.
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The Journal Of Chemical Physics 128, 044317 (2008)

View Patch [from 104 to 122]
