Physics with high-energy cluster beams

COMPUTATIONAL MATERIALS SCIENCE ELSEVIER

Computational Materials Science 2 (1994) 571-577

Physics with high-energy cluster beams B. F a r i z o n , M . F a r i z o n , M . J . G a i l l a r d , S. O u a s k i t

1

lnstitut de Physique Nucl~aire de Lyon, IN2P3-CNRS / Univ. Claude Bernard, 43, bd du 11 Novembre 1918, 69622 Villeurbanne Cedex, France

(Received 1 December 1993; accepted 9 February 1994)

Abstract The interest of physicists in working with high energy cluster beams is increasing, in particular in France where the hydrogen cluster accelerator at Lyon has been recently upgraded to deliver H~ beams in the energy range 60-100 keV/u, n < 51, up to 3 MeV and where the 15 MV Tandem accelerator at Orsay which already accelerates n+ n+ C60 -C70 clusters will produce beams of metallic clusters. As a matter of fact, the use of mass-selected high-energy clusters as projectiles appears to be an important source of information on the interaction of particles and clusters with matter (solid, gas, electron, plasma) and related phenomena, and on the clusters themselves. Results (experiments and Monte Carlo simulation) on the interaction of H~+ clusters with thin foils and some perspectives of investigation with fast clusters are presented.

1. Introduction Since many years, fast molecular projectiles which offer specific possibilities for studying basic aspects of atomic collisions in solids have been extensively used by physicists. More recently, the penetration of swift hydrogen clusters in solids has received considerable interest [1-7] in connection with charge exchange processes, convoy electron and secondary electron productions, energy loss, etc. In addition, the use of clusters as projectiles can also give informations on the clusters themselves [8]. For such studies, the H~+ clusters are of special interest, for both the experimental and the theoretical point of view, because of their relative

1 Permanent address: Universit6 Hassan II, Facult6 des Sciences II, Casablanca, Maroc.

simplicity. These clusters can be described as H 2 molecules surrounding an H~- core. Up to now, the Hn+ clusters produced are mainly singly charged species of odd mass numbers. Their theoretical structures have been studied by ab initio methods [9,10]. Using a triple-zeta-plus polarization basis set, self-consistent field calculations have been carried out for n = 2-21, odd. From another point of view, since there are hydrogen clusters in interstellar clouds, experimental data and theoretical predictions on interaction of hydrogen clusters with matter are of space-technical interest.

2. The hydrogen cluster facility at Lyon At the Institut de Physique Nucl6aire de Lyon, hydrogen cluster beams of total energy varying from 40 to 650 keV are currently delivered by a

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B. Farizon et al. / Computational Materials Science 2 (1994) 571-577

Cockroft-Walton type accelerator equipped with a cryogenic source. After acceleration, the cluster beams are selected in mass and velocity by electrostatic and magnetic analysers. This facility has been upgraded recently by adding a variable energy Radio Frequency Quadrupole (RFQ) which post-accelerate H + clusters (n = 3 to 49, odd) up to 3 MeV [11] in a high-energy beam line. Various experiments have been performed with H~+ clusters as projectiles, in particular on measurements of angular distributions of hydrogen fragments resulting of the dissociation of these clusters (n < 23) in very thin carbon foils (100-300 ,~ thick), of charge state distributions at emergence [2,5] and of secondary emission yields under cluster bombardment [6]. Mass and velocity of clusters are always variable parameters in these experiments.

3. A Monte Carlo computer program

These experimental results have motivated the development of a Monte Carlo computer routine allowing a quantitative treatment of the different processes involved in the interaction of the cluster with the solid [8]. In a first step, the procedure has been developped to determine the trajectories of the fragments inside the solid. Each incident Hn+ cluster with its three dimensional structure is initially randomly oriented relative to the incident ion beam direction and is assumed to dissociate upon contact with the foil. Inside the foil divided into a large number of thin parallel slabs, the motion is determined classically. The nuclear scattering is treated in each slab as a single event where each cluster fragment can change direction. From one slab to the another one, the calculation of the particule trajectories takes into account the electronic energy loss, the effect of the superposed wake potentials and the screened Coulomb explosion. This process is repeated until the fragments reach the exit surface of the foil. A large number of clusters ions are followed through the foil (for details, see [8]).

4. Interaction of fast hydrogen clusters with thin carbon foils

4.1. Angular distributions The first investigation of the proximity effects inside the foil was the study of the angular distributions of hydrogen fragments [2,8] resulting from the dissociation of fast (above the Bohr velocity) Hn+ clusters (n = 2, then 3 to 21, odd) in a thin carbon foil (2 ixg/cm2). It has been observed at a given velocity (Fig. 1, filled symbols) that the angular width "saturates" at n = 5. These angular distributions mainly reflect the combined effects of the screened Coulomb repulsion and of the multiple scattering in the foil since it is reasonable to neglect repulsion in vacuum of a neutral fragment with protons or other neutral fragments. The angular distributions computed with the Monte Carlo routine first have been compared with experimental data obtained for clusters of 60 k e V / p (Fig. l(a)). The results concerning the case of H~- and H~- incident molecular ions show that the computed values are too large. As the calculation is good for the proton case, this overestimated effect comes from the Coulomb explosion calculation which is strongly dependent on the initial internuclear distances in the cluster. With inter-proton distances larger than those obtained by ab initio calculations for atomic molecules in low vibrational states, one can fit the experimental results for this energy (60 keV/p) and then a good agreement is also obtained at all the other energies (30 to 80 keV/p, Fig. l(b)) with these initial distance distributions. For cluster of mass higher than 3, the Monte Carlo and experimental results are quantitatively in good agreement when the initial bond lengths calculated by ab initio methods are used in the routine. This means that in the incident cluster of the H~- core and the H 2 subunits are in low vibrational states. In this velocity range the multiple scattering screens the main part of the informations on the

B. Farizon et aL / Computational Materials Science 2 (1994) 571-577

4. 2. Neutral fractions

cluster structure. Nevertheless, the Coulomb explosion technique combined with Monte Carlo simulations can be helpful to investigate the structures of hydrogen clusters. At very high velocities (4%), the effect of the multiple scattering on the direction of the velocity of fragments inside a thin foil is so small that the trajectories are not perturbated by the foil which only remove all the bonding electrons of the cluster. Then the resulting Coulomb explosion, strongly dependant on the initial internuclear distances, will determine the trajectories of the constituants of the cluster. These trajectories will reflect the initial structure of the cluster as shown in Fig. 2(a) and 2(b) in the H~- case. In these figures, one can see the three different "peaks" which are expected for the angular distribution. These three peaks are connected to the three distances which are predicted in the H~ cluster structure. Transverse velocities at emergence of the foil can be measured, and comparison with results of simulations including structures of clusters can help to assess the accurateness of the theoretical structures.

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In a next step, the Monte Carlo program has been used to built a model of charge exchange for protons resulting from the break up of hydrogen clusters in thin carbon foils. We have interpreted experimental results on the total neutral fractions at emergence of a 2.1 p,g/cm 2 foil at various velocities (Fig. 3) and on the number of atoms in the 2p states at emergence per incident proton (Fig. 4). Assumptions made to built this model of charge exchange inserted in the Monte Carlo routine are described in Ref. [12]. The results of calculations presented in the same figures indicate a good description of charge exchange processes and of the screening and vicinity effects introduced in the model. In particular, this study shows that a decrease of the electronic loss cross section with respect to the isolated proton case due to proximity effects in the cluster case can explain the main part of the cluster effect observed on charge exchange [12]. In addition, the saturation effect observed with

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carbon foil. The projectile velocities are indicated on the figure (filled symbols for experimental results, open symbols for calculated results).

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B. Farizon et al. /Computational Materials Science 2 (1994) 571-577

the cluster size has to be connected to the structure of the clusters. Since the fraction normalised to the proton case is constant versus the number of H 2 molecules in the incident cluster for n > 7, that means proximity effect between two H 2 molecules of the cluster is negligible. It has to be noted that the distance between the Hoe subunits in the cluster are greater than 1.5 A and are greater than the length of the dynamic screening due to the electrons of the target (0.7-1 ,~ in the carbon, in the velocity range studied here).

4.3. Secondary electron emission (SEE) The informations so obtained on the penetration of clusters in solids and on the structures of these

clusters (vibrationnal state, internuclear separation in the cluster) are helpful to interpret results of other cluster-matter experiments even without specific model, as shown now. We have measured the secondary electron emission yield induced by fast hydrogen clusters. The experimental results (Fig. 5) have revealed a strong inhibition effect with respect to the atomic case [6]. This effect increases with increasing n up to n = 5 - 7 and then reaches a saturation value. We have interpreted these results in the same framework and the variation with n of the inhibition effect has been connected to the structure of the incident projectile (nucleation of H z molecules around an H~ core). Indeed, the increase of the inhibition effect cannot be associ-

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ated only to the vicinity effect between the molecules of the cluster which are close together when reaching the foil since a saturation with n is observed for a small n u m b e r of molecules in the cluster. Therefore, the saturation value of the inhibition effect should have to be compared to the inhibition effect that one could expect with a b e a m of H 2 molecules of the same velocity but in low vibrationnal states, as the H2 subunits are in the weakly bound H + clusters. The distances between the two protons in these subunits which are close to the theoretical distance 0.74 A [8,10] are of the same order of magnitude than the length of the dynamic screening due to the electrons of the target while the m e a n distance between the protons in hot H~- ions is much higher (typically 1.3 ,~). We have shown that the proton

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proximity decreases the electronic loss cross section with respect to the isolated proton case [12]. So an electron which would have been captured in the foil will stay bounded to the protons of a cold H 2 subunit of a cluster over a distance greater than if we h a d used an H~- beam. This leads to a greater screening effect of the protons by an accompanying electron in the cold H 2 molecules case and could explain the strong inhibition effect observed on the total SEE yield induced by clusters.

4.4. Cluster stopping-power The cluster stopping-power ratio can also be calculated with the Monte Carlo routine [8] and

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Fig. 3. Total neutral fractions.

that has been done for light hydrogen clusters (n = 2, 3 to 9, odd). At the velocity corresponding to 60 keV/p, the stopping power ratio is larger than one and saturates for mass numbers n > 5. This is due to the fact that, when the cluster size increases, the relative proportion of the number of cold H 2 molecules in the cluster increases, and all the effects are mainly due to the simultaneous penetration of almost independent H 2 molecules in the foil, in agreement with previous results.

5. Conclusion

Strong effects have been observed in the interaction of clusters with carbon foils compared to the atomic or molecular projectile cases. The

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main part of these effects are connected to proximity effects of the protons in the H 2 subunits of the cluster. The proximity of the various H 2 molecules in the incident clusters does not seem to contribute to the cluster effect observed. This is directly connected to the distances between the protons in the cluster compared to the length of the dynamic screening due to the target electrons. Various cluster effects could be expected by changing the dynamic screening length which depends in particular on the projectile velocity and on the plasma frequency of the target. The simulation is also used to connect in a quantitative way the distances between the protons at the entrance of the foil to the transverse velocities of the fragments at the exit of the foil. Associated to Coulomb explosion experiments, this Monte Carlo code could provide other information on the structure of the dusters themselves.

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B. Farizon et al. /Computational Materials Science 2 (1994) 571-577

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