Fission channels of multiply charged sodium clusters near the Rayleigh limit

Abstract

Fission of multiply charged sodium clusters Na n qϩ produced in collisions of neutral clusters with protons at 20 keV is investigated with an event-by-event acquisition technique. The analysis of fragment correlations shows that clusters undergo a strongly asymmetrical binary fission with Na ϩ , Na 2 ϩ , Na 3 ϩ , Na 4 ϩ , and Na 5 ϩ as the small fragments, Na 3 ϩ dominating with approximately 70%. For a given charge q, the branching ratio of Na 3 ϩ over Na ϩ emission increases with n, which is interpreted in terms of a decreasing temperature of the parent cluster following proton impact.Charged alkali-metal clusters become unstable when the long-range Coulomb repulsion due to the net positive electric charge overcomes the electronic binding. This instability is analogous to that prevailing in heavy nuclei. Nuclear fission involves a large amplitude collective motion resulting in a more or less symmetric binary fragmentation. Symmetric fission of heavy nuclei is expected from the nuclear liquid-drop model ͓1͔. Within this model, metal clusters are different from atomic nuclei because they are highly polarizable conducting droplets and not homogeneously charged ones. In the absence of mass to charge coupling ͑as for neutrons and protons in nuclei͒, one may expect a charge splitting that is different from the mass splitting. In any case, the equilibrium shape for a neutral drop is spherical. For a charged drop, the dependence of both the surface and the Coulomb energy upon small deformations is such that infinitesimal quadrupole fluctuations trigger a shape instability once the ratio X of the Coulomb energy to twice the surface energy exceeds the Rayleigh limit Xϭ1 ͓2͔. This ratio, called the fissility parameter, is proportional to q 2 /n:where q is the net electric charge and n is the number of constituents of the cluster. The factor ␣ is about 0.02 for nuclear matter, whereas it is about 2.5 for sodium ͑of interest in this paper͒. Treating sodium clusters as liquid drops, one thus expects the critical sizes for stability to be about 10,23,40,63, . . . for charges qϭ2,3,4,5, . . . , respectively. These critical sizes are hard to reach experimentally because it requires forming multiply charged sodium clusters at zero temperature. Otherwise fission can be activated thermally.There have been essentially two experimental methods used so far to prepare multiply charged clusters and to study their instability. The first one uses a multistep photoionization technique ͓3͔. Due to the photon energy, there is a sizedependent limit for obtaining multiply charged clusters. Moreover, multiply charged clusters produced this way turn out to be stable towards fission. To obtain fission, it is necessary to evaporate a substantial fraction of atoms until the cluster size has reached the size for which the height of the barrier against charge splitting becomes smaller than the dis-sociation energy for evaporation, 1 eV for sodium. Thus the measured appearance sizes n app (q) that are defined as the minimum size of q-fold clusters ap...

Rayleigh Instabilities in Multiply Charged Sodium Clusters

“…(1), is indicated. resulting in highly excited multiply charged clusters [21]. (ii) When z increases, the appearance size n app ͑q # 7͒ decreases.…”

On the fragmentation of multiply charged sodium clusters

“…This puzzling behavior is due to the fact that as the charge of a fixed-mass cluster is increased, the long-range Coulomb repulsive force overwhelms the much weaker short-range van der Waals attractive forces with the result that the cluster becomes unstable even at zero excitation energy. Such a situation has been observed experimentally by Chandezon et al [14,15] who investigated the critical sizes necessary for the production of multiply charged sodium clusters and found that for a charge of 5, the smallest mass of the cluster would be 200 ± 5 atoms, a result slightly dependent on the method used for producing and ionizing the cluster. For a total cluster charge of 4 the critical size is about 120.…”

Ion beams of carbon clusters and multiply charged fullerenes produced with electron cyclotron resonance ion sources

“…The measured beam intensities range between 1 and 20 nA. In order to better interpret the complex spectra, we have applied a deconvolution technique based on the interpolation of intensities of well-identified peaks, 13 yielding spectra for individual charge states. In addition, the separation method described further below, which uses selective collision reactions, has also been applied ͑see Sec.…”