Density-functional calculation of the fragmentation of doubly ionized spherical jelliumlike metallic microparticles

The fragmentation of doubly charged $X_N$ ${}^{2+}$ (X=Na,Mg) model microparticles into two singly charged fragments $X_N$ ${}^{2+}$→$X_P$ ${}^{+}$+$X_{N\mathrm{-}P}$ ${}^{+}$ has been studied as a function of N and P, by using the density-functional formalism. In contrast to naive expectations which would predict the most asymmetric channel (P=1) to be the most favorable one, we find that the main factor controlling the most favorable channel is the tendency for fragments to have a ‘‘magic’’ number of electrons: 2, 8, 18, etc. These magic numbers, which correspond to filled electronic shells in a spherically symmetric potential, are already familiar from the analysis of experiments of the relative abundance of alkaline-atom clusters produced by supersonic expansion. Our results suggest the existence of a critical number (larger than 100) for Coulomb explosion of ${\mathrm{Na}}_{\mathrm{N}}$ ${\mathrm{}}^{2+}$ clusters.