Coulomb barriers in the dissociation of doubly charged clusters

The barrier height for the most asymmetric fission decay of doubly charged sodium clusters (${\mathrm{Na}}_{\mathit{N}}^{2+}$) into singly ionized fragments has been computed with use of density-functional theory and the jellium model. We have found that the barrier is sizable for large or intermediate-size clusters, but vanishes for N≤9. We have also computed the energy Δ${\mathit{H}}_{\mathit{e}}$ needed to evaporate a neutral monomer from ${\mathrm{Na}}_{\mathit{N}}^{2+}$. For N≤40, the barrier height is smaller than Δ${\mathit{H}}_{\mathit{e}}$, and emission of a ${\mathrm{Na}}^{+}$ ion is the preferred decay channel of hot ${\mathrm{Na}}_{\mathit{N}}^{2+}$ clusters. On the other hand, the barrier height is larger than Δ${\mathit{H}}_{\mathit{e}}$ for N>40 and, in this case, monomer evaporation becomes competitive. The critical cluster size, ${\mathit{N}}_{\mathit{c}}$=40, for the transition from one decay mode to the other is in reasonable agreement with the experimental result. Our calculations suggest that the mechanism for neutral-monomer evaporation is different from the one currently assumed.