Electronic-shell effects in small doubly charged lead clusters

Lead-cluster mass spectra, the lead clusters being generated by the gas aggregation technique and ionized by electron impact, reveal, besides the well-known relative abundance maxima for singly charged species, relative concentration maxima for the doubly charged ones. Among the most intense peaks the following ones for ${\mathrm{Pb}}_{\mathrm{n}}^{2+}$: n=9, 15, 23, 27, and 35 were found. Since lead is tetravalent, the total numbers of valence electrons for the above-mentioned ions are 34, 58, 90, 106, and 138 per cluster (i.e., 4n-2), respectively. These numbers are exactly those for which the shell closing of the valence electrons within a spherically symmetric potential is achieved. This result demonstrates the importance of electronic effects on the stability, not only for neutral and singly charged metal clusters, but also for doubly charged ones.