On a single particle potential for atomic clusters

摘要

The single-particle potential V(r) = -V_0[1 + (r/R)~#beta#]~(-1), which has been proposed in the recent years for atomic metal clusters, is studied analytically in the case #beta# = 2. By using perturbation-type techniques, approximate analytic expressions are obtained for the energy eigenvalues and other physically interesting quantities showing the variation of these quantities with the number of valence electrons. The accuracy is tested for Al clusters and is usually very good.