On a single particle potential for atomic clusters

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 ana lytically in the case beta = 2. By using perturbation-type techniques, appr oximate analytic expressions are obtained for the energy eigenvalues and ot her physically interesting quantities showing the variation of these quanti ties with the number of valence electrons. The accuracy is tested for Al cl usters and is usually very good. (C) 1999 Elsevier Science B.V. All rights reserved.