Quasiclassical analysis of the spectra of two groups of central potentials

Abstract

A method is suggested for analyzing the spectra of central attractive potentials either with Coulomb singularity (intra-atomic potentials) or finite at zero point (potentials in spherical clusters and nuclei). It is shown that, if the orbital degeneracy is removed, then $$\varepsilon _{nl} - \varepsilon _{n0} \cong a_{\varepsilon _{n0} } (l + 1/2)^2 $$ for small l in the shell n. In atoms and ions, the coefficient a ε is nonnegative, so that the energy in the n shell increases with l. The validity of this formula for the inner electrons is illustrated by calculating the spectrum of the mercury atom. In cluster potentials, the opposite situation, as a rule, occurs: the larger l, the lower the corresponding level (a ε<0). However, in the soft potentials of small clusters, spectral regions with different signs of a ε coexist and the orbitally degenerate level exists in the spectral region where a ε=0. Aluminum clusters AlN are taken as an example to find out how the position of the region with the degenerate level varies with varying cluster size N, and it is found that this region is “pushed out” to higher energies with an increase in N. In this connection, the presence of multiply ionized AlN clusters of the corresponding size in a low-temperature aluminum plasma is discussed.