Sums of products of Coulomb wave function over degenerate states

Abstract

The sums of products of Coulomb wave function over degenerate states are expressed in terms of quadratic forms that depend on the wave function of only one state with zero orbital angular momentum l = m = 0. These sums are encountered in many fields in the physics of atoms and molecules, for example, in investigations of the perturbation of degenerate atomic energy levels of a small potential well, a delta-function potential. The sums were found in an investigation of the limit of the Coulomb Green's function G(r, r', E), where the energy parameter E approaches an atomic energy level: E --> E-n, E-n = -Z(2)/2n(2). The Green's function found by L. Hostler and R. Pratt in 1963 was used. The result obtained is a consequence of the degeneracy of the Coulomb energy levels, which in turn is due to the four-dimensional symmetry of the Coulomb problem. (C) 2000 MAIK "Nauka/Interperiodica".