Sums of products of Coulomb wave function over degenerate states

The sums of products of Coulomb wave function over degenerate states are ex pressed in terms of quadratic forms that depend on the wave function of onl y one state with zero orbital angular momentum l = m = 0. These sums are en countered 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 o f the Coulomb energy levels, which in turn is due to the four-dimensional s ymmetry of the Coulomb problem. (C) 2000 MAIK "Nauka/Interperiodica".