New summation rules for Coulomb wave functions

Sums of products of the Coulomb wave functions over degenerate manifolds ha ve been obtained in a closed form. These sums appear in many atomic and mol ecular problems. The sums have been obtained making use of the properties o f the Coulomb Green's function G(r, r', E), in the limit E --> E-n, where E -n, is the eigenenergy of the hydrogenlike atomic ion. The closed Hostler-P ratt form of G in the coordinate representation has been used. The sums cal culated are a consequence of the n degeneracy of the Coulomb atomic energy levels. This itself, as is well known, follows from the four-dimensional sy mmetry of the Coulomb problem for the hydrogen atom.