DIFFERENTIAL-EQUATION FOR THE SPHERICAL DIPOLE MATRIX-ELEMENTS OF HYDROGEN

A differential equation in l for hydrogenic radial dipole matrix elements is generated from the recursion relations of Infeld and Hull [Rev. Mod. Phys. 23, 31 (1951)]. The equation is valid for all (n,n)1, for all nieqn-n, and for bound-free transitions from excited states. Approximate solutions are obtained for the case ln and are found to be equivalent to those of other workers when n1. We also present a power-series solution in l good for all n. General features of the dependence of the matrix elements on l are explained. © 1990 The American Physical Society.