Abstract
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')\ensuremath{\gg}1, for all \ensuremath{\Vert}\ensuremath{\Delta}n\ensuremath{\Vert}ieq\ensuremath{\Vert}n'-n\ensuremath{\Vert}, and for bound-free transitions from excited states. Approximate solutions are obtained for the case l\ensuremath{\ll}n and are found to be equivalent to those of other workers when \ensuremath{\Vert}\ensuremath{\Delta}n\ensuremath{\Vert}\ensuremath{\gg}1. We also present a power-series solution in l good for all \ensuremath{\Vert}\ensuremath{\Delta}n\ensuremath{\Vert}. General features of the dependence of the matrix elements on l are explained.
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