Semiclassical description of dipole matrix elements for arbitrary nl-->n'l' transitions in nonhydrogenic ions.

Abstract

A semiclassical formula for dipole matrix elements of single-electron nl\ensuremath{\rightarrow}n'l' transitions with arbitrary quantum numbers in nonhydrogenic ions is derived. Only the energies and angular momenta of the initial and final states are needed as input along with the charge of the ion. The definition of the intermediate state is a key element in the derivation. Results are compared with experimental values and self-consistent-field calculations for Na-like ions. The formula is shown to coincide with the exact quantum-mechanical result for hydrogen in the limit n'\ensuremath{\gg}n\ensuremath{\gg}1, l\ensuremath{\ll}n.