Screened hydrogenic radial integrals

Abstract

The screened hydrogenic radial integral for discrete-discrete and discrete-continuum transitions is expressed in forms suitable for obtaining closed-form expressions for specific transitions. Two effective-charge parameters, for the initial state and for the final state, are retained in these formulas. As examples, explicit expressions for a few transitions are derived, and a method for obtaining a series for a discrete-discrete radial integral, suitable for large final-state principal quantum numbers, is indicated.