A General Formula for the Calculation of Atomic Photo-ionization Cross Sections

Abstract

The general formula is derived by considering the model of a single electron moving in a central field. Approximate bound–state radial functions, accurate for large radial distances, may be obtained once the effective quantum numbers |$\nu(=n^\ast)$| are known. Bates and Damgaard have shown that such functions may be used to obtain good estimates for bound–bound transition integrals. For bound–free transitions use is made of approximate free-state radial functions having exact asymptotic forms, their phases being given by |$\delta=\pi\mu$| where μ is the extrapolated quantum defect ( |$\mu=n-\nu$| ).