Multiple-scattering approaches to the electron transfer process. I. Some calculable approximations

Abstract

Explicit expressions for capture of an electron to and from arbitrary hydrogenic states are presented for various multiple-scattering approaches, namely approximate forms of the strong-potential Born (SPB) and impulse approximations (IA) as well as the continuum distorted-wave (CDW) approximation. In the latter case, however, the authors limit the calculation to an initial 1s state. The transition amplitudes are reduced in all cases to closed-form analytical formulae leaving a single numerical integration to obtain the capture cross sections. The author discusses some symmetry and scaling properties of the post (+) and prior (-) forms of the different methods and, as a first application of the newly gained analytical amplitudes, the author extracts some new asymptotic results. The necessary mathematical tools for the evaluation of a common matrix element appearing in the SPB, IA and CDW are provided in an appendix, where it is shown how the relevant transition amplitudes can all be obtained from one generating integral.