The second Born approximation to the electron transfer cross section

Abstract

An approximate analytic form is given for the second Born approximation to the amplitude for charge transfer from an initial n'l'm to a final nlm hydrogenic one-electron state. This amplitude contains the correct double-scattering form at asymptotically high velocities and the cross section for charge transfer may be obtained by a single numerical integration. The transfer 1s to nlm is presented as a particular example and analytic forms for the asymptotic cross section are derived in this case.