Closed-form expression for 1s-->1s electron-capture amplitude in a second-order Faddeev approximation.

Abstract

Within a second-order approximation to the Faddeev treatment of the exact transition operator for 1s\ensuremath{\rightarrow}1s electron capture in ion-atom collisions, expressions are derived in terms of ${F}_{4}$ generalized hypergeometric functions for that part of the full amplitude involving electronic-nuclear potentials only. For totally symmetric collisions, the amplitude is evaluated in terms of $_{3}\mathrm{F}_{2}$ functions. When near-the-energy-shell anomalies of the Coulomb scattering are neglected, the amplitude is seen to reduce to a symmetric impulse-approximation form, and, when the explicit Coulomb nature of the problem is neglected, to a second-order Born approximation form. As a special case, the amplitude is evaluated at the momentum transfer value where the differential cross section exhibits a local maximum---the Thomas peak. The values of the various amplitude norms at the Thomas peak are compared.