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.
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Briggs et al. (1980) studied this question.
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