Abstract
The halfway house phase-integral variational continuum distorted wave (PIVCDW) theory of non-relativistic Thomas double scattering electron capture is developed within the distorted wave perturbation approximation and has the distinct advantage of satisfying all known short and long range boundary conditions. Closed analytical results are obtained for both first-order (PIVCDW1) and second-order (PIVCDW2) amplitudes of this theory for transitions from an initially excited n'l'm' state to a final nlm hydrogenic one-electron state. Both the first- and second-order amplitudes contain the correct single and double scattering form respectively at asymptotically high velocities. Moreover the PIVCDW2 approximation is used to derive simple analytic formulae for the double differential cross section (DDCS) for electron capture to the continuum.
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