Abstract
Starting with the impulse approximation, we analyse second-order effects in relativistic electron capture. The relation of this model with relativistic distorted-wave approximations is clarified. In particular it is shown that the second-order spin-coupling terms in the RCDW theory are consistent with the correct form given by perturbation theory. In the semirelativistic limit, the RCDW results are shown to accord with the formulae of Moiseiwitsch for flip and nonflip transitions in the ultra-relativistic limit. This confirms that the continuum-distorted-wave model generalises to relativistic spinors, and highlights the defects of scalar models. We also present a new symmetric eikonal theory which gives reliable results for capture without change of spin, but leads to a divergent total cross section for spin-flip transitions in the second-order term. This effect, which is quite distinct from the spurious spin-flip amplitudes of the scalar symmetric eikonal theory, is taken as further evidence that the eikonal approximation is not valid for magnetic transitions.
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