2ND-ORDER RELATIVISTIC ELECTRON-CAPTURE

Starting with the impulse approximation, we analyse second-order effec ts in relativistic electron capture. The relation of this model with r elativistic distorted-wave approximations is clarified. In particular it is shown that the second-order spin-coupling terms in the RCDW theo ry are consistent with the correct form given by perturbation theory. In the semirelativistic limit, the RCDW results are shown to accord wi th the formulae of Moiseiwitsch for flip and nonflip transitions in th e ultrarelativistic limit. This confirms that the continuum-distorted- wave model generalises to relativistic spinors, and highlights the def ects of scalar models. We also present a new symmetric eikonal theory which gives reliable results for capture without change of spin, but l eads to a divergent total cross section for spin-flip transitions in t he second-order term. This effect, which is quite distinct from the sp urious spin-flip amplitudes of the scalar symmetric eikonal theory, is taken as further evidence that the eikonal approximation is not valid for magnetic transitions.