Distorted-wave theories for electron capture and the associated high-energy behavior of cross sections

Distorted-wave theories satisfying Coulomb boundary conditions are classified with respect to the behavior of the distorting potentials around the origin R=0. The ‘‘soft’’-type distorting potentials that are regular at R=0 lose their effect on the capture cross sections at high energies, and their cross sections converge to the Oppenheimer-Brinkman-Kramers (OBK) limit. On the other hand, the ‘‘hard’’-type distorting potentials that are singular at the origin as $R^{\mathrm{-}1}$ continue to have an effect in the high-energy limit so that a finite difference remains between the distorted-wave and the OBK cross sections. This feature, peculiar to electron capture, is attributed to the rapid decrease of the interaction region with the projectile velocity. The eikonal approximation is also analyzed from this point of view. Comparison with experimental data indicates that the ‘‘hard’’-type distorting potential is preferable for a first-order description of electron capture.