Distorted-wave Born approximation for inelastic collisions: Application to electron capture by positrons from hydrogen atoms

We have re-examined the distorted-wave Born approximation for inelastic collisions. We find that the distortion in the relative motion of the collision partners cannot be neglected even for high-energy ion-atom collisions. Furthermore, if the distortion in the relative motion is not treated exactly, post-prior discrepancies will occur. We have applied the distorted-wave Born approximation, with distortion included through first order, to ground-state-to-ground-state electron capture by positrons from hydrogen atoms. The results are presented in this paper. We have also examined the nonrelativistic asymptotic behavior of the cross section for electron capture from hydrogen by positrons incident with a speed $v\sim \infty$. We find that, for $\frac{e^2}{\hslash v}\ll 1$, capture occurs primarily to states of positronium that have an odd orbital-angular-momentum quantum number. It follows that the cusp signifying charge transfer to the continuum will, for positron impact, be symmetric when $\frac{e^2}{\hslash v}\ll 1$.