Impact Ionization in the Proton-H-Atom System. IV. Improved Values for Radial Transition Matrix Elements

Papers I-III of this series describe a theory of direct-impact ionization in slow ${\mathrm{H}}^{+}-\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collisions, and the first steps in the calculation of the cross sections ${\sigma }_I\left(\epsilon \right)$. It was found that electronic matrix elements for direct-impact ionization are extremely sensitive to the form of the kinematic factor representing radial transport of the electron by a moving heavy particle. In III a heuristic criterion for systematic improvement of the factor and a variational trial form for it were proposed. Using this proposal we have recomputed radial electronic transition matrix elements for ionization. There is an optimum choice of variational parameters which greatly reduces the over-all size of transition matrix elements. In particular, contributions at large internuclear distances (judged to be spurious in the results of Paper II) are now eliminated, and (except at high electron energies) the contributions to higher partial waves in the electronic continuum are reduced by orders of magnitude. The present results give reasonable confidence that convergence on a "best" first-order transition matrix for the effects of radial motion has been obtained. The existence of a similar optimization problem for the Coriolis-coupling ionization matrix elements is pointed out.