Numerical solution of the time-dependent Schrödinger equation for intermediate-energy collisions of antiprotons with hydrogen

Abstract

We study the behavior of ionization in intermediate-energy collisions of antiprotons with atomic hydrogen by direct solution of the time-dependent Schr\"odinger equation represented on a three-dimensional Cartesian lattice. Total cross sections for these processes are computed over the collision energy range of 0.2 to 500 keV from knowledge of the asymptotic state probabilities as a function of impact parameter. The computed ionization cross sections are in good agreement with results from recent experiments conducted at CERN [Phys. Rev. Lett. 74, 4627 (1995)]. In the energy range from 0.2 to 30 keV, for which measurements are not available, our calculations are in qualitative agreement with other results based on classical-trajectory and coupled-channel methods, confirming the predicted significant difference from the analog proton-impact ionization process. This contrast with proton-hydrogen collisions is also explored qualitatively by employing a model two-dimensional space in which lattice solutions are less computationally intensive. \textcopyright{} 1996 The American Physical Society.