Fast numerical calculations of ion-atom collisions

Abstract

When an ion impinges on an atom, the cross sections for electronic transitions can be described in the independent electron model by functions of single electron amplitudes. A single centered expansion of the time-dependent wave functiion of an electron about the heavier nucleus, with charge Z N, is shown to be moderately successful in explaining the dependence of K-shell hole production on the charge, Z rmp , of the projectile. However, capture of electrons by the projectile is important for a complete understanding and can be incorporated, in principle, in the single-center approach by evaluation of a transition matrix element involving a final state on the projectile. This is not an easy theoretical problem even in an asymmetric ( Z p⪡ Z N) collision, because long times are involved which aggravate the inadequacies of a couple-state calculation where the continuum is replaced by a discrete set of pseudostates. Nevertheless a method has been devised which allows convergence in the truncated expansion of Hilbert states. Comparisons are made to experiment. Future developments are discussed.