Effective single-electron treatment of ion collisions with multielectron targets without using the independent-event model

Abstract

In ion-atom collisions involving multielectron targets the role of inner-shell electrons becomes important with increasing collision energy. Usually, processes involving the outer-shell and inner-shell electrons are treated using an independent-event model. However, the independent-event model becomes impractical when the number of shells is more than two. We develop an effective single-electron approach to ion collisions with multielectron atomic targets that overcomes this difficulty by treating all the atomic electrons on an equal footing. The approach allows the calculation of single-ionization and single-electron transfer cross sections by including the excitation of any one of the inner- or outer-shell target electrons. Accordingly, the approach does not differentiate which one of the many target electrons is captured or ionized. This is a unique feature of the proposed approach. The ground-state wave function for the target atom obtained in the multiconfiguration Hartree-Fock approach is used to calculate the probability density for the whole atom. The latter is then averaged over the spatial coordinates and spin variables of all of the target electrons except for the position of one electron from the nucleus. The obtained single-electron probability density is then used to derive a pseudopotential describing the interaction of one electron with an effective field produced by the target nucleus and the other electrons. The procedure reduces the many-body Schr\"odinger equation governing the collision system effectively into a three-body one. The reduced Schr\"odinger equation is solved using the two-center wave-packet convergent close-coupling approach. As an illustrative example we calculate integrated cross sections for single-electron transfer and ionization in proton collisions with lithium, sodium, and potassium. The results obtained agree very well with available experimental data for electron transfer. However, we find significant discrepancies with experiment for single ionization of Na and K, which warrant further experimental and theoretical investigations.