Barkas effect in a central collision: Exact numerical results and the tenth-order Born series

Abstract

The time-dependent Schr\"odinger equation for a central collision between a heavy point charge and a harmonically bound electron is solved numerically. This is done in a basis of energy eigenfunctions of the undisturbed electron. Our numerical method also provides the coefficients of the Born series for the collision. We compare the Born expansion with the exact results. In agreement with other calculations we find a significant Barkas effect for some collision parameter values. At low velocities the Barkas correction is shown to be very large, but at higher velocities it becomes very small even for ions with high charges.