Exact stopping cross section of the quantum harmonic oscillator for a penetrating point charge of arbitrary strength

Abstract

The time-dependent Schr\"odinger equation for a Coulomb collision between a heavy point charge and a harmonically bound electron is solved exactly numerically. The energy transferred to the electron is studied as a function of impact parameter and projectile charge. Special attention is given to the Barkas effect and the transition from light-ion to heavy-ion stopping. The results are contrasted with classical and recent approximate results, whose precision and ranges of validity are discussed. Comparison with experimental data is made on the basis of an oscillator model of atomic stopping.