Nonlinear ion-stopping calculations for a classical free-electron gas at high projectile energies

Abstract

In this work, we solved the classical equations of motion and Poisson equation self-consistently, equivalent to the nonlinear Vlasov-Poisson equation, for a projectile moving in a static free-electron gas to calculate the full noncentral self-consistent electron-ion potential, and thus the ion stopping power. We investigated the origin of the Barkas effect, namely, the first nonlinear effect for projectiles at high velocities responsible for the difference between the energy-loss results for positively and negatively charged ions traversing the same target. This effect is strongly enhanced by the multipolar part of the electron-ion potential as first suggested by Lindhard [J. Lindhard, Nucl. Instr. and Meth. 132, 1438 (1976)]. Moreover, this effect is partially related to the nonconservation of the angular momentum in electron-ion collisions. These nonlinear calculations are applied to understanding the stopping of protons and antiprotons in Al at high projectile energies