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

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.

Automated summary

In this study, the classical equations of motion and Poisson equation were solved self-consistently to calculate the electron-ion potential and ion stopping power for a projectile in a free-electron gas. The origin of the Barkas effect, which is responsible for the energy-loss difference between positively and negatively charged ions in the same target, was investigated. The effect is strongly enhanced by the multipolar part of the electron-ion potential and is partially related to the nonconservation of angular momentum in electron-ion collisions. These calculations were applied to understand the stopping of protons and antiprotons in aluminum at high energies.