Swift charged particles in a degenerate electron gas: An estimation for the charge-sign effect in stopping

Abstract

Motivated by the recently introduced [Phys. Rev. A 94, 042704 (2016)] and already investigated [J. Phys. B: At. Mol. Opt. Phys. 50, 185201 (2017)] new approximate form for the stopping power in terms of scattering phase shifts, here we show analytically that within such a modeling of the observable an exact leading phase shift may contain that information which is completely enough to characterize the asymptotic charge-sign-independent Bethe term (∝Z21) and a charge-sign-dependent (Barkas) term (∝Z31) in the stopping force of a degenerate electron gas for fast projectiles with charge . Our study is based on a spherical potential with velocity-dependent screening as in the above works. The next term in an asymptotic expansion, the Bloch term (∝Z41), measures the difference of the exact and first-order Born treatments with Coulomb potential.