Electronic stopping power of protons and alpha particles in nickel

Abstract

The electronic stopping power of nickel for protons and alpha particles at velocities below and around the Fermi velocity has been obtained to high accuracy using time-dependent density functional theory. For the wide range of projectile velocities considered, we observed different regimes of electronic stopping due to the alternative participation of $s$- and $d$-band electrons. Despite the sharp discontinuity in the electronic density of states near the Fermi energy characteristic of the nickel band structure, we do not find an anomalous nonlinear electronic stopping power limit as a function of velocity. However, we find a crossover region above $v=0.15\phantom{\rule{0.28em}{0ex}}\mathrm{a}.\mathrm{u}.$ both for protons and alpha particles, related to the increase in participating host electrons and, in the case of alpha particles, to an increase of the charge state. We compare our calculated results with widely available experimental data and analyze the low velocity limits in the context of Lindhard's linear response theory and previous nonlinear density functional calculations. The comparison shows good accord with the lowest velocity experiments available. This may indicate that the adiabatic local density approximation is already a good theory to calculate electronic stopping power in materials at low velocity.