First-principles study of the electronic stopping power of indium for protons and He ions

Abstract

The electronic stopping power of protons and He ions traveling along the channeling and off-channeling trajectories in indium is reported based on time-dependent density functional theory combined with Ehrenfest molecular dynamics simulations. We provided an intuitive description of the electronic stopping power for a wide range of ion energies, and revealed the microcosmic excitation mechanism of the semicore $4d$ electrons of In. The velocity-proportional electronic stopping power and the kink velocity which is due to $4d$-electron excitation are reproduced in the low-energy regime. Because the $5s5p$ valence electrons are uniformly distributed in indium, the electronic excitation of valence electrons via Coulomb scattering is independent of the impact parameter in the investigated velocity range. On the contrary, due to the highly localized nature of semicore electrons, the excitation of $4d$ electrons increases significantly with decreasing of the impact parameter, which suggests that it is triggered by direct ion-electron collision. Our calculated stopping power is in quantitative agreement with the experimental data up to the stopping maximum, and showed that the stopping power obtained from the off-channeling geometry is greatly improved in comparison with the channeling results. Finally, we examined the extent to which the linear response theory is applicable to describe the electronic stopping power by quantifying the velocity dependence of the mean steady-state charge of protons and $\ensuremath{\alpha}$ particles and the effective charge state for $\ensuremath{\alpha}$ particles, and it is found that the linear response theory can be used to predict the stopping power in a wider energy range if the mean steady-state charge is used instead of assuming fully ionized charges.