Electronic stopping power of magnesium including inner-electron excitation

Abstract

The electronic stopping power of magnesium for protons and He ions is studied by a nonequilibrium approach based on real-time time-dependent density-functional theory combined with Ehrenfest molecular-dynamics simulation. The electronic stopping power of Mg for energetic protons and He ions is calculated, and the microscopic excitation mechanism for the inner $2p$ electron of Mg and its contribution to electronic stopping power is revealed. In the low-energy range, the velocity proportionality of the electronic stopping power of Mg for protons is displayed. The low-energy stopping power of Mg for He ions displays deviations from the velocity proportionality, which is ascribed to the electronic structure of He ions that enables an additional energy-loss channel due to charge exchange. Our calculated stopping power is in a quantitative agreement with the experimental data up to the stopping maximum, and the stopping power including also $2p$-electron excitation is considerably improved compared to that with only the valence electron taken into account. Our results showed that the contribution of $p$-electron excitation to the electronic stopping is remarkable in the high-velocity regime. The scaling relationship $\sqrt{{S}_{\ensuremath{\alpha}}/{S}_{H}}$ = ${\overline{q}}_{\ensuremath{\alpha}}/{\overline{q}}_{H}$ can be extended to low velocities provided that the mean steady-state charge is employed instead of assuming fully ionized charges and considering also $2p$-electron excitation of Mg.