Electronic stopping of protons in magnesium from first principles

The electronic energy loss rate from an energetic proton to electrons of an alkali metal magnesium (Mg) is investigated using real-time time-dependent density functional theory. Nonequilibrium simulations under various impact geometries are conducted to elucidate the role of the impact parameter in the dissipation mechanism. Unlike electronic stopping, which is significantly underestimated under channeling trajectories in the velocity regime around and above the stopping maximum, the predicted electronic stopping along the off-channeling trajectory, which explicitly accounts for the occasionally strong interaction with tightly bound inner-shell electrons, demonstrates quite satisfactory agreement with the experimental data throughout the velocity regime considered. This suggests that the impact parameter plays a crucial role when inner-shell excitation is concerned. Moreover, we conduct a quantitative analysis of the effect of the impact parameter on the electronic excitation in specific bands. An important conclusion drawn is that reducing the impact parameter significantly increases the intensity of the inner-shell excitation, especially for regimes around and above the stopping maximum, and it would also shift the excitation threshold to a lower velocity.