Contribution of f -electron excitation to electronic stopping power of platinum for protons

Abstract

The electronic stopping power of protons traveling along the channeling and off-channeling trajectories in platinum (Pt) is reported based on time-dependent density functional theory calculations for electrons combined with Ehrenfest molecular dynamics simulations for ions in real time and real space. We provided an intuitive description of the electronic stopping power for a wide range of ion energies, and revealed the excitation mechanism for the inner $4f$ electrons of Pt. The comparison of calculation results with experimental data showed that conduction electrons are sufficient to describe the electronic stopping power of Pt accurately in the low-energy range. The excitation of $4f$ electrons contributes substantially to the electronic stopping power of Pt as the proton velocity exceeds 1.0 a.u. 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, the velocity dependence of the mean steady-state charge of protons was quantified, and the results showed that the instantaneous charge state of protons exhibits periodic oscillations in the low-energy region, while the periodic oscillations disappears in the high-energy region due to more ionization of protons.