First-principles study of inner-electron excitation of tungsten under proton and helium ion irradiation

Real-time time-dependent density functional theory (RT-TDDFT) combined with Ehrenfest molecular dynamics (EMD) is employed to study the electronic stopping power of tungsten for protons and helium ions over a wide range of ion energies. The microscopic mechanism of inner-electron excitation (including $4f$ and $5p$ electrons) in tungsten is investigated. In the low-velocity regime, our nonequilibrium simulations showed that the electronic stopping power of protons is linear with velocity, while that of helium ions deviates from the velocity proportionality due to more pronounced excitation of inner electrons. As the velocity of protons and helium ions increases, not only the contribution of $4f$-electron excitation to the electronic stopping power is verified to be significant, but also the contribution of $5p$-electron excitation is required, especially for an accurate description of the stopping maximum of tungsten. In order to provide insight into the relationship between inner-electron excitation and energy loss, the population of electron-hole pairs generated by the electron excitation is calculated. The total number of holes induced by helium ions is found to be four times as large as that induced by protons in the middle- and high-velocity regime, which is in line with the stopping ratio between helium ions and protons. The contribution of inner-electron excitation to electronic stopping power is quantitatively evaluated for both protons and helium ions. It illustrates that the inner-electron excitation is more significant for helium ions compared to protons at ion velocities below 3.0 a.u., in which the projectile ions cannot be treated as fully ionized. Given that energetic holes are crucial for the energy loss at high velocities, the energy distribution of the holes is also obtained. This distribution demonstrates that the majority of holes move towards deeper energies as the projectile velocity increases.