Electronic stopping power in titanium for proton and helium ions from first-principle calculations

The energy loss rate from energetic proton and helium ions to electrons of a transition metal titanium (Ti) is studied using real-time time-dependent density functional theory. Nonequilibrium simulations with and without semicore electrons explicitly included in describing the electronic structure of target atoms are performed to understand their involvement in the dissipation mechanism. It is found that the low-lying $3s$ and $3p$ semicore excitations play significant roles in determining the profile of the stopping curve around and above the stopping maximum. Additionally, we investigate the effect of impact geometry on electronic stopping. An important conclusion is that although off-channeling geometry, which makes possible the strong interaction with tightly bound electrons, indeed improves the amplitude of the stopping curve, especially for the regime around the stopping maximum, it does not shift the position of the stopping maximum. Our results about the relation between effective charge and electronic stopping are in qualitative agreement with the linear response theory.