Time-dependent density-functional theory for the stopping power of an interacting electron gas for slow ions

Based on the time-dependent density-functional theory, we have derived a rigorous formula for the stopping power of an interacting electron gas for ions in the limit of low projectile velocities. If dynamical correlation between electrons is not taken into account, this formula recovers the corresponding stopping power of non-interacting electrons in an effective Kohn-Sham potential. The correlation effect, specifically the excitonic one in electron-hole pair excitations, however, is found to considerably enhance the stopping power for intermediately charged ions, bringing our theory into good agreement with experiment.