Ground- and excited-state scattering potentials for the stopping of protons in an electron gas

The self-consistent electron-ion potential V(r) is calculated for H+ ions in an electron gas system as a function of the projectile energy to model the electronic stopping power for conduction-band electrons. The results show different self-consistent potentials at low projectile-energies, related to different degrees of excitation of the electron cloud surrounding the intruder ion. This behavior can explain the abrupt change of velocity dependent screening-length of the potential found by the use of the extended Friedel sum rule and the possible breakdown of the standard free electron gas model for the electronic stopping at low projectile energies. A dynamical interpolation of V(r) is proposed and used to calculate the stopping power for H+ interacting with the valence electrons of Al. The results are in good agreement with the TDDFT benchmark calculations as well as with experimental data.