Dynamic nonlinear screening of slow ions in an electron gas

We have used the ensemble Kohn-Sham method with the local-density approxima tion to determine self-consistently the dynamic screening cloud around an i mpurity moving adiabatically through a uniform electron gas with velocity b elow the Fermi velocity. The asymmetry of the induced field and electronic density caused by the impurity motion is fully taken into account. We discu ss the forward-backward asymmetry for the case of bare positive and negativ e charges as well as for hydrogen atoms. We show that the stopping power of the electron gas varies linearly with the projectile velocity up to veloci ties close to the Fermi velocity. We study the asymmetry of the bound state s, its contribution to the stopping power and the evolution of the binding energy as a function of projectile velocity. Finally, we give a complete de rivation of the low energy behavior of the stopping power and the generaliz ation of the Friedel sum rule and oscillations for the case of moving impur ities. [S0163-1829(99)03104-5].