Screening of a proton in an electron gas

Abstract

Calculations are reported of the nonlinear screening of a proton in an electron gas of densities corresponding to ${r}_{s}=1\ensuremath{-}6$. Results for charge densities and total energies are presented from self-consistent Kohn-Sham ground-state calculations. The results differ markedly from the case of linear screening, particularly at low densities. The occurrence of a bound state around the proton for ${r}_{s}>1.9$ indicates that hydrogen in jellium is in the form of a screened ${\mathrm{H}}^{\ensuremath{-}}$ ion. It is also found that at metallic densities the induced polarization around the proton is insensitive to ${r}_{s}$, and the screening length is almost constant (0.65) for $2<{r}_{s}<6$.