Screening of a proton in an electron gas

Calculations are reported of the nonlinear screening of a proton in an electron gas of densities corresponding to $r_s=1-6\mathrm{}$. 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 $r_s>1.9\mathrm{}$ indicates that hydrogen in jellium is in the form of a screened ${\mathrm{H}}^{-}$ 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 $2<\mathrm{}{r}_s<6\mathrm{}$.