Electronic structure of hydrogen in simple metals

Abstract

Based on the Hohenberg-Kohn-Sham formalism a fully self-consistent calculation of the electron density distribution around a proton in the metallic density range is presented. The calculation takes into account the first gradient correction to the exchange-correlation potential, hitherto treated only in the local density approximation. Very shallow bound states are found to exist for all metallic densities ($r_s=2.07-5\mathrm{}$) considered. The physical picture regarding the electronic structure of a proton in the metallic density range is that of an extended ${\mathrm{H}}^{-}$ ion accompanied by an equally extended compensating hole in the uniform electron gas. Assuming that a positive muon (${\mu }^{+}$) constitutes a heavy impurity in an electron gas, the Knight shift at ${\mu }^{+}$ site as a function of electron density ($r_s$) has also been calculated and the results are compared with experiment.