Static response of a jellium surface: The image potential and indirect interaction between two charges

Abstract

We present detailed numerical results for the energy of interaction between a static charge and a jellium surface and for the total energy of interaction between two static charges placed in the surface region. In the latter case we obtain some novel results showing the disappearance of the bulk oscillatory behavior in the total interaction energy as the two charges are brought from inside the metal surface and placed outside the jellium edge. Both response calculations are performed by first computing the static electron-density response function in the random-phase approximation. The response function for noninteracting electrons (the irreducible part of the linear response) is obtained on the basis of a computational method that renders the eigenfunctions ${\psi }_{\nu }\left(\overrightarrow{\mathrm{x}}\right)$ of the Kohn-Sham equations of a jellium slab in semianalytical form. This method consists of expanding the dependence of ${\psi }_{\nu }\left(\overrightarrow{\mathrm{x}}\right)$ on the coordinate normal to the jellium surfaces in a sine series and solving a nonlinear matrix version of the Kohn-Sham self-consistent problem.