Impurities in jellium

Recently, x-ray absorption spectra of halide and rare-gas impurities in alkali metals have been measured. We study these systems by treating the alkali metal as jellium with a spherical cavity in which the halide or rare-gas impurity is placed. We use the density functional formalism with self-interaction corrections to find self-consistent solutions for the ground states and the states with a core hole. Specifically, we study ${\mathrm{F}}^{-}$ in Na, ${\mathrm{F}}^{-}$ in K, and Ne in K. We present charge densities and self-consistent potentials for these systems. We are able to find a self-consistent solution for both the ground state and the core hole state only for ${\mathrm{F}}^{-}$ in Na. For ${\mathrm{F}}^{-}$ in Na we calculate the exponent ${\alpha }_0$ which describes the many-body enhancement of the spectrum near the edge, and find that it confirms the experimental observation that the enhancement is small. We did not calculate the exponent ${\alpha }_0$ for Ne in K because we were unable to determine a self-consistent ground state for Ne in K. We consider one possible reason for our not finding a self-consistent ground state and discuss the possible relevance of this difficulty to understanding the large rounding seen in the x-ray edge spectra of rare-gas impurities in alkalis.