Self-consistent optical potential for atoms in solids at intermediate and high energies

We develop an approximation for the optical potential in a solid valid at intermediate and high energies, say, energies from 50 eV and larger. The approximation builds on the GW expression. We separate the random phase approximation polarization propagator in a core electron and a valence electron part, and then have a corresponding separation of the optical potential. For the valence electron optical potential we use a local density approximation because the charge density changes fairly slowly, whereas we use a nonlocal optical potential for the core electron part. We apply this method to electron-Ar and -Kr elastic scattering, and also to electron scattering from atoms in van der Waals solids, semiconductors, and metals. We find satisfactory agreement with the observed results. We also study the importance of using a nonlocal potential for the core part and the sensitivity to a parameter, the average excitation energy. We compare the present results with those calculated by the Hartree-Fock, Dirac-Hara, and Hedin-Lundqvist potentials. The Hedin-Lundqvist potential is rather good for the description of large-angle scattering, whereas none of the local potentials can describe small-angle scattering well.