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.

We present a full-potential multiple scattering (FPMS) scheme for the interpretation of several x-ray spectroscopies that is a straightforward generalization of the more conventional muffin-tin version. Like this latter, it preserves the intuitive description of the physical process under consideration and overcomes some of the limitations of the existing FPMS codes. It hinges on a fast and efficient method for solving the single-cell scattering problem that avoids the convergence drawbacks of the angular momentum expansion of the cell shape function; it relies on an alternative derivation of the multiple scattering equations that allows us to work reliably with only one truncation parameter, i.e., the number of local basis functions in the expansion of the global scattering function determined by the classical relation $l_{\max }\sim kR$.