Optical potential and escape depth for electron scattering at very low energies

Electron spectroscopy at low kinetic energies, e.g., valence band photoemission with vacuum ultraviolet light, is sensitive to the fine structure of the electron damping, i.e., to the magnitude and energy dependence of the optical potential. The basis of this quantity is usually given by a semiquantitative analytical derivation together with empirical findings from the escape depth. Only recently the optical potential has been determined ab-initio via calculating the self-energy. Here, this approach is used to calculate the self-energy and from this the wave functions in the conduction band regime with scattering boundary conditions for the surface system. For the former, the GW approximation is applied. For the latter, algebraic solvers in the Laue representation have been used to solve the Schrodinger equation for arbitrary potentials. The wave function is investigated to extract physical quantities, like the angle and energy dependent escape depth, which are significant in discussing electron scattering.