Effect of Lattice Vibrations in a Multiple-Scattering Description of Low-Energy Electron Diffraction. I. Formal Perturbation Theory

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Abstract
A diagrammatic version of perturbation theory is developed for the description of the influence of lattice vibrations on the elastic and inelastic scattering cross sections of low-energy electrons from surfaces of single-crystal solids. The formalism describes the effects on the cross sections of a thermodynamic-equilibrium distribution of both bulk and surface phonon modes. The relationships between our general formalism and the conventional single-scattering analysis of inelastic electron-solid scattering are displayed. Multiple-scattering and virtual-phonon emission from a given ion core are included in the theory via vertex renormalizations of the electron-ion-core scattering vertices. Propagator renormalization is estimated to be small and consequently neglected. The diagrammatic contributions to the elastic scattering cross section are summed explicitly using the approximation that diagrams with internal phonon propagators are small relative to those without such propagators. In this approximation we obtain a set of coupled integral equations for appropriately renormalized scattering amplitudes describing elastic electron scattering from planar layers of ion cores.