Long-range scattering of electrons by phonons at metal surfaces

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Abstract
We examine the inelastic scattering of electrons by phonons at metal surfaces. A dielectric-function formulation for calculating the loss probability is first summarized. Then, using the Bohm-Staver description of a metal's response, we derive formulas for the spectra of single-phonon losses near the specular electron beam. Both bulk and surface phonons contribute. Finally, we compare the thermal diffuse scattering predicted in our model to that due to impact scattering. The former can dominate the latter at low incident-electron energies.