Many-body theory of inelastic electron scattering from adsorbate vibrations

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Abstract
The theory of one-quantum inelastic electron scattering from adsorbate vibrations is developed using field theoretical methods. The relevant S-matrix element is expressed in terms of a mixed boson-fermion Green function. This matrix element is shown to involve one-particle amplitudes (LEED wavefunctions), and the functional derivative with respect to an external potential of the electron self-energy for fixed nuclei. If the self-energy is local in time, a simple formula is obtained from which numerical calculations can be made with roughly the same labour as for angle-resolved photoemission. The limitations of the muffin-tin potential for this work, particularly the absence of the long-range dipole potential, are discussed.