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The effects of the phonon structure of a Cu(100) surface on the elastic scattering probabilities are considered for D₂ and He at low energies and temperatures. The calculation is based on iteratively solving the Schr\"odinger equation for the scattering of a particle from a flat surface with the Born approximation for the self-energy as a nonlocal and energy-dependent optical potential. The phonon contribution to this self-energy has been evaluated by performing surface lattice dynamics of a semi-infinite Cu(100) crystal.
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Mats Persson (1987) studied this question.
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