Thermal attenuation in atom-surface scattering : the two phonon contribution

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Abstract
The specular intensity produced by the scattering of monoenergetic incident particles by a flat surface is calculated as a function of the crystal temperature including one and two virtual phonon processes. The exact procedure developed previously [1, 2] is employed in order to get the matrix elements of the seven different two phonon diagrams. For all the different systems studied (He-Cu, H2-Cu, Ne-Cu) the results show that the most efficient two-phonon term is the diagram of highest order in the perturbation expansion. The total intensity is greater than that obtained by considering the one phonon process alone except at very low crystal temperature. The temperature for which the two phonon contribution becomes non-negligeable is in general low. Comparison with available experimental data gives good agreement in the temperature domain where higher order phonon processes could be neglected