Temperature dependence in atom-surface scattering

It is shown that a straightforward measure of the temperature dependence of energy resolved atom-surface scattering spectra measured under classical conditions can be related to the strength of the surface corrugation. Using classical perturbation theory combined with a Langevin bath formalism for describing energy transfer, explicit expressions for the scattering probabilities are obtained for both two-dimensional, in-plane scattering and full three-dimensional scattering. For strong surface corrugations results expressed as analytic closed-form equations for the scattering probability are derived which demonstrate that the temperature dependence of the scattering probability weakens with increasing corrugation strength. The relationship to the inelastic rainbow is briefly discussed.