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We develop a multidimensional coupled channel method suitable for studying the interplay of bound state resonance and phonon assisted scattering of inert gas atoms from solid surfaces in one, two and three dimensions. This enables us to get insight into the features that depend on the dimensionality of inelastic resonant processes typically encountered in low energy He atom scattering from surfaces, in general, and to elaborate on the observability of recently conjectured near threshold resonances in scattering from Einstein phonons, in particular.

One derives simple and exact expressions for the leading quantum corrections to the angular and energy distributions of an atom scattered inelastically from a solid crystalline surface. The quantum corrections are given in terms of classical trajectories and equilibrium correlation functions for the solid surface. Our results are useful when the incident atom has an energy of about 1 electron volt and the surface has a temperature less than or comparable to the Debye temperature.

Consider an atom scattered inelastically from a surface and derive a formula for the exact semiclassical limit of the expectation value of an arbitrary, smooth function of the scattered atom's final momentum. The formula expresses this semiclassical limit in terms of equilibrium correlations for the atoms which compose the surface and quantities which can be calculated from classical scattering trajectories. We give numerical results for a simple one- dimensional example and compare these results with those given by the trajectory approximation. Keywords: Classical scattering trajectories, Trajectory approximation, Atomic scattering.

A calculation of the inelastic scattering rate of Xe atoms on Cu(111) is presented. We focus in the regimes of low and intermediate velocities, where the energy loss is mainly associated to the excitation electron-hole pairs in the substrate. We consider trajectories parallel to the surface and restrict ourselves to the Van der Waals contribution. The decay rate is calculated within a self-energy formulation. The effect of the response function of the substrate is studied by comparing the results obtained with two different approaches: the Specular Reflection Model and the Random Phase Approximation. In the latter, the surface is described by a finite slab and the wave functions are obtained from a one-dimensional model potential that describes the main features of the surface electronic structure while correctly retains the image-like asymptotic behaviour. We have also studied the influence of the surface state on the calculation, finding that it represents around 50% of the total probability of electron-hole pairs excitation.