Semiclassical theory of atom-surface inelastic scattering

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Abstract
A non-perturbative theory of the movement of an atom interacting with a solid substrate is constructed in which substrate excitations (phonons, electron-hole pairs) are described quantum-mechanically. Starting from a path-integral formulation of the transition probability, substrate coordinates are integrated out and the influence of substrate degrees of freedom is expressed through a functional of the atom path, which is calculated in various models. A stationary exponent argument leads to an equation of motion which has a real solution, representing some « average » or « classical » path, and complex solutions resulting in different energy exchange owing to quantum and thermal fluctuations of the solid. The corresponding transition probability is calculated by a Gaussian approximation of the path integral. Various boundary régimes, including the slow régime, are examined The method applies to sticking as well as backscattering. It might be of special interest when inelastic effects are too strong to allow the use of an approximation of the trajectory either by an unperturbed one or even by an average one, for instance in the presence of an important sticking probability