Noble-gas-solid-surface beam-scattering spectroscopy in the eV range. Nuclear channel, formal theory

We discuss the use of high-energy beams (i.e., in the eV range) of heavy noble-gas atoms to study surface dynamics for relatively high energy and momentum loss in both the nuclear and electronic channels. We give a general formulation of this problem for the nuclear channel, which can be generalized to include the electronic channel. The reflection probability is evaluated using the path-integral notation and applying semiclassical methods (stationary-phase approximation) on a multiple integral corresponding to a perturbationlike form of the reflection probability amplitude. The final form is locally similar to that predicted by the "rippling mirror" model (i.e., the dynamical Kirchhoff approximation), provided that the impulse approximation for the gas-surface dynamics holds. This similarity becomes global if the amplitude of the surface corrugation is much larger than the effective range of the gas-solid forces in the vicinity of the solid termination. The calculational procedure suggested by this formulation is tractable and is general enough to include anharmonic excitations such as desorption, structural damage, or low-energy sputtering as well as harmonic excitations (i.e., multiphonon excitations).