Inelastic scattering from surfaces

A treatment of inelastic scattering of low-energy probes from surfaces is developed that bridges the gap between the zero- and single-quantum regime and the multiquantum regime. Observations of the multiphonon background directly give the form factor of the unit cell, which in turn provides information on the interaction potential. A semiclassical limit is extracted in which the differential reflected intensity appears as the product of a form factor for scattering from a unit cell, a Debye-Waller factor, a structure factor, and an energy exchange factor. This is compared with previously developed semiclassical scattering approximations. Good agreement is obtained with recently measured multiphonon backgrounds in the scattering of He by alkali halide and metal surfaces over a large range of surface temperatures and incident conditions. The comparisons with experiment demonstrate the rather large difference in interaction potentials between He scattering from an alkali halide and a metal surface.