Scattering of atomic beams by surface and bulk phonons

The general expressions obtained in a previous work are further developed to get general formulae for one-phonon scattering of atomic beams in closed form. The scattering by bulk and surface phonons are discussed separately and the respective scattered energy spectra and behaviour near the Bragg angles are carefully treated. Interesting differences are found, which may have experimental importance in separating events of scattering from different modes. The expressions for the inelastic scattering differential cross-sections obtained are applied to the experiment by Williams et al. on the He/NaF(001) system. Despite the use of estimated values for the unknown parameters, a good quantitative agreement with the experiment is obtained, and the structure observed by Williams near the specular peak is clearly explained. The contribution of transverse bulk modes is found to be about 30% of that of transverse surface modes. The contribution of longitudinal modes in smaller than the contribution of the respective transverse modes by a factor 0.01.