Zone edge focused two-phonon processes in He atom scattering from a   simple prototype system: Xe(111)
  We present a theoretical analysis of the multiphonon features appearing in the angular and energy resolved scattering spectra of low energy He atoms inelastically scattered from surface phonons. By applying the recently developed fully quantum multiphonon scattering formalism to the benchmark system Xe(111) we are able to reproduce with great accuracy the experimental data and also demonstrate how in the transition from a single- to a few- to a multiphonon scattering regime the one- and the many-phonon components of the scattering spectra evolve as the mean number of exchanged phonons increases with the increase of He atom incident energy. We show how the two-phonon processes may give rise to distinct peaks in the scattering spectrum as a result of the zone edge focusing effects and how the many-phonon features may still produce a structured background before the true multiphonon limit characterised by a Gaussian spectral shape is reached. These findings should prove useful in the interpretation of multiphonon He atom scattering spectra from other systems with similar surface vibrational properties. 
Antonio Siber and Branko Gumhalter