Zone edge focused two-phonon processes in He atom scattering from a simple prototype system: Xe(1 1 1)

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(1 1 1) 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.