  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.
