  The surface phonon dispersion curves of commensurate Xe monolayers on Cu(111)
and incommensurate Xe monolayers on Cu(001) surfaces have been measured using
He atom scattering (HAS) time of flight (TOF) spectroscopy. The TOF spectra are
interpreted by combining quantum scattering calculations with the dynamical
matrix description of the surface vibrations. Both a vertically polarized
Einstein-like mode and another, acoustic-like mode of dominantly longitudinal
character, are identified. The latter mode is characterized by the presence and
absence of the zone center frequency gap in the commensurate and incommensurate
adlayers, respectively. The microscopic description of the TOF spectral
intensities is based on the extensive theoretical studies of the interplay of
the phonon dynamics, projectile-surface potentials, multi-quantum interference
and projectile recoil, and their effect on the HAS spectra. Both single and
multi-quantum spectral features observed over a wide range of He atom incident
energies and substrate temperatures are successfully explained by the theory.
