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.
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