We have investigated the collision between He-atoms and the xe(root 3x
root 3)R30 degrees overlayer on Cu(111) under the conditions in which
multiple phonons of the Einstein-like, vertically polarized Xe-vibrat
ion are excited and annihilated. The measurements are compared to theo
retical results which were obtained using a recently developed formali
sm for calculating the multiphonon scattering spectra in the collision
regimes in which both the motion of the scattered particle and surfac
e vibrations must be treated quantum-mechanically. The energy and late
ral momentum resolved scattering spectra are expressed in the form of
a cumulant expansion in terms of uncorrelated and correlated phonon ex
citation amplitudes and the correlated ones can be neglected under the
scattering conditions typical of He atom scattering. By introducing t
he one phonon interaction parameters into the obtained expressions we
can calculate the multiphonon scattering spectra which are in a good a
greement with the experimental data.