Theoretical analysis of neutron scattering spectra of ⁴He films on graphite

We compare microscopic calculations of the dynamic structure function of helium films adsorbed to a graphite substrate with neutron scattering data. Starting from a generalized Feynman theory of collective excitations, we include successively, three-phonon interactions, self-energy corrections, and experimental broadening and thereby improve the agreement between theoretical predictions and experiments. The inclusion of three-phonon vertices allows high-lying excited states to decay into lesser energetic ones and thus leads to a natural linewidth. It is shown that the theoretical linewidth of the excitations is typically smaller than the experimental resolution, and that much structure of the spectrum in the neutron scattering data is obscured under a broad plateau between the ripplon and the phonon excitations. This analysis leaves little doubt of the existence of layer-phonons and that the observed shoulder in the dynamic structure function, near the roton minimum, is actually a 2D roton propagating in the inner-most liquid layer.