Hydrogen and He3 atoms on He4 surfaces: Bound states and scattering features

We develop a microscopic theory of atom scattering from inhomogeneous quantum liquids. Methods developed previously for elastic atom scattering and sticking are extended to describe transport currents and inelastic processes. The theory is applied to examine scattering processes of atomic hydrogen and He3 impinging on the surface of liquid He4 at arbitrary angles. For that purpose, we first calculate the ground state of H and He3 on the surface of liquid He4. We obtain for H a binding energy of about 1 K in good agreement with experiments, and calculate the deformation of the He4 background and impurity-background distribution functions. The angular distribution of the outgoing particle currents generated by inelastic processes is calculated. We pay special attention to the case of small deflection angles as well as to low-energy scattering off third sound modes of the He4 film and off ripplons of the free He4 surface, respectively. In both cases, we obtain an E2 law for the total direct inelastic scattering probability. Since the self-energy ("optical potential") obtained in our approach is consistent with unitarity, the sticking probability can be calculated using the results for elastic and inelastic scattering. We also investigate the sensitivity of our low-energy results to the long-ranged van der Waals potential of the substrate and to the film thickness.