Hydrogen and 3He atoms on 4He 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 (3)He impinging on the surface of liquid (4)He at arbitrary angles. For that purpose, we first calculate the ground state of H and (3)He on the surface of liquid (4)He. We obtain for H a binding energy of about 1 K in good agreement with experiments, and calculate the deformation of the (4)He 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 (4)He film and off ripplons of the free (4)He surface, respectively. In both cases, we obtain an E(2) 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.