Quantum Sticking, Scattering, and Transmission ofH4eatoms from SuperfluidH4eSurfaces

We develop a microscopic theory of the scattering, transmission, and sticking of ${}^4\mathrm{He}$ atoms impinging on a superfluid ${}^4\mathrm{He}$ slab at near normal incidence, and inelastic neutron scattering from the slab. The theory includes coupling between different modes and allows for inelastic processes. We find a number of essential aspects that must be observed in a physically meaningful and reliable theory of atom transmission and scattering; all are connected with multiparticle scattering, particularly the possibility of energy loss. These processes are (a) the coupling to low-lying (surface) excitations (ripplons/third sound) which is manifested in a finite imaginary part of the self-energy, and (b) the reduction of the strength of the excitation in the maxon/roton region.