Microscopic theory for quantum evaporation from a superfluid surface

Abstract

Beliaev’s microscopic theory of superfluidity in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is applied to an inhomogeneous system with a free surface. The equations of motion are analyzed within a local-density approximation and a set of WKB solutions are found. Perturbation theory is used to provide the mixing between these states. The probabilities for evaporation, reflection, and adsorption from the surface are calculated for excitations in the system. The probabilities for the evaporation of phonons and rotons are in reasonable agreement with experiment. We find that low-energy incident atoms tend to condense as phonons and high-energy atoms condense as ${\mathit{R}}^{+}$ rotons. These results are again in qualitative agreement with experiment, provided that the short lifetimes of phonons with energies