  We study the scattering of atoms, rotons and phonons at the free surface of
$^4$He at normal incidence and calculate the evaporation, condensation and
reflection probabilities. Assuming elastic one-to-one processes and using
general properties of the scattering matrix, such as unitarity and time
reversal, we argue that all nonzero probabilities can be written in terms of a
single energy-dependent parameter. Quantitative predictions are obtained using
linearized time dependent density functional theory.
