We study the scattering of atoms and quasiparticles at the surface of
He-4 at T=0 K. Using the microscopic theory of Beliaev in areal-space
formulation we derive an equation of motion for the quasiparticles val
id in bulk helium, through the surface and in the vacuum. Assuming nor
mal incidence, we solve the equation and calculate probabilities for t
he various surface scattering processes for a range of energies (betwe
en 7.5 and 15 K). Some of the scattering rates obtained are markedly d
ifferent from those reported recently.