  The scattering of atoms and rotons at the free surface of superfluid 4He is
studied in the framework of linearised time dependent mean field theory. The
phenomenological Orsay-Trento density functional is used to solve numerically
the equations of motion for the elementary excitations in presence of a free
surface and to calculate the flux of rotons and atoms in the reflection,
condensation, and evaporation processes. The probability associated with each
process is evaluated as a function of energy, for incident angles such that
only rotons and atoms are involved in the scattering. The evaporation
probability for R+ rotons is predicted to increase quite rapidly from zero,
near the roton minimum, to 1 as the energy increases. Conversely the
evaporation from R- rotons remains smaller than 0.25 for all energies. Close to
the energy of the roton minimum the mode-change process is the dominant one.
The consistency of the results with general properties of the scattering
matrix, such as unitarity and time reversal, is explicitly discussed. The
condensation of atoms into bulk excitations is also investigated.
