Quantum evaporation from the free surface of superfluid 4He

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 (phonon forbidden region). The evaporation probability for R+ rotons (positive group velocity) is predicted to increase quite rapidly from zero, near the roton minimum, to 1 as the energy increases. Conversely the evaporation from R- rotons (negative group velocity) remains smaller than 0.25 for all energies. Close to the energy of the roton minimum, Δ, the mode-change process R+ ↔ R- 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. The condensation probability is almost 1 at high energy in agreement with experiments, but it lowers significantly when the energy approaches the roton minimum in the phonon forbidden region