ar X iv : c on d - m at / 9 50 51 21 v 1 2 5 M ay 1 99 5 Rotons and Quantum Evaporation from Superfluid 4 He

The probability of evaporation induced by R+ and R rotons at the surface of superfluid helium is calculated using time dependent density functional theory. We consider excitation energies and incident angles such that phonons do not take part in the scattering process. We predict sizable evaporation rates, which originate entirely from quantum effects. Results for the atomic reflectivity and for the probability of the roton change-mode reflection are also presented. PACS number: 67.40.-w, 67.40.Db Typeset using REVTEX 1 Quantum evaporation occurs in superfluid He when a high-energy phonon or roton propagates to the surface where it annihilates and an atom is ejected in the free space (see, for example, Ref. [1]). This phenomenon is especially interesting because of the peculiar dispersion law exhibited by rotons. Despite the significant experimental [2–8] and theoretical [9–14] efforts made in the last years, the fundamental mechanisms underlaying the phenomenon of quantum evaporation are not yet understood. The experiments by Wyatt and co-workers [1,5,6] have revealed that the main process is a one to one process (one excitation to one atom). This behavior is confirmed by the separate conservation of the energy and of the momentum parallel to the surface in the evaporation process. In contrast measurements of atom condensation [15] have instead pointed out the importance of non linear processes associated with the excitation of ripplons. The theoretical studies have not yet provided a clear and consistent picture of quantum evaporation. The reason is that it is very difficult to develop a reliable description of this phenomenon on a microscopic basis. In fact a good theory should be able to account for several effects: • (i) a correct description of the structure of the free surface, as well as of the elementary excitations of the system; • (ii) a quantum description of the scattering processes involving the elementary excitations at the surface; • (iii) the inclusion of inelastic channels (multi-phonons, multi-ripplons). A useful discussion concerning the role of quantum effects has been recently made in Refs. [13,14] where it has been pointed out that, due to the peculiar form of the maxon-roton dispersion exhibited by superfluid helium, there are severe constraints on the structure of the classical orbits associated with the elementary excitations when they cross the interface. In particular one finds that only phonons and rotons above the maxon energy (about 14 K) can