Theory of atomic scattering at the free surface of liquidHe4

Abstract

The scattering of free helium atoms at the surface of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at zero temperature is discussed in terms of the Feynman variational method. If the scattered atom is distinguishable from those in the liquid target, as is true for the scattering of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, the problem reduces to the motion of a single particle in an effective potential. Above the surface the effective potential is the same as the real van der Waals potential and, in the surface and below, it is related to the density and kinetic-energy distribution in the liquid ground state. If the theory is applied to the scattering of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, neglecting the indistinguishability of the scattered atom, an excellent fit to the experimental reflection coefficient is obtained. When the trial wave function is fully symmetrized to calculate the reflection coefficient for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ more realistically, the theory describes the production of a single excitation (phonon) from each absorbed atom. The resulting reflection coefficient disagrees with experiment, predicting total reflection at certain critical angles. Even when multiple production of low-energy phonons is considered, total reflection will still occur. It follows that the multiple production of some other type of excitation, in particular low-energy ripplons, must be a dominant process in agreement with the calculations of Echenique and Pendry. It seems that the simple unsymmetrized theory fits the data because the reflection coefficient is mainly determined by the static van der Waals potential outside the liquid where the effects of symmetry, inelastic scattering, etc., are negligible. An atom which penetrates below this region is then effectively lost as far as the original beam is concerned because it begins to produce low-energy ripplons and is incoherently scattered. The problem of determining the density profile at the liquid surface from the experimental scattering data is briefly considered.