Quantum-mechanical treatment of the one-phonon inelastic scattering of gas atoms in three dimensions by a simplified continuum model of a solid

Abstract

A quantum-mechanical treatment of the one-phonon inelastic scattering of gas atoms in three dimensions by a solid surface is presented. Three major approximations made in the calculations are (i) the method of Cabrera, Celli, Goodman and Manson [Surface Science 19 (1970) 67] is used to calculate the relevant transition probabilities, (ii) atoms near the surface of the solid are treated at first as though they were in the bulk, although the fact that surface atoms differ dynamically from bulk atoms is taken into account later in a simple way, and (iii) the gas-surface interaction is represented by a potential which consists of an infinite repulsive step with zero well-depth, thus eliminating the possibility of bound states of gas atoms at the surface. The theory is a generalization to three dimensions of the one-dimensional theory reviewed by F.O. Goodman [Surface Science 24 (1971) 667]. Some of the problems associated with comparing any such theory with experiment are discussed in some detail, and, for the system HeAg, comparisons are made with experimental scattering distributions and speed measurements of the type reported by R. B. Subbarao and D. R. Miller [J. Chem. Phys. 51 (1969) 4679]. With a (bulk) Debye temperature of 226 K for Ag, satisfying qualitative agreement between theory and experiment is found.