A model Hamiltonian for phonon energy transfer in gas—solid collisions

Abstract

Using the formalism of second quantization in the occupation number representation, a model Hamiltonian of the form H = H loc + H nonloc + H loc− nonloc is developed. H loc describes the gas atom-phonon system when the gas atom is near the surface, and the phonon operators are only in this term. H nonmloc describes the gas atom moving in a static potential with no bound states, and H loc-nonloc couples these two parts of H. The method of solution is to diagonalize H loc and then to embed it in the continuum of scattering states of H nonloc. The model is designed so that this diagonalization can be performed essentially exactly for a large class of gas-metal systems. The procedure is illustrated with a simple example which nevertheless shows how multi-phonon processes can dominate in desorption.