Model for handling the transmission problem in sticking at cold solid surfaces

The sticking rate is calculated for a simple model Hamiltonian, which assumes a one-dimensional motion of the incident gas atom together with a one- to three-dimensional phonon density of states. The gas-atom-phonon interaction is of short range and treated in a localized basis set. After solving exactly for this short-range interaction the localized wave functions are embedded into the continuum of scattering states. This embedding problem is solved in an approximate way. The calculated sticking coefficient at zero kinetic energy of the incoming particle and zero substrate temperature is unity for a two- and three-dimensional phonon density of states, and finite between zero and one for a one-dimensional phonon density of states. Many phonon events are found to dominate the sticking process.