Quantum theory of sticking: equivalence of various approaches and application to a simple model

The basic formulae of four different quantum mechanical approaches to the calculation of the sticking coefficient of an atom on a cold solid are re-examined in order to discuss the connections between them. All approaches pursued exactly give the same result, and this is exhibited for a one-dimensional model which is exactly solvable to provide closed-form formulae for the sticking coefficient. Numerical results, which reproduce the qualitative behaviour of atomic sticking, are presented for different assumed densities of substrate excitations responsible for the energy loss, including the physically important cases of low-energy single phonons, and low-energy electron-hole pairs in a metal.