Abstract
A quantum mechanical theory is presented for the scattering of atoms from a crystal surface. The surface is represented by a moving, infinitely repulsive potential. A formal theory is presented which enables the scattering cross section to be evaluated, in principle, to all orders in the surface displacement. This is illustrated by evaluating the one-phonon scattering for He on Ag, showing that the experimental results cannot be explained by these one-phonon terms.