Improvements to the Trajectory Approximation in Atom-Surface Scattering

Abstract

We consider atom-phonon scattering in a one-dimensional model with coupling linear in phonon displacements and calculate the probability p(E) of the atom-losing energy E as a Fourier transform of a time function π(α). Employing a path integral formulation, and taking the limit of zero de Broglie wavelength of the atom, non-perturbational corrections to the Trajectory Appromixation are obtained as a series in one upon atom mass m. The 1/m terms give rise to a-dependent trajectories, which are shown to be consistent with the TA energy transfer, and lead to energy gain for a slow-particle on a hot surface.