Theory of inelastic atom-surface scattering: Average energy loss and energy distribution

Theoretical results for the energy distributionP() of atoms scattered by solid surfaces are presented. An exact expression for the first moment (the average energy loss) ofP() is derived involving the force-force correlation of the scattering particle and the susceptibility of the lattice. An approximate result forP() is derived in which the same two quantities occur. The forces are treated statically (i.e. neglecting the response of the lattice) and semiclassically (i.e. neglecting their noncommutativity). Quantum effects of the lattice are taken into account properly. No approximations are made concerning the number of excited phonons. An expression for the reduction of elastic scattering due to inelastic processes (generalized Debye-Waller factor) is found containing the dynamic and finite size effects discussed in the literature.