  We calculate the inelastic scattering probabilities in the wide band limit of
a local polaron model with quadratic coupling to bosons. The central object is
a two-particle Green function which is calculated exactly using a purely
algebraic approach. Compared with the usual linear interaction term a quadratic
interaction term gives higher probabilities for inelastic scattering involving
a large number of bosons. As an application we consider the problem hot
electron mediated energy transfer at surfaces and use the delta self-consistent
field extension of density functional theory to calculate and compare coupling
parameters and probabilities for exciting different vibrational modes of CO
adsorbed on a Cu(100) surface.
