Semiclassical Theory of Inelastic Scattering: An Infinite-Order Distorted-Wave Approximation

A previously derived semiclassical theory of inelastic scattering is generalized to include collisions where the trajectory is nonlinear. Schrödinger's equation is expressed as an infinite-order perturbation series using the radial wavefunctions corresponding to the spherically symmetric part of the potential as the unperturbed solution. In the classical limit this series simplifies, and the scattering matrix is obtained by exponentiating a phase shift matrix which is obtained as a simple integral over the classical trajectory corresponding to the spherically symmetric part of the potential. A second-order term is obtained to correct for the deviation from this trajectory.