PATH INTEGRAL METHODS FOR INELASTIC-SCATTERING

Corrections to the primitive semi-classical amplitude for multiple inelastic scattering are obtained from a path integral formulation of scattering theory. The path integrals are calculated by making an expansion about a classical orbit describing elastic scattering. Terms are collected to give a series in inverse powers of the reduced mass m of relative motion of the target and projectile. The leading term is the primitive semi-classical amplitude for multiple excitation and explicit formulae are given for the corrections of order 1 m. These are calculated in detail for a one-dimensional model. It is shown that some, but not all, of the corrections can be included by evaluating the primitive amplitude with a symmetrized orbit. © 1983