Semiclassical Theory of Inelastic Scattering: Diagonalization of the Phase Shift Matrix

The previously obtained semiclassical phase shift matrix is diagonalized in the classical limit by a simple transformation. In the diagonal representation, the various scattering expressions can be simplified appreciably by the method of stationary phase to resemble the semiclassical expressions for elastic scattering. Analogous equations are obtained for the scattering angle and the collision lifetime. A perturbation method is derived to cover deviations from the classical and sudden-approximation limits.