Semiclassical approximations for low-energy inelastic scattering

Several semiclassical methods are developed to treat low-energy vibrationally and rotationally inelastic scattering. The quantal close coupling (CC) equations are approximated by treating the orbital angular momentum in a classical limit. This removes l from the coupled equations and introduces a dependence in the potential on the classical orbital angle. Unlike the coupled states (CS) approximation, l is not frozen. Next, the rotational motion is treated in the sudden approximation. For vibrationally inelastic scattering, this yields an approximation which involves the solution of N coupled differential equations for N vibrational states. For the pure rotational case, the theory reduces to a sudden approximation superior to the current alternatives. Unlike the traditional approach, it is not a perturbation theory based on an elastic trajectory. Unlike the infinite order sudden approximation (IOS), it converges properly at large impact parameters. Indeed, the IOS is obtained as a special case by freezing the orbital motion. A fast numerical procedure is derived for evaluating the matrices occurring in the sudden approximation.