In-out decomposition for inelastic collisions as subdynamics. III. Perturbation theory and the semiclassical limit

A new representation for the subdynamics is given such that the resultant coupling matrix becomes identical with the semiclassical expression away from turning points. A perturbation theory is developed which also reduces to semiclassical theory away from the turning points. The subdynamic perturbation expression is therefore capable of making up for the deficiencies of the semiclassical theory at the turning points. A numerical illustration is given.