Simple semiclassical calculation of fine-structure transition probability

Abstract
The construction of a semiclassical multichannel scattering matrix in the matching approximation is discussed. The accuracy of the matching approximation is demonstrated by comparison of the calculated semiclassical fine-structure transition probability P12 to 3/2/(b) with the rigorous quantum calculation of Reid and Rankin (see ibid., vol.11, p.55 (1978)) for the Li(2Pj)-He system.