Semiclassical theory of rearrangement and exchange collisions

Abstract

A semiclassical theory of rearrangement and exchange collision processes is developed as an extension of the semiclassical theory of inelastic collisions reported in the earlier papers in this series. The uniform WKB solutions are again used to obtain the WKB solutions of a set of intergrodifferential equations that describe the relative motions of the collision fragments in various channels. The solutions obtained are free of the turning point difficulty characteristic of the usual WKB solutions and thus most suitable for various calculations. The S matrix is constructed from the WKB solutions and given in terms of quadratures involving Airy functions. Approximation of the S matrix thus constructed is also discussed along with a discussion on a possibility of exploiting curve crossings.