Theory of Inelastic Collisions: Uniform Asymptotic (WKB) Solutions and Semiclassical Scattering Matrix Elements for Multichannel Problems

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Abstract
The method developed for the semiclassical solutions of two‐channel problems is generalized for a semiclassical solution of multichannel problems. The semiclassical scattering matrix elements are constructed from the solution, which are given in terms of well defined quadratures involving the Airy functions. The results obtained are valid without curve crossings and do not require the usual assumption of a sufficiently wide separation of the turning points and crossing points. It is shown that an approximate solution of an N‐channel problem can be constructed from the solutions of local two‐channel problems, if the curves cross pairwise in sequence.

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