ApproximateS-matrix elements for three-state curve-crossing problem

Approximate solutions are developed and tested for multichannel uniform WKB theory of inelastic scattering. Although the approximate solutions are obtained specifically for a three-channel problem, they are cast in forms suggestive of an easy generalization to problems of a larger number of channels. It is found that the modified Magnus approximation, which was used for the two-channel version, is again sufficiently accurate. The stationary phase method developed elsewhere by us is found again very efficient for evaluating integrals involved in the modified Magnus approximation and saves computing time significantly in comparison with a numerical solution method of the corresponding three-channel coupled Schroedinger equations. The results of the approximate solutions obtained are compared with those by numerical solutions of the corresponding Schroedinger equations and the equations of motion in uniform WKB theory. The agreements are found excellent.