A generalized JWKB approximation for multichannel scattering

The Well-known JWKB approximation is generalized to handle multichannel scattering problems. Included is a discussion of how the JWKB connection formulas can be applied to the multiple classical turning points which, occur in the multichannel case. A new and useful form or the distorted wave transformation is derived and applied to the two state curve crossing problem. The result is a useful factorization and parameterization of the S-Matrix. The parameters are evaluated approximately by a method due originally to Zenc: to obtain Landau-Zener type formulas. It is also shown bow the equations of the impact parameter method with straight line trajectories can be derived from our generalized JWKB equations.