The two-channel S-matrix in the quasi-classical approximation

The curve-crossing problem in slow collisions has been considered within the consistent quasi-classical approximation. The two-channel S-matrix has been found for two levels intersecting either with similar or different slopes. A consistent use of the WKB method (Zwaan-Stueckelberg's technique and parabolic cylinder function method) made it possible both to write the final results in a general form suitable for applications to realistic potential curves and to find the additional phase arising from a non-adiabatic transition. The results obtained can be used to describe different quantum effects in many-channel scattering and for calculation of predissociation spectra.