Abstract
A general representation of the S-matrix of resonant scattering is derived for the two-state curve crossing problem considering both "inner" and "outer" crossings. Analytical expressions for the poles of the S-matrix are obtained under quasi-classical conditions for both over-barrier and under-barrier transitions in cases when four turning points can be considered pairwise. In case of intermediate coupling where the quasi-classical approximation does not permit the finding of analytical expressions, recourse can be made to numerical results for the T-matrix, recently presented by Edsberg and Oppelstrup. The present analytical results are compared with these numerical calculations as well as with previous analytical work.The results obtained can be used in the theory of resonant scattering in slow collisions, for analysis of predissociation phenomena as well as for certain problems of wave propagation, solid state physics, etc., based on the solution of the same system of coupled differential equations.
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