Transition probabilities for curve-crossing collisions

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Abstract
An exact parametrisation of the two-state close-curve-crossing reduced scattering matrix for the BNO or DT model is used to discuss the semiclassical single-trajectory probabilities for impact parameters close to and beyond the crossing radius. These probabilities contain the Nikitin exponent and a correction factor, and connect smoothly with the ones defined from the Stueckelberg scattering matrix for smaller impact parameters. In the crossing region the probabilities differ from earlier expressions, and it is argued that this could lead to different interpretations of scattering data. Useful approximate expressions for the non-trivial quantities of the exact parametrisation are derived, both for strong and weak coupling. The resulting approximate formulae for the inelastic transition probability are discussed and compared with earlier results. In particular it is found that the Stueckelberg approximation is valid also for close-curve-crossing collisions as long as the phase lag is large enough.

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