The two-state S matrix for the Landau-Zener potential curve crossing model: predissociation and resonant scattering

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Abstract
A rigorous phase integral analysis is made of the Stueckelberg scattering matrix for the linear curve crossing model which describes predissociation and resonant scattering (i.e. when the curves intersect with slopes of opposite sign). The model contains the two parameters beta and epsilon , which measure respectively the strength of the coupling between diabatic curves and the collision energy. For the cases when mod epsilon mod >1, essentially exact results are derived. A comparison equation technique enables the unknown phase and correction factor to be determined when the coupling region is well separated from the classical turning points. Phase integrals which arise are expressed in terms of motion under the adiabatic potentials. The case of weak coupling is also treated perturbatively. These results allow interpolating forms for the S matrix and transition probabilities to be proposed for the case when mod epsilon mod <1. Except in the strong and weak coupling regimes, the expressions break down when beta mod epsilon mod approximately 1: this is to be expected because whilst the turning point cannot be neglected, the coupling is too large for a perturbation treatment.

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