Theory of Reactive Scattering. IV. Exact Quantum Mechanical Study of Angular Independent and Angular Dependent Models for Three Dimensional Rearrangement Collisions

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Abstract
In this paper we consider some three dimensional models for reactive scattering which can be treated analytically using the coupled channel τ operator formalism. The models are characterized by the fact that the potential energy surface governing the interaction of the three particles is in general angular dependent. As in earlier studies, it is again found that the equations can be reduced to a form essentially equivalent to that encountered in collinear reactive scattering. The most important restriction as to the validity of the model is that the mass of one of the atoms be infinite. Numerical calculations of reaction probabilities and cross sections are reported for several types of angular independent and angular dependent potential surfaces. The calculations constitute exact quantum mechanical results.