Theory of Reactive Scattering. II. Application of the τ Operator Formalism to a Linear Model for Three Body Rearrangements

Coupled operator equations for the rearrangement channel operators ταα and τβα are employed in considering a simple collinear model for three body rearrangement collisions. The model is sufficiently general to permit dissociation of the bound atoms and in a certain limit the model becomes identical with that considered by Hulburt and Hirschfelder. We have been able to obtain analytical solutions for the coupled equations which may be used to calculate reactive and nonreactive scattering probabilities for both, when dissociation can occur and for the model of Hulburt and Hirschfelder. The numerical results for the Hulburt and Hirschfelder nondissociative model agree exactly with the results of Tang, Kleinman, and Karplus, and additional new numerical results are given for the more general model also. The present coupled equations may be generalized to three dimensional reactive collisions in a straightforward fashion.