Theory of Reactive Scattering. III. Exact Quantum-Mechanical Calculations for a Three-Dimensional Model for Three-Body Rearrangements

The problem of three-body reactive scattering in three dimensions is considered using coupled-channel operator equations. The discussion is in terms of two arrangement channels but the procedures employed may be used to treat the general case. Coupled integral equations are obtained which may be solved by a number of methods. In particular, simultaneous algebraic equations occur which are analogous to those encountered in previous studies of collinear reactive scattering. A model for a three-dimensional reactive process is considered for which one atom is infinitely massive and the interaction potential surface is isotropic. Exact calculations of the cross-sections and reaction probabilities are reported for a range of collision energies and differing degrees of internal excitation. The angular distribution of products is completely isotropic. The effects of varying the two finite masses are discussed.