Quantum Reactive Scattering for Three Particle Systems using Hyperspherical Coordinates

Quantum reactive scattering or rearrangement processes continue to be of considerable theoretical and experimental interest. A review of our Adiabatically-adjusting, Principal Axes Hyperspherical (APH) coordinates method will be presented. Basis functions defined as a product of Wigner rotation matrices [5] times surfaces functions will be defined. We will briefly describe four methods for obtaining accurate surface functions and give relative merits of each. The surface functions methods are: Finite Element Method (FEM)Discrete Variable Representation (DVR)Analytic Basis set Method (ABM)Distributed Approximating Functions (DAF)Our choice of product basis functions giverisetoasetof second-order differential outline the solution tothese equations and present a new method equations. We will for smoothly transforming from hyperspherical to Jacobi coordinates outside the rear-rangement region. This new procedure eliminates the two dimensional projection used demonstrate that Quantum resonances are important forsomere-previously. We will arrangement processes. We also argue that it is important for theoreticians to properly the experimental parameters for a complete comparison with experiment.