EXTENSION OF THE PACK-PARKER QUANTUM REACTIVE SCATTERING METHOD TO INCLUDE DIRECT CALCULATION OF TIME DELAYS

A direct method for determining time delays for quantum reactive scattering is developed for three atoms scattering in three physical dimensions. The method is a simple extension of the Pack-Parker approach to reactive scattering. In their formulation, adiabatically adjusted-principle axis-hyperspherical (APH) coordinates are used to generate coupled equations for the exchange region. These solutions are then projected onto Delves coordinate wave functions to generate the corresponding set of coupled equations that must be propagated out into the asymptotic region. The Delves wave functions are then mapped onto the Jacobi coordinate wave functions from which the reactive scattering S matrix is obtained. The extension of this method to include the direct calculation of the time delays for state-to-state reactive scattering processes involves three essential steps: (1) Modification of the log-derivative method for propagating accurate solutions to the coupled equations so that the log-derivative and its energy derivative are propagated simultaneously; (2) establishing that the APH to Delves projection is independent of the energy; and (3) extension of the energy dependent Delves to Jacobi mapping to include the global R matrix and its energy derivative. The necessary mathematical expressions for accomplishing each of these steps are developed in sufficient detail so that the power and simplicity of the method can be understood and so that the method can be efficiently implemented.