Spherical wave close coupling wave packet formalism for gas phase nonreactive atom–diatom collisions

Publisher Website
Google Scholar
Abstract
In this paper we discuss the use of the total angular momentum representation in the close coupling-wave packet (CCWP-J) method for solving the time dependent Schrödinger equation for inelastic, nonreactive gas phase atom–diatom collisions. This enables the wave packet propagation for the relative motion to be reduced from three dimensions to one. The approach utilizes a close coupling expansion of the wave packet into subpackets labeled by quantum numbers for total angular momentum J, z-component of angular momentum m0, rotor angular momentum j, and orbital angular momentum l. The number of coupled subpackets is less than the number for the plane wave boundary condition CCWP method when J<jmax and they are equal when J≥jmax. The present method requires solving for the time evolution of such coupled subpackets for 0≤J≤jmax +lmax, where lmax is the largest orbital angular momentum for which significant scattering occurs. However, the number of grid points required in the fast Fourier transform portion of the evolution of the wave packet will be far fewer since only a 1D FFT transform is required in the present version of the CCWP-J. All the other attractive features of the CCWP method are common to both the total angular momentum and plane wave representation versions of the CCWP; namely, results are obtained over the range of energies included in the initial packet, the labor scales as the number of rotor states squared, and standard approximation methods may be used in conjunction with the formalism. We also present the l-labeled coupled states or centrifugal sudden wave packet (CSWP) formalism as an example approximate version of this approach. The CCWP-J method is illustrated by application to a model atom–diatom collision problem. The extension to treat collisions involving a vibrating rotor is given in an Appendix. Finally, we compare features of the CCWP-J and CSWP with standard close coupling, CS approximation, and the plane wave basis CCWP methods.