Three-dimensional reaction cross sections from planar scattering data

Abstract

A method is proposed for calculating differential and total reaction cross sections for three-dimensional (3D) scattering processes from S-matrix elements computed for planar (2D) systems. By approximating each 3D S-matrix element by an average for both initial and final orbital angular momenta, and forcing the planar reaction probabilities at each total angular momentum to be transferable to 3D, we use the 2D S-matrix to calculate the 3D helicity amplitude. Both differential and total reaction cross sections may be calculated from the helicity amplitude. The method is applied to the hydrogen exchange reaction in which the 2D scattering data (obtained via the distorted wave Born approximation) is converted to 3D and then compared with the results of other 3D calculations on the Porter-Karplus surface.