Nearside–farside analysis of state-selected differential cross sections for reactive molecular collisions

Abstract

The usual theoretical procedure for evaluating the differential cross section (DCS) of a molecular collision consists of numerically summing a partial wave series (PWS) for the scattering amplitude. The PWS typically has many numerically significant terms making it difficult (or impossible) to gain physical insight into the origin of structure in a DCS. A nearside–farside (NF) analysis of a DCS decomposes the PWS scattering amplitude into two subamplitudes: one nearside, the other farside. This decomposition is successful if the magnitudes of the two subamplitudes are never much greater than that of the scattering amplitude itself. It is then often possible to gain a clear physical picture of the origin of structure in a DCS, and hence obtain information on the collision dynamics. A new NF theory called the restricted NF decomposition is described. We present the first application of this NF decomposition to reactive molecular collisions whose PWS are expanded in a basis set of reduced rotation matrix elements. The reactions whose DCSs we NF analyze are: F+H₂→FH+H, F+HD→FH+D (or FD+H) and H+D₂→HD+D. Exact quantum scattering matrix elements are employed as input to the NF analyses. DCSs are also computed using a simple semiclassical optical model. We demonstrate that the restricted NF decomposition provides valuable physical insights into the structured angular distributions of these three chemical reactions. Applications of NF methods to elastic and inelastic molecular angular scattering are also described.