Nearside–farside analysis of differential cross sections using Jacobi functions of the first and second kinds: Application to Ar+N2 rotationally inelastic scattering

Abstract

We report the first nearside–farside (NF) analysis of angular scattering for an inelastic molecular collision in which the partial wave series for the scattering amplitude is expanded in a basis set of reduced rotation matrix elements dmf,miJ(θ), where θ is the scattering angle, J is the total angular momentum quantum number, and mi,mf are initial and final helicity quantum numbers, respectively. The practical implementation of the NF theory is described in detail; it exploits in an essential way the properties of a function that we denote emf,miJ(θ) and call a reduced rotation matrix element of the second kind. The caustic structure of dmf,miJ(θ) and emf,miJ(θ) is taken into account via a restricted nearside–farside (resNF) decomposition of the scattering amplitude. The NFres theory is used to analyze polarization and degeneracy averaged differential cross sections for the Ar+N2(ji=2,mi=0,±1,±2)→Ar+N2(jf=2,mf=0,±1,±2) collision system, treated as an atom+rigid-rotor. The NFres analysis always provides a clear physical interpretation of the scattering (except sometimes for θ≈0°,180°) for phenomena such as diffraction oscillations and potential rainbows, as well as for more complicated (unnamed) interference effects. We also report results for some approximations to the NFres theory. Mathematical properties of the emf,miJ(θ) required for the NFres analysis are derived.