Theory of forward glory scattering for chemical reactions: accuracy of semiclassical approximations using a J -shifted Eckart parameterization for the scattering matrix element

Abstract

The accuracy of the semiclassical theory of forward glory scattering for a state-to-state chemical reaction is investigated using a J-shifted Eckart parameterization for the scattering matrix element. The parameters are chosen initially to model the angular scattering of the H+D2→HD(vf=3)+D reaction, following D. Sokolovski (Chem. Phys. Lett., 370, 805 (2003)). Then the parameters are systematically varied to generate different scattering patterns. The theory assumes that the scattering amplitude can be expanded in a Legendre partial wave series (PWS). The theoretical techniques applied to the PWS include: a nearside–farside decomposition, and a local angular momentum (LAM) analysis; both techniques include resummations of the PWS. The semiclassical techniques used include: a uniform semiclassical approximation (USA), a primitive semiclassical approximation, a classical semiclassical approximation, an integral transitional approximation, a semiclassical transitional approximation and a semiclassical LAM. The LAM for the classical collision of two hard spheres is also employed. It is demonstrated that the USA can accurately describe glory oscillations for scattering angles on and near the forward direction (as defined by the axial caustic associated with the glory); in favourable cases the USA is accurate for sideward scattering angles and even for angles close to the backward direction.