Nearside-Farside Analysis of the Angular Scattering for the State-to-State H + HD → H₂ + D Reaction: Nonzero...

We theoretically analyze the differential cross sections (DCSs) for the state-to-state reaction, H + HD(v_i = 0, j_i = 0, m_i = 0) → H₂(v_f = 0, j_f = 1,2,3, m_f = 1,..,j_f) + D, over the whole range of scattering angles, where v, j, and m are the vibrational, rotational, and helicity quantum numbers for the initial and final states. The analysis extends and complements previous calculations for the same state-to-state reaction, which had j_f = 0,1,2,3 and m_f = 0, as reported by Xiahou, C.; Connor, J. N. L. Phys. Chem. Chem. Phys. 2021, 23, 13349-13369. Motivation comes from the state-of-the-art experiments and simulations of Yuan et al. Nature Chem. 2018, 10, 653-658 who have measured, for the first time, fast oscillations in the small-angle region of the degeneracy-averaged DCSs for j_f = 1 and 3 as well as slow oscillations in the large-angle region. We start with the partial wave series (PWS) for the scattering amplitude expanded in a basis set of reduced rotation matrix elements. Then our main theoretical tools are two variants of Nearside-Farside (NF) theory applied to six transitions: (1) We apply unrestricted, restricted, and restrictedΔ NF decompositions to the PWS including resummations. The restricted and restrictedΔ NF DCSs correctly go to zero in the forward and backward directions when m_f > 0, unlike the unrestricted NF DCSs, which incorrectly go to infinity. We also exploit the Local Angular Momentum theory to provide additional insights into the reaction dynamics. Properties of reduced rotation matrix elements of the second kind play an important role in the NF analysis, together with their caustics. (2) We apply an approximate N theory at intermediate and large angles, namely, the Semiclassical Optical Model of Herschbach. We show there are two different reaction mechanisms. The fast oscillations at small angles (sometimes called Fraunhofer diffraction/oscillations) are an NF interference effect. In contrast, the slow oscillations at intermediate and large angles are an N effect, which arise from a direct scattering, and are a "distorted mirror image" mechanism. We also compare these results with the experimental data.