Nearside−Farside and Local Angular Momentum Analyses of Time-Independent Scattering Amplitudes for the H + D2 (vi = 0, ji = 0) → HD (vf = 3, jf = 0) + D Reaction

Abstract

The scattering dynamics of the state-to-state reaction H + D2 (v(i) = 0, j(i) = 0, m(i) = 0) --> HD (v(f) = 3, j(f) = 0, m(f) = 0) + D is investigated, where vi, ji, mi and vf, jf, mf are initial and final vibrational, rotational, and helicity quantum numbers, respectively. We use accurate quantum scattering matrix elements for total energies in the range 1.52-2.50 eV (calculated stepwise in 0.01 eV increments). The theoretical tools used are a nearside-farside (NF) analysis of the partial wave series (PWS) for the scattering amplitude, together with NF local angular momentum (LAM) theory. We find that the backward scattering, which is the energy-domain analog of the time-direct reaction mechanism, is N dominated, whereas the forward scattering (time-delayed analog) is a result of NF interference between the more slowly varying N and F subamplitudes. The LAM analysis reveals the existence of a "trench-ridge" structure. We also resum the PWS up to three times prior to making the NF decomposition. We show that such resummations usually provide an improved physical interpretation of the NF differential cross sections (DCSs) and NF LAMs. We analyze two resummed scattering amplitudes in more detail, where particular values of the resummation parameters give rise to unexpected unphysical behavior in the N and F DCSs over a small angular range. We analyze the cause of this unphysical behavior and describe viable workarounds to the problem. The energy-domain calculations in this paper complement the time-domain results reported earlier by Monks, P. D. D.; Connor, J. N. L.; Althorpe, S. C. J. Phys. Chem. A 2006, 110, 741.