Abstract
We report two new contributions for understanding the quantum dynamics of the benchmark state-to-state reaction, F + H2(vi, ji, mi) → FH(vf, jf, mf) + H, where (vi, ji, mi) and (vf, jf, mf) are the initial and final vibrational, rotational, and helicity quantum numbers, respectively. We analyze product differential cross sections (DCSs) for the transitions, 000 → 300, 000 → 310, and 000 → 320, at a translational energy of 0.04088 eV using the potential energy surface of Fu-Xu-Zhang. The two new contributions are as follows: (1) We exploit the recently introduced QP decomposition of J. N. L. Connor [ J. Chem. Phys . 2013 , 138 , 124310 ] to transform numerical partial-wave scattering (S) matrix elements for the three transitions into parametrized (analytic) formulas, in which all terms in the three parametrized S matrices have a direct physical interpretation. In particular, they contain the positions and residues of Regge poles in the first quadrant of the complex angular momentum (CAM) plane. We obtain very close agreement between the values of the parametrized and numerical S matrix elements. (2) We then apply a uniform asymptotic Watson/CAM theory, which allows a Regge pole to be close to a saddle point. It uses the parametrized S matrices and is applied to the partial wave series (PWS) representation for the scattering amplitude to understand structure in a DCS in terms of three contributing subamplitudes. We prove using this powerful CAM theory that resonance Regge poles contribute to the small-angle scattering in the DCSs for all three transitions, with the oscillations at larger angles arising from nearside-farside interference. We obtain very good agreement between the uniform asymptotic Watson/CAM DCSs and the corresponding PWS DCSs, except for angles close to the forward and backward directions, where (as expected) the Watson/CAM formulas become nonuniform.
Highlights
The calculation of the scattering matrix (S matrix) is a key problem in the theory of state-to-state chemical reactions,[1−3] because it provides a complete characterization of a reaction
(2) We apply a uniform asymptotic Watson/complex angular momentum (CAM) theory, which allows a Regge pole to be close to a saddle point
It uses the parametrized S matrices and is applied to the partial wave series (PWS) representation for the scattering amplitude to understand structure in a differential cross sections (DCSs) in terms of three contributing subamplitudes. We prove using this powerful CAM theory that resonance Regge poles contribute to the small-angle scattering in the DCSs for all three transitions, with the oscillations at larger angles arising from nearside−farside interference
Summary
The calculation of the scattering matrix (S matrix) is a key problem in the theory of state-to-state chemical reactions,[1−3] because it provides a complete characterization of a reaction. The first application of the QP decomposition was to a stateto-state transition in the FH(vf = 3) reaction,[16] at a translational energy corresponding to the experiments of Neumark et al, namely Etrans = 0.119 eV.[7] More recently, Wang et al.[19] have reported new FH(vf = 3) DCS measurements using fully quantum-state-selected crossed molecular beams, together with high resolution and high sensitive Rydberg tagging of the H atom These DCS measurements for the benchmark F + H2 reaction are the current state-of-the-art, and it is important to understand them as thoroughly as possible, because of the detailed dynamical information contained within plots of the angular scattering versus reactive scattering angle.
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