Complex angular momentum theory of state-to-state integral cross sections: Resonance effects in the $F + HD \to HF(v' = 3) + D$ reaction
State-to-state reactive integral cross sections (ICSs) are often affected by quantum mechanical resonances, especially near a reactive threshold. An ICS is usually obtained by summing partial waves at a given value of energy. For this reason, the knowledge of pole positions and residues in the complex energy plane is not sufficient for a quantitative description of the patterns produced by resonance. Such description is available in terms of the poles of an S-matrix element in the complex plane of the total angular momentum. The approach was recently implemented in a computer code, available in the public domain [Comput. Phys. Commun., 2014, 185, 2127]. In this paper, we employ the package to analyse in detail, for the first time, the resonance patterns predicted for integral cross sections (ICSs) of the benchmark F + HD â†’ HF(vâ€² = 3) + D reaction. The v = 0, j = 0, Î© = 0 â†’ vâ€² = 3, jâ€² = 0, 1, 2, and Î©â€² = 0, 1, 2 transitions are studied for collision energies from 58.54 to 197.54 meV. For these energies, we find several resonances, whose contributions to the ICS vary from symmetric and asymmetric Fano shapes to smooth sinusoidal Regge oscillations. Complex energies of metastable states and Regge pole positions and residues are found by PadÃ© reconstruction of the scattering matrix elements. The accuracy of the code, relation between complex energies and Regge poles, various types of Regge trajectories, and the origin of the J-shifting approximation are also discussed.