Dynamics of the I + HI → IH + I reaction: application of nearside–farside, local angular momentum and resummation theories using the Fuller and Hatchell decompositions

Abstract

The differential cross section (DCS) for the I + HI(v(i) = 0, j(i) = 0) --> IH(v(f) = 0, j(f) = 2) + I reaction at a translational energy of 21.3 meV is studied, where v(i), j(i) and v(f), j(f) are vibrational, rotational quantum numbers for the initial and final states respectively. We apply new theoretical developments (since 2001) in nearside-farside (NF) theory to provide insights into intricate oscillatory structures in its DCS. It is shown that a simple physically-meaningful parameterization of the scattering (S) matrix, using a background Gaussian term plus a single Regge pole and a quadratic phase, can reproduce, in the forward and sideward directions, the intricate angular scattering obtained from numerical S matrix elements computed from a quantum Born-Oppenheimer-Centrifugal-Sudden scattering technique. This encouraging result suggests that many S matrix elements obtained from computer-intensive calculations can be parameterized in a similar physically-meaningful way. The manner in which the full and NF DCSs change when the Regge pole becomes progressively less important compared to the Gaussian term is also investigated. We report the first application to reactive scattering of the Hatchell NF decomposition, including resummations of the Legendre partial wave series for the scattering amplitude. The Hatchell NF resummed DCSs are compared with the corresponding Fuller NF resummed DCSs for resummation orders of r = 0, 1, 2 and 3. We find that the Fuller NF decomposition always provides a better physical interpretation of the angular scattering. Resummation usually cleans the NF DCSs of unphysical oscillations, especially in the farside (F) DCSs, with the greatest cleaning effect on going from no resummation (r = 0) to first order resummation (r = 1). Identities are derived which relate the Fuller and Hatchell NF subamplitudes for resummation orders, r > 0, to the NF unresummed subamplitudes, r = 0. These identities help us understand the origin of unexpected peaks, which sometimes appear in NF resummed DCSs, together with a simple procedure to remove them. We report Local Angular Momentum (LAM) and DCS x LAM (CLAM) analyses of the angular scattering for r = 0 and r = 1 using the Fuller NF decomposition. The LAM and CLAM analyses provide complementary (yet consistent) information to that obtained from the NF resummed DCSs. It is shown that the "l window representation", as used to analyse elastic scattering in the presence of strong absorption, is a special case of the general resummation theory developed in this paper.

The 6Hankel asymptotic approximation for the uniform description of rainbows and glories in the angular scattering of state-to-state chemical reactions: derivation, properties and applications

“…In practice, we resum the PWS (46) three times (r = 3) before carrying out the NF decomposition because it is known this helps ''clean'' the N and F unresummed dDCSs and LAMs of unphysical structure. [21][22][23][24] We then write PWS/N/r = 3 and PWS/F/r = 3 for the N and F resummed subamplitudes respectively. Totenhofer et al 24 have presented a detailed account of resummation theory for a Legendre PWS; this theory is not repeated here.…”

“…[21][22][23][24] We then write PWS/N/r = 3 and PWS/F/r = 3 for the N and F resummed subamplitudes respectively. Totenhofer et al 24 have presented a detailed account of resummation theory for a Legendre PWS; this theory is not repeated here. Fig.…”

Resonance Regge poles and the state-to-state F + H2 reaction: QP decomposition, parametrized S matrix, and semiclassical complex angular momentum analysis of the angular scattering

“…Section III describes the theory of the QP decomposition for the S matrix and the scattering amplitude, and makes an application to the F + H 2 reaction using quantum numerical S matrix elements. 6 The techniques of nearside-farside (NF) decomposition 8,18,19,22,23, and Local Angular Momentum (LAM) analysis 22,23,31,34,[36][37][38][39][40][41][42][43][45][46][47][48] for resummed Legendre PWS 22,23,30,31,36,38,[42][43][44][45][46][47] are also employed in Sec. III.…”

“…The Qmod and Pmod PWS subamplitudes (19) and (20) can also be resummed if desired 22,23,30,31,36,38,[42][43][44][45][46][47] before making the NF decompositions, since it is known this helps "clean" the N and F un-resummed DCSs and LAMs of unphysical structure. The resummation equations have been described in detail by Totenhofer et al; 42 they are easily adapted to Eqs. (19) and (20).…”

“…8,37,41,42 r The parametrization (42) forQ param J can be generalized using polynomials of higher degree in the phase, the pre-exponential factor, or in the argument of the exponential function.…”