Rainbows and glories in the angular scattering of the state-to-state F + H2 reaction at Etrans = 0.04088 eV

Abstract

State-of-the-art differential cross sections (DCSs) have been reported by Wang et al. [Proc. Nat. Acad. Sci. (U.S.), 2008, 105, 6227] for the state-to-state F + H(2)→ FH + H reaction using fully quantum-state-selected crossed molecular beams. We theoretically analyze the angular scattering of this reaction, in order to quantitatively understand the physical content of structure in the DCSs. Three transitions are studied, v(i)=0, j(i)=0, m(i)=0 → v(f)=3, j(f)=0, 1, 2, m(f)=0 at a translational energy of 0.04088 eV, where v, j, m are the vibrational, rotational and helicity quantum numbers respectively for the initial and final states. The input to our analyses consists of accurate quantum scattering (S) matrix elements computed for the Fu-Xu-Zhang potential energy surface, as used by Wang et al. in a computational simulation of their experimental DCSs. We prove that the pronounced peak at forward angles observed in the experimental and simulated DCSs for all three transitions is a glory. At larger angles, it is demonstrated that the 000 → 300 and 000 → 310 DCSs both possess a broad farside rainbow, which is accompanied by diffraction oscillations. We confirm the conjecture of Wang et al. that these diffraction oscillations arise from nearside-farside (NF) interference. We find that the reaction is N dominant for all three transitions. The theoretical techniques used to analyze the angular scattering include uniform semiclassical theories of glory and of rainbow scattering. We also make the first application of a semiclassical formula that is uniform for both glory + rainbow scattering. In addition, structure in the DCSs is analyzed using NF theory and local angular momentum theory, in both cases with three resummations of the partial wave series for the scattering amplitude. We make the first explicit application of the Thiele rational interpolation formula to extract the position and residue of the leading Regge pole from a set of S matrix elements, thereby making contact with complex angular momentum theories of DCSs, which interpret the angular scattering in terms of Regge resonances. Our calculations complement the exit-valley vibrationally-adiabatic analysis of Wang et al.

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.…”

“…If there is Airy-type rainbow in the DCS, then we also expect Re J 0 ≈ J r , where J r is the rainbow angular momentum variable, which separates the bright and dark sides of the rainbow. 5,22,23,27,55,56 The imaginary part of J 0 is related to the life-angle (written 0 θ R ) by 0 θ R = 1/ (2ImJ 0 ); it controls the decay of a surface (or creeping) wave which propagates around the interaction zone. Note that the life-angle can be very small (short-lived or direct scattering), or very large (for long-lived collisions), as well as taking any value in between.…”

Semiclassical glory analyses in the time domain for the H + D2(vi = 0, ji = 0) → HD(vf = 3, jf = 0) + D reaction

“…11, 12, 17-20, 22, 24 The purpose of this paper is to apply semiclassical (SC), i.e., asymptotic (¯→ 0), techniques to the T-domain scattering amplitude in order to provide physical insight into the forward scattering of the delayed mechanism. We prove that the forward scattering is an example of a glory; we do this by applying SC methods developed earlier for the E-domain, 7,[25][26][27][28][29][30] to the T-domain. Our work is the first application of (uniform) SC techniques to the PWP formalism and the first discovery of a glory in the T-domain.…”

“…In this section, we shall present an example for the H + D 2 reaction, where the direct E-domain SC glory theory 7,[25][26][27][28][29][30] fails at E = 1.82 eV, yet by following the solid blue path in Fig. 1 and carrying out a SC glory analysis in the T-domain, we can obtain an improved description of the glory scattering in the E-domain.…”

Computer Software for Understanding Resonances and Resonance-Related Phenomena in Chemical Reactions

“…Future work Angular distributions, also known as differential cross sections (DCS), contain other detailed information of the reaction mechanism, and are more difficult to interpret. Although there has been much work on the analysis of DCSs in terms of trajectories and resonance poles 12,13,16,14,18,19,27,26, no computer codes have yet been produced for public use. This Section is, therefore, more a statement of intent than a description of existing software.…”