A New Rainbow: Angular Scattering of the F + H2(vi= 0,ji= 0) → FH(vf= 3,jf= 3) + H Reaction

Abstract

The angular scattering of a state-to-state chemical reaction contains fundamental information on its dynamics. Often the angular distributions are highly structured and the physical interpretation of this structure is an important and difficult problem. Here, we report a surprising finding for the benchmark F + H(2) --> FH + H reaction, when the product molecule FH is in a vibrational state with quantum number = 3 and a rotational state with quantum number = 3. We demonstrate that the differential cross section (DCS) is an example of (attractive) rainbow scattering, being characterized by an Airy function and its derivative. The rainbow reveals its presence in the DCS by interference with the repulsive (or nearside) scattering producing characteristic diffraction oscillations. The rainbow is broad, which explains why it has not been recognized in the many earlier theoretical and experimental investigations of this reaction. There is an angular region in the DCS where the rainbow dominates, but with the unusual property that the DCS is less intense than in adjoining angular regions. The reaction investigated is F + H(2)(v(i) = 0, j(i) = 0, m(i) = 0) --> FH(v(f) = 3, j(f) = 3, m(f) = 0) + H, where v(i), j(i), m(i) and v(f), j(f), m(f) are initial and final vibrational, rotational and helicity quantum numbers, respectively. The relative translational energy is 0.119 eV. We use rigorous semiclassical (asymptotic) techniques that provide physical insight as well as a mathematically sound and numerically accurate description of the angular scattering. The semiclassical DCS agrees very closely with the exact quantum DCS. The semiclassical scattering amplitude is used to assess the physical effectiveness of the Fuller nearside-farside decomposition for the partial wave series of the F + H(2) reaction, including the effect of one resummation. We also compare the semiclassical and exact quantum nearside, farside, and full local angular momenta and find good agreement. Although our new rainbow has unusual and unexpected properties, similar rainbows are predicted to occur in the DCSs of many state-to-state chemical reactions, since the semiclassical analysis is generic and not specific to the present F + H(2) example.