How to observe the elusive resonances in H or D + H₂ → H₂ or HD + H reactive scattering

Short-lived collision complexes in H or D + H₂ (v = j = 0) → H₂ or HD (v′, j′) + H reactive scattering give rise to broad resonance structure. Though this structure is not observable in the energy dependence of the integral cross section, it is readily seen in the energy dependence in the differential cross section σ(θ,E), as a peak along a line in the E-θ plane. The equation of this resonance line is E = E_r(J(θ)), where E_r(J) is the resonance energy as a function of total angular momentum J (i.e., the rotational quantum number of the complex) and J(θ) is the inverse function of θ(J), the effective classical deflection function for the transition. Observation of this resonance structure requires cross sections to individual final (v′, j′) states; it is quenched by summing over j′. It is even more enhanced in cross sections to specific final m′ states with m′ ≠ 0. (m′ is the helicity of the final state, the projection of the final diatomic molecule rotational angular momentum onto the final relative translational velocity vector.) The results reported are all from rigorous three-dimensional quantum mechanical reactive scattering calculations for these cross sections.