Jost function description of near threshold resonances for coupled-channel scattering

We study the effect of resonances near the threshold of low energy (εε) reactive scattering processes, and find an anomalous behavior of the s  -wave cross sections. For reaction and inelastic processes, the cross section exhibits the energy dependence σ∼ε-3/2σ∼ε-3/2 instead of the standard Wigner’s law threshold behavior σ∼ε-1/2σ∼ε-1/2. Wigner’s law is still valid as ε→0ε→0, but in a narrow range of energies. We illustrate these effects with two reactive systems, a low-reactive system (H2 + Cl) and a more reactive one (H2 + F). We provide analytical expressions, and explain this anomalous behavior using the properties of the Jost functions. We also discuss the implication of the reaction rate coefficients behaving as K∼1/TK∼1/T at low temperatures, instead of the expected constant rate of the Wigner regime in ultracold physics and chemistry.

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