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

Abstract

We study the effect of resonances near the threshold of low energy ($\epsilon$) 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 $\sigma \sim {\epsilon }^{-3/2}$ instead of the standard Wigner's law threshold behavior $\sigma \sim {\epsilon }^{-1/2}$. Wigner's law is still valid as $\epsilon \to 0$, but in a narrow range of energies. We illustrate these effects with two reactive systems, a low-reactive system (H${}_2$ + Cl) and a more reactive one (H${}_2$ + 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 $K\sim 1/T$ at low temperatures, instead of the expected constant rate of the Wigner regime in ultracold physics and chemistry.

15 pages, 12 figures

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Cited by in corpus (3)

• Molecular Hydrogen: a benchmark system for Near Threshold Resonances at higher partial waves
• Phase-amplitude formalism for ultra-narrow shape resonances
• Resonances at very low temperature for the reaction D${}_2$+H