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

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 similar to epsilon(-3/2) instead of the standard Wigner's law threshold behavior sigma similar to epsilon(-1/2). Wigner's law is still valid as epsilon -> 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 similar to 1/T at low temperatures, instead of the expected constant rate of the Wigner regime in ultracold physics and chemistry. (C) 2015 Elsevier B.V. All rights reserved.