Threshold resonance effects in reactive processes

Abstract

We investigate the effect of near threshold resonances in reactive scattering at low energy. We find a general type of anomalous behavior of the cross sections, and illustrate it with a real system (${\text{H}}_{2}+\text{Cl}$). For inelastic processes, the anomalous energy dependence of the total cross section is given by $\ensuremath{\sigma}\ensuremath{\sim}{k}^{\ensuremath{-}3}$ (with $k\ensuremath{\propto}\sqrt{\ensuremath{\varepsilon}}$). The standard threshold behavior given by Wigner's law ($\ensuremath{\sigma}\ensuremath{\sim}{k}^{\ensuremath{-}1}$) is eventually recovered at vanishing energies, but its validity is now limited to a much narrower range of energies. The anomalous behavior leads to reaction rate coefficients behaving as $K\ensuremath{\sim}1/T$ instead of the expected constant rate of the Wigner regime. We also provide analytical expressions for $s$-wave cross sections, and discuss the implication in ultracold physics and chemistry.