Threshold resonances in ultracold chemical reactions

We analyze the effects of near threshold resonances on the low energy behavior of cross sections for reactive scattering systems with reaction a barrier ({\em e.g.} Cl + H$_2$, D + H$_2$). We find an anomalous behavior when a resonance pole is very close to the threshold of the entrance channel. For inelastic processes, including reactive ones, the anomalous energy dependence of the cross sections is given by $\sigma\sim E^{-3/2}$. However, at vanishingly low energies, the standard Wigner's threshold behavior ($\sigma\sim E^{-1/2}$) is eventually recovered, but limiting to much narrower range of energies. When the cross sections are averaged to obtain rate coefficients, the anomalous behavior persists; indeed, we find an intermediate regime of ultralow temperatures, where the inelastic rate coefficients behave as $K\sim 1/T$.