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.

arXiv comment15 pages, 12 figures

References in corpus (18)

• Theory of Bose-Einstein condensation in trapped gases
• Feshbach Resonances in Ultracold Gases
• Theory of ultracold Fermi gases
• Quantum computation with trapped polar molecules
• Cold and Ultracold Molecules: Science, Technology, and Applications
• Evidence for Efimov quantum states in an ultracold gas of cesium atoms
• Controlling the quantum stereodynamics of ultracold bimolecular reactions
• Schemes for robust quantum computation with polar molecules
• Observation of Quantum Effects in sub Kelvin Cold Reactions
• Feshbach resonances in ultracold atomic and molecular collisions: threshold behaviour and suppression of poles in scattering lengths
• Giant formation rates of ultracold molecules via Feshbach Optimized Photoassociation
• Cold heteromolecular dipolar collisions
• Interactions and dynamics in Li + Li_2 ultracold collisions
• Efficient formation of ground state ultracold molecules via STIRAP from the continuum at a Feshbach resonance
• Dramatic reductions in inelastic cross sections for ultracold collisions near Feshbach resonances
• Controlling ultracold chemical reactions via Rydberg-dressed interactions
• Controllable binding of polar molecules and meta-stability of 1-D gases with attractive dipole forces
• Threshold resonance effects in reactive processes

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