Near-threshold scaling of resonant inelastic collisions at ultralow temperatures

Abstract

We show that the cross sections for a broad range of resonant {\it inelastic} processes accompanied by excitation exchange (such as spin-exchange, Förster resonant, or angular momentum exchange) exhibit an unconventional near-threshold scaling $E^{\Delta m_{12}}$, where $E$ is the collision energy, $\Delta m_{12}=m_1^{\prime }+m_2^{\prime }-m_1-m_2$, and $m_i$ and $m_i^{\prime }$ are the initial and final angular momentum projections of the colliding species ($i=1,2$). In particular, the inelastic cross sections for $\Delta m_{12}=0$ transitions display an unconventional $E^0$ scaling similar to that of elastic cross sections, and their rates vanish as $T^{\Delta m_{12}+1/2}$. For collisions dominated by even partial waves (such as those of identical bosons in the same internal state) the scaling is modified to ${\sigma }_{\text{inel}}\propto E^{\Delta m_{12}+1}$ if $\Delta m_{12}$ is odd. We present accurate quantum scattering calculations that illustrate these modified threshold laws for resonant spin exchange in ultracold Rb+Rb and O${}_2$+O${}_2$ collisions. Our results illustrate that the threshold scaling of collision cross sections is determined only by the energetics of the underlying process (resonant vs. exothermic) rather than by whether the internal states of colliding particles is changed in the collision.

References in corpus (11)

• Cold molecules: Progress in Quantum Engineering of Chemistry and Quantum Matter
• Coherent dipole-dipole coupling between two single atoms at a Förster resonance
• Resonant collisional shielding of reactive molecules using electric fields
• Precision test of statistical dynamics with state-to-state ultracold chemistry
• Spin Exchange Rates in Electron-Hydrogen Collisions
• Life and death of a cold BaRb${}^{+}$ molecule inside an ultracold cloud of Rb atoms
• Feshbach resonances in ultracold 85Rb-87Rb and 6Li-87Rb mixtures
• Spin Exchange Rates in Proton-Hydrogen Collisions
• Complete quantum coherent control of ultracold molecular collisions
• High-energy-resolution measurement of ultracold atom-ion collisional cross section
• Interaction potentials and ultracold scattering cross sections for the ${}^7$Li${}^{+}$-${}^7$Li ion-atom system