We show that the cross sections for a broad range of resonant inelastic processes accompanied by excitation exchange (such as spin exchange, Förster resonance, or angular momentum exchange) exhibit a near-threshold scaling $E^{\mathrm{\Delta }{m}_{12}}$, where $E$ is the collision energy, $\mathrm{\Delta }{m}_{12}=m_1^{\prime }+m_2^{\prime }-m_1-m_2$, 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 $\mathrm{\Delta }{m}_{12}=0$ transitions display an unconventional $E^0$ scaling similar to that of elastic cross sections, and their rates vanish as $T^{\mathrm{\Delta }{m}_{12}+1/2}$. For collisions dominated by even partial waves (such as those of identical bosons in the same internal state) the scaling is modified to ${\sigma }_{\text{inel}}\propto E^{\mathrm{\Delta }{m}_{12}+1}$ if $\mathrm{\Delta }{m}_{12}$ is odd. We present accurate quantum scattering calculations that illustrate these modified threshold laws for resonant spin exchange in ultracold $\text{Rb}+\text{Rb}$ and ${\mathrm{O}}_2+{\mathrm{O}}_2$ collisions. Our results illustrate that the well-known $k^{-1}$ threshold scaling of inelastic cross sections only applies to exothermic, rather than resonant, inelastic processes.

Close

PrevNext

View figure in article

• Cold and ultracold molecules
• Scattering theory
• Ultracold collisions