Unitarity-limited elastic collision rate in a harmonically trapped Fermi gas

We derive the elastic collision rate for a harmonically trapped Fermi gas in the extreme unitarity limit where the s-wave scattering cross section is $\sigma \mathrm{}\left(k\right)=4\mathrm{}\pi {/k}^2,$ with $ħk$ the relative momentum. The collision rate is given in the form $\Gamma =\gamma {I(T/T}_F)$—the product of a universal collision rate $\gamma {=k}_B{T}_F/\left(6\mathrm{}\pi ħ\right)$ and a dimensionless function of the ratio of the temperature T to the Fermi temperature $T_F.$ We find that I has a peak value of $\simeq 4.6$ at ${T/T}_F\simeq 0.4,$ $I\simeq 82{(T/T}_F{)}^2$ for ${T/T}_F<~0.15,$ and $I\simeq {2(T}_F{/T)}^2$ for ${T/T}_F>\mathrm{1.5.}\mathrm{}$ We estimate the collision rate for recent experiments on a strongly-interacting degenerate Fermi gas of atoms.