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 σ(k)=4π/k², with ħk the relative momentum. The collision rate is given in the form Γ=γI(T/T_F)—the product of a universal collision rate γ=k_BT_F/(6πħ) 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 ≃4.6 at T/T_F≃0.4, I≃82(T/T_F)² for T/T_F<~0.15, and I≃2(T_F/T)² for T/T_F>1.5. We estimate the collision rate for recent experiments on a strongly-interacting degenerate Fermi gas of atoms.