Unitarity-Limited Elastic Collision Rate in a Harmonically-Trapped Fermi Gas

Abstract

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 $\sigma (k)=4\pi /k^2$, with $\hslash k$ the relative momentum. The collision rate is given in the form $\Gamma =\gamma I(T/T_F)$--the product of a universal collision rate $\gamma =k_B{T}_F/(6\pi \hslash )$ and a dimensionless function of the ratio of the temperature $T$ to the Fermi temperature $T_F$. We find $I$ has a peak value of $\simeq 4.6$ at $T/T_F\simeq 0.4$, $I\simeq 82(T/T_F{)}^2$ for $T/T_F\le 0.15$, and $I\simeq 2(T_F/T{)}^2$ for $T/T_F>1.5$. We estimate the collision rate for recent experiments on a strongly-interacting degenerate Fermi gas of atoms.

4 pages, 2 figures, revTeX4, submitted to PRA