On the Stability of the Repulsive Fermi Gas with Short-Range Interactions

We study the stability of a homogeneous spin-1/2 Fermi gas with repulsive short-range interactions. This many-body repulsive 'branch' is metastable towards the formation of Feshbach bound states, via three-body recombination. We measure the universal recombination coefficient $K_3$ and observe universal scalings with the average kinetic energy per particle and two-body scattering length. The scaling exponents are in excellent agreement with the linear energy dependence arising from a three-body threshold law involving two indistinguishable fermions and the $a^{6}$ scaling for three-body collisions in two-component Fermi gas under zero-range approximation. The interplay of the momentum dependence of the recombination coefficient and the Fermi statistics leads to non-trivial temperature dynamics, alternatively heating or cooling depending on the initial quantum degeneracy. The universal scaling with interactions extends over four orders of magnitude and beyond the expected range of validity of the three-body recombination law.