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Structure Factors of The Unitary Gas Under Supernova Conditions

We compute with lattice field theory the vector and axial static structure factors of the unitary gas for arbitrary temperature above the superfluid transition and for fugacities 0.1 < z < 1.0. Using the lattice formulation, we calculate beyond the validity of the virial expansion, a commonly used technique in many-body physics. We find qualitative differences in the behavior of the structure factors at high fugacity compared to the predictions of the virial expansion. Due to the large scattering length of neutrons, we expect the unitary gas structure factors to approximate the structure factors of hot neutron gases, and we therefore expect our calculations to be useful in supernova simulations, where neutron gas structure factors are needed to compute in-medium neutrino-neutron scattering rates.