# Structure Factors of The Unitary Gas Under Supernova Conditions

## TL;DR

This paper calculates the static structure factors of the unitary gas at various temperatures and fugacities using lattice field theory, providing insights beyond traditional virial expansion methods relevant for supernova physics.

## Contribution

It introduces a lattice field theory approach to compute structure factors of the unitary gas at high fugacities, surpassing virial expansion limitations.

## Key findings

- Qualitative differences in structure factors at high fugacity compared to virial predictions
- Calculations applicable to neutron gases in supernova environments
- Potential to improve neutrino scattering rate estimates in astrophysics

## Abstract

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.