We study the three-point equal-time correlations of the density in a weakly interacting spin-1/2 Fermi gas and present two results. First, we compute the three-point correlation $s_3^{\rho }({\mathbf{q}}_1,{\mathbf{q}}_2)$ for the total density $\rho ={\rho }_{\uparrow }+{\rho }_{\downarrow }$ exactly as a function of ${\mathbf{q}}_1$ and ${\mathbf{q}}_2$ to first order in a dimensionless interaction parameter $\mathcal{I}$. This generalizes a previous result that related the singularity in $s_3^{\rho }({\mathbf{q}}_1,{\mathbf{q}}_2)$ to the Landau Fermi liquid parameters $F_0^s$ and $F_0^a$ that applied in a certain long-wavelength collinear limit of ${\mathbf{q}}_1$ and ${\mathbf{q}}_2$. Second, we compute the leading order $\mathcal{O}\left({\mathcal{I}}^3\right)$ interaction correction to the same-spin three-point correlation function $s_3^{\uparrow }({\mathbf{q}}_1,{\mathbf{q}}_2)$ in the long-wavelength collinear limit. These results are directly relevant to current experiments on atomic Fermi gases using quantum gas microscopy.

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• Fermi gases
• 2-dimensional systems
• Fermi liquid theory