I will present recent joint work with M. Christiansen and P. T. Nam.
We consider a fermionic system interacting via Coulomb potential, scaled by $k_F= N^{1/3}$, denoted as mean-field Coulomb, on the unit periodic box. 
We establish the analog of the Gell-Mann—Brueckner formula. More precisely, we show that the correlation energy is of the form $c_1 k_F log k_F + c_2 k_F + o(k_F)$ for specific constants $c_1, c_2$, where $k_F$ is the Fermi-momentum. 
org: GIULIANI Alessandro