If the temperature is extremely low, the behavior of the electrons comes close to the quantum mechanical model of a Fermi gas. We thus approximate T by the kinetic energy of an additional electron in the Fermi gas model, which is simply the Fermi energy E F. The Fermi energy for a 3D system is related to the density of electrons (including spin degeneracy) by ρ ρ = 2 1 ( 2 π π ) 3 ( 4 3 π π k F 3 ) , E F = ℏ ℏ 2 k F 2 2 m , where k F is the Fermi wavevector. Perturbing to first order, we find that Δ Δ ρ ρ ≃ ≃ 3 ρ ρ 2 E F Δ Δ E F .