Accurate and simple analytic representation of the electron-gas correlation energy

We propose a simple analytic representation of the correlation energy εc for a uniform electron gas, as a function of density parameter rₛ and relative spin polarization {ζ}. Within the random-phase approximation (RPA), this representation allows for the rₛ^-3/4 behavior as rₛ{→}{∞}. Close agreement with numerical RPA values for εc(rₛ,0), εc(rₛ,1), and the spin stiffness αc(rₛ)=∂²{{{ε}}}c$(${r}ₛ, ζ=0)/δ{{{ζ}}}²$, and recovery of the correct ${r}ₛ$ln${r}ₛ$ term for ${r}ₛ${→}0, indicate the appropriateness of the chosen analytic form. Beyond RPA, different parameters for the same analytic form are found by fitting to the Green's-function Monte Carlo data of Ceperley and Alder [Phys. Rev. Lett. 45, 566 (1980)], taking into account data uncertainties that have been ignored in earlier fits by Vosko, Wilk, and Nusair (VWN) [Can. J. Phys. 58, 1200 (1980)] or by Perdew and Zunger (PZ) [Phys. Rev. B 23, 5048 (1981)]. While we confirm the practical accuracy of the VWN and PZ representations, we eliminate some minor problems with these forms. We study the {ζ}-dependent coefficients in the high- and low-density expansions, and the rₛ-dependent spin susceptibility. We also present a conjecture for the exact low-density limit. The correlation potential μc^σ(rₛ,{ζ}) is evaluated for use in self-consistent density-functional calculations.