Pair distribution function of the spin-polarized electron gas: A first-principles analytic model for all uniform densities

We construct analytic formulas that represent the coupling-constant-averaged pair distribution function $\gxcav(r_s,ζ, k_Fu)$ of a uniform electron gas with density parameter $r_s =(9π/4)^{1/3}/k_F$ and relative spin polarization $ζ$ over the whole range $0