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We construct analytic formulas that represent the coupling-constant-averagedpair distribution function $\gxcav(r_s,\zeta, k_Fu)$ of a uniform electron gaswith density parameter $r_s =(9\pi/4)^{1/3}/k_F$ and relative spin polarization$\zeta$ over the whole range $0<r_s<\infty$ and $-1<\zeta<1$, withenergetically-unimportant long range ($u\to \infty$) oscillations averaged out.The pair distribution function $g_{xc}$ at the physical coupling constant isthen given by differentiation with respect to $r_s$. Our formulas areconstructed using {\em only} known theoretical constraints plus the correlationenergy $\ec(r_s,\zeta)$, and accurately reproduce the $g_{xc}$ of the QuantumMonte Carlo method and of the fluctuation-dissipation theorem with theRichardson-Ashcroft dynamical local-field factor. Our $g_{xc}$ seems to becorrect even in the high-density ($r_s\to 0$) and low-density ($r_s \to\infty$) limits. When the spin resolution of $\ec$ into $\uu$, $\dd$, and $\ud$contributions is known, as it is in the high- and low-density limits, ourformulas also yield the spin resolution of $g_{xc}$. We also analyze thekinetic energy of correlation into contributions from density fluctuations ofvarious wavevectors.Comment: new version, with three new figures, and two new subsection

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