Short-range correlation in the uniform electron gas: Extended Overhauser model

We use the two-electron wave functions (geminals) and the simple screened Coulomb potential proposed by Overhauser [Can. J. Phys. 73, 683 (1995)] to compute the pair-distribution function $g(r)$ for a uniform electron gas, finding the exact $g(0)$ for this model and extending the results from $g(0)$ to $g(r).$ We find that the short-range (r<rₛ) part of this $g(r)$ is in excellent agreement with quantum Monte Carlo simulations for a wide range of electron densities. We are thus able to estimate the value of the second-order (r²) coefficient of the small interelectronic-distance expansion of the pair-distribution function. The coefficients of the small-r expansion of the spin-resolved g_σσ^'(r) have density or rₛ dependencies which we parametrize in a way that makes it easy to find their coupling-constant averages. Their spin-polarization or ζ dependencies are estimated from a proposed spin-scaling relation.