Correlation energy of the uniform electron gas from an interpolation between high- and low-density limits

We show that known or knowable information about the high-(r(s)-> 0) and low- density (r(s) -> infinity) asymptotes can be used to predict the correlation energy per electron, e(c)(r(s), 0), of the three-dimensional uniform gas over the whole range of the density parameter (0 <= r(s) < infinity) and relative spin polarization (0 <=vertical bar 1 vertical bar <= 1), without quantum Monte Carlo or other input. For zeta=0, the high- density limit through order rs is known exactly from many-body perturbation theory, and for all zeta, the low- density limit through order 1/r(s)(2) is known accurately from a simple, intuitive, and accurate model. We propose a single interpolation formula with the expected analytic structure to all orders in both limits, and use it to predict e(c)(r(s), 0) in excellent agreement with quantum Monte Carlo data. For vertical bar zeta vertical bar>0, we derive the zeta dependence of the coefficient a(1)(zeta) of the r(s) In r(s) term, previously known only for vertical bar zeta vertical bar=0 and 1. For b(1)(zeta), the coefficient of the r(s) term (not yet derived for zeta not equal 0), we approximately extend the known b(1)(0) by using a simplification of the available quantum Monte Carlo information that replaces the second- order transition over 50 < r(s) < 100 by a sudden transition to full spin polarization at r(s)=75.