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-(rₛ→0) and low-density (rₛ→∞) asymptotes can be used to predict the correlation energy per electron, ec(rₛ,ζ), of the three-dimensional uniform gas over the whole range of the density parameter (0≤rₛ<∞) and relative spin polarization (0≤|ζ|≤1), without quantum Monte Carlo or other input. For ζ=0, the high-density limit through order rₛ is known exactly from many-body perturbation theory, and for all ζ, the low-density limit through order 1/rₛ² 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 ec(rₛ,0) in excellent agreement with quantum Monte Carlo data. For |ζ|>0, we derive the ζ dependence of the coefficient a₁(ζ) of the rₛ ln rₛ term, previously known only for |ζ|=0 and 1. For b₁(ζ), the coefficient of the rₛ term (not yet derived for ζ≠0), we approximately extend the known b₁(0) by using a simplification of the available quantum Monte Carlo information that replaces the second-order transition over 50<rₛ<100 by a sudden transition to full spin polarization at rₛ=75.