Spin scaling of the electron-gas correlation energy in the high-density limit

The ground-state correlation energy per particle in a uniform electron gas with spin densities n_↑ and n_↓ may be expressed as ɛ_c(ζ,r_s)=I(ζ,r_s)ɛ_c(0,r_s), where r_s=[3/4π(n_↑+n_↓)]^1/3 is the density parameter and ζ=(n_↑-n_↓)/(n_↑+n_↓) is the relative spin polarization. We find an analytic expression for the spin-scaling factor (SSF) I(ζ,r_s) in the high-density limit r_s→0. It decreases from the value 1 at ζ=0, approaching the value 1/2 with slope -∞ as ζ approaches 1. A simple approximation to this SSF which displays the correct qualitative behavior is g³(ζ), where g(ζ)=[(1+ζ)^2/3+(1-ζ)^2/3]/2. We find that g(ζ) is the SSF for the coefficient of the ‖∇n‖²/n^4/3 term of the spin-density gradient expansion of the exchange energy, and a good approximation to the SSF for that of correlation: scrC_x(ζ)/scrC_x(0)=g(ζ) and scrC_c(ζ, r_s→0)/scrC_c(0, r_s→0)≊g(ζ). We also find that the ‖∇ζ‖² contribution to the correlation energy is always negligible.