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 εc({ζ},rₛ)=I({ζ},rₛ)εc(0,rₛ), where rₛ=[3/4{π}(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},rₛ) in the high-density limit rₛ{→}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 {}{∇}n²/n4/3 term of the spin-density gradient expansion of the exchange energy, and a good approximation to the SSF for that of correlation: scrCₓ({ζ})/scrCₓ(0)=g({ζ}) and scrCc({ζ},rₛ{→}0)/scrCc(0, rₛ{→}0){}g({ζ}). We also find that the {}{∇}{ζ}² contribution to the correlation energy is always negligible.