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 ₂ (, rₒ) =I (, rₒ) ₂ (0, rₒ), where rₒ=3/4 (n_+n_) ^1/3 is the density parameter and = (n_-n_) / (n_+n_) is the relative spin polarization. We find an analytic expression for the spin-scaling factor (SSF) I (, rₒ) in the high-density limit rₒ0. It decreases from the value 1 at =0, approaching the value 1/2 with slope - as approaches 1. A simple approximation to this SSF which displays the correct qualitative behavior is g^3 (), where g () = (1+) ^2/3+ (1-) ^2/3/2. We find that g () is the SSF for the coefficient of the ^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: scrCₗ () /scrCₗ (0) =g () and scrC₂ (, rₒ0) /scrC₂ (0, rₒ0) (). We also find that the ^2 contribution to the correlation energy is always negligible.