Spin resolution of the electron-gas correlation energy: Positive same spin contributions

The negative correlation energy ε_c(r_s,ζ) per particle of a uniform electron gas of density parameter r_s and spin polarization ζ is well known, but its spin resolution into ↑↓, ↑↑, and ↓↓ contributions is not. Widely used estimates are incorrect, and hamper the development of reliable density functionals and pair distribution functions. For the spin resolution, we present interpolations between high- and low-density limits that agree with available quantum Monte Carlo data. In the low-density limit for ζ=0, we find that the same-spin correlation energy is unexpectedly positive, and we explain why. We also estimate the ↑ and ↓ contributions to the kinetic energy of correlation.