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

The negative correlation energy epsilon(c)(r(s),zeta) per particle of a uniform electron gas of density parameter r(s) and spin polarization zeta is well known, but its spin resolution into up arrowdown arrow, up arrowup arrow, and down arrowdown arrow 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 zeta=0, we find that the same-spin correlation energy is unexpectedly positive, and we explain why. We also estimate the up arrow and down arrow contributions to the kinetic energy of correlation.