Correlation energy of the spin-polarized uniform electron gas at high density

The correlation energy per electron in the high-density uniform electron gas can be written as $\Ec(r_s,\zeta) = \lam_0(\zeta) \ln r_s + \eps_0(\zeta) + \lam_1(\zeta) ,r_s \ln r_s + O(r_s)$,where$r_s$istheSeitzradiusand$\zeta$istherelativespinpolarization\mathrm{.}Wederiveanexpressionfor$\lam_1(\zeta)$whichisexactforany$\zeta$, including the paramagnetic and ferromagnetic limits, ${\text{lam}}_1(0)$ and ${\text{lam}}_1(1)$, and discover that the previously published ${\text{lam}}_1(1)$ value is incorrect. We trace this error to an integration and limit that do not commute. The spin-resolution of ${\text{lam}}_1(\zeta )$ into contributions of electron pairs is also derived.