  An accurate analytical parametrization for the exchange-correlation free
energy of the homogeneous electron gas, including interpolation for partial
spin-polarization, is derived via thermodynamic analysis of recent restricted
path integral Monte-Carlo (RPIMC) data. This parametrization constitutes the
local spin density approximation (LSDA) for the exchange-correlation functional
in density functional theory. The new finite-temperature LSDA reproduces the
RPIMC data well, satisfies the correct high-density and low- and high-$T$
asymptotic limits, and is well-behaved beyond the range of the RPIMC data,
suggestive of broad utility.
