  In the unitary regime, fermions interact strongly via two-body potentials
that exhibit a zero range and a (negative) infinite scattering length. The
energy density is proportional to the free Fermi gas with a proportionality
constant $\xi$. We use a simple density functional parametrized by an effective
mass and the universal constant $\xi$, and employ Kohn-Sham density-functional
theory to obtain the parameters from fit to one exactly solvable two-body
problem. This yields $\xi=0.42$ and a rather large effective mass. Our approach
is checked by similar Kohn-Sham calculations for the exactly solvable Calogero
model.
