  We present calculations for spin $ 1/2 $ fermions at unitarity limit, where
the effective range of the interaction is zero and the scattering length is
infinite. We compute the ground-state energy for a system of 6, 10,14,18 and 20
particles, with equal numbers of up and down spins in a periodic cube in the
full ground-state constrained-path Monte Carlo (CPMC) method using the
extended, attractive Hubbard model. Our results in a careful extrapolation to
the thermodynamic limit may suggest that the ratio of the ground-state energy
to that of a free Fermi gas is $ \xi = 0.43(4) $, which can compare with recent
experimental results and consistent with the fixed node Green's function Monte
Carlo and novel lattice approaches results. We also obtain results for
interactions with different effective ranges and find that the energy is
consistent with a universal linear dependence on the product of the Fermi
momentum and the effective range.
