  A Fermi gas of cold atoms allows precise control over the dimensionless
effective range, $k_\mathrm{F} R_\mathrm{eff}$, of the Feshbach resonance. Our
pseudopotential formalism allows us to create smooth potentials with effective
range, $-2 \leq k_\mathrm{F} R_\mathrm{eff} \leq 2$, which we use for a
variational and diffusion Monte Carlo study of the ground state of a unitary
Fermi gas. We report values for the universal constants of $\xi = 0.388(1)$ and
$\zeta = 0.087(1)$, and compute the condensate fraction, momentum distribution,
and pair correlations functions. Finally, we show that a gas with $k_\mathrm{F}
R_\mathrm{eff} \gtrsim 1.9$ is thermodynamically unstable.
