  Various quantities of an attractively interacting fermion system at the
unitary limit are determined by extrapolating Monte Carlo results of
low-density neutron matter. Smooth extrapolation in terms of $1/(k_F a_0)$
($k_F$ is the Fermi momentum, and $a_0$ is the ${}^1S_0$ scattering length) is
found with the quantities examined: the ground-state energy, the pairing gap at
$T \approx 0$, and the critical temperature of the normal-to-superfluid phase
transition. We emphasize proximity of the physics of low-density neutron matter
to that at the unitary limit. The extrapolated quantities are in a reasonable
agreement with those in the literature.
