  Experiments with cold Fermi atoms can be tuned to probe strongly interacting
fluids that are very similar to the low-density neutron matter found in the
crusts of neutron stars. In contrast to traditional superfluids and
superconductors, matter in this regime is very strongly paired, with gaps of
the order of the Fermi energy. We compute the T=0 equation of state and pairing
gap for cold atoms and low-density neutron matter as a function of the Fermi
momentum times the scattering length. Results of quantum Monte Carlo
calculations show that the equations of state are very similar. The neutron
matter pairing gap at low densities is found to be very large but, except at
the smallest densities, significantly suppressed relative to cold atoms because
of the finite effective range in the neutron-neutron interaction.
