Low-density neutron matter and the unitary limit

Abstract

We review the properties of neutron matter in the low-density regime. In particular, we revise its ground state energy and the superfluid neutron pairing gap, and analyze their evolution from the weak to the strong coupling regime. The calculations of the energy and the pairing gap are performed, respectively, within the Brueckner-Hartree-Fock approach of nuclear matter and the BCS theory using the chiral nucleon-nucleon interaction of Entem and Machleidt at N 3 LO and the Argonne V18 phenomenological potential. Our results are compared with those of quantum Monte Carlo calculations for neutron matter and cold atoms. The Tan contact parameter in neutron matter is also calculated finding a reasonable agreement with experimental data with ultra-cold atoms only at very low densities. We find that low-density neutron matter exhibits a behavior close to that of a Fermi gas at the unitary limit, although, this limit is actually never reached. We also review the properties (energy, effective mass and quasiparticle residue) of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons, already studied by the author in a recent work, and include new results which confirm that these properties are very close to those of an attractive Fermi polaron in the unitary limit.