From odd-even staggering to the pairing gap in neutron matter

Abstract

The properties of neutron matter are integral to the correct description of neutron stars as well as the description of neutron-rich nuclei. One key property of neutron matter is its superfluid behavior in a range of densities relevant to the inner crust of neutron stars. This work investigates the finite-size effects in the pairing gap of a pure neutron matter superfluid system at densities found in the inner crust of cold neutron stars. The BCS (Bardeen-Cooper-Schrieffer) treatment of superfluidity gives rise to the mean-field pairing gap, while a projection after variation (PBCS theory) can provide a beyond-mean-field pairing gap through an odd-even staggering formula. While these two pairing gap results should agree in the thermodynamic limit, in this work we demonstrate that this is the case for systems far from the thermodynamic limit as well. These results can prove valuable to the study of neutron matter since they can connect ab initio approaches to other approaches found in the literature. This is a first step towards a model-independent extraction of the pairing gap in neutron matter.