$^1S_0$ pairing in neutron matter

TL;DR

This paper calculates the superfluid pairing gap in neutron matter using realistic nucleon-nucleon interactions and advanced many-body techniques, providing insights into neutron superfluidity relevant for nuclear physics and astrophysics.

Contribution

It introduces a detailed correlated-basis formalism and Fermi hypernetted-chain methods to accurately compute neutron pairing gaps with realistic interactions.

Findings

No dimerization instability found at nuclear saturation density.

Different FHNC-EL implementations agree within 1%.

Realistic interactions do not lead to divergence in in-medium scattering length.

Abstract

We report calculations of the superfluid pairing gap in neutron matter for the $^1S_0$ components of the Reid soft-core $V_6$ and the Argonne $V_{4}'$ two-nucleon interactions. Ground-state calculations have been carried out using the central part of the operator-basis representation of these interactions to determine optimal Jastrow-Feenberg correlations and corresponding effective pairing interactions within the correlated-basis formalism (CBF), the required matrix elements in the correlated basis being evaluated by Fermi hypernetted-chain techniques. Different implementations of the Fermi-Hypernetted Chain Euler-Lagrange method (FHNC-EL) agree at the percent level up to nuclear matter saturation density. For the assumed interactions, which are realistic within the low density range involved in $^1S_0$ neutron pairing, we did not find a dimerization instability arising from divergence of the in-medium scattering length, as was reported recently for simple square-well and Lennard-Jones potential models (Phys. Rev. A {\bf 92}, 023640 (2015)).