$^1S_0$ pairing in neutron matter

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)).