${}^{1}S_0$ Superfluid Phase Transition in Neutron Matter with Realistic Nuclear Potentials and Modern Many-Body Theories

The ${}^{1}S_0$ pairing in neutron matter is studied using realistic two- and three-nucleon interactions. The auxiliary field diffusion Monte Carlo method and correlated basis function theory are employed to get quantitative and reliable estimates of the gap. The two methods are in good agreement up to the maximum gap density and both point to a slight reduction with respect to the standard BCS value. In fact, the maximum gap is about 2.5 MeV at $k_F\sim 0.8{\mathrm{fm}}^{-1}$ in BCS and 2.2–2.4 MeV at $k_F\sim 0.6{\mathrm{fm}}^{-1}$ in correlated matter. In general, the computed medium polarization effects are much smaller than those previously estimated within all theories. Truncations of Argonne $v_{8^{\prime }}$ to simpler forms give the same gaps in BCS, provided the truncated potentials have been refitted to the same $NN$ data set. The three-nucleon interaction provides an additional increase of the gap of about 0.35 MeV.

Figure 1

${}^{1}S_0$ gaps for different nucleon-nucleon potentials and methods. See text.