  We report ab initio calculations of the S wave pairing gap in neutron matter
calculated using realistic nuclear Hamiltonians that include two- and
three-body interactions. We use a trial state, properly optimized to capture
the essential pairing correlations, from which we extract ground state
properties by means of auxiliary field diffusion Monte Carlo simulations. We
extrapolate our results to the thermodynamic limit by studying the finite-size
effects in the symmetry-restored projected Bardeen-Cooper-Schrieffer (PBCS)
theory and compare our results to other ab initio studies done in the past. Our
quantum Monte Carlo results for the pairing gap show a modest suppression with
respect to the mean-field BCS values. These results can be connected to cold
atom experiments, via the unitarity regime where fermionic superfluidity
assumes a unified description, and they are important in the prediction of
thermal properties and the cooling of neutron stars.
