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We report results of the equation of state of neutron matter in thelow--density regime, where the Fermi wave vector ranges from $0.4 fm^{-1} \leqk_F \leq 1.0 fm^{-1}$. Neutron matter in this regime is superfluid because ofthe strong and attractive interaction in the $^1S_0$ channel. The properties ofthis superfluid matter are calculated starting from a realistic Hamiltonianthat contains modern two-- and three--body interactions. The ground stateenergy and the $^1S_0$ superfluid energy gap are calculated using the AuxiliaryField Diffusion Monte Carlo method. We study the structure of the ground stateby looking at pair distribution functions as well as the Cooper-pair wavefunction used in the calculations.

Equation of state of low--density neutron matter and the $^1S_0$ pairing gap