  We study in detail the dependence of the 1S0 superfluid pairing gap on
nuclear interactions and on charge-independence breaking at the BCS level.
Starting from chiral effective-field theory and conventional nucleon-nucleon
(NN) interactions, we use the renormalization group to generate low-momentum
interactions V_{low k} with sharp and smooth regulators. The resulting BCS gaps
are well constrained by the NN scattering phase shifts, and the cutoff
dependence is very weak for sharp or sufficiently narrow smooth regulators with
cutoffs Lambda > 1.6 fm^{-1}. It is therefore likely that the effect of
three-nucleon interactions on 1S0 superfluidity is small at the BCS level. The
charge dependence of nuclear interactions has a 10% effect on the pairing gap.
