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We apply parquet-diagram summation methods for the calculation of thesuperfluid gap in $S$-wave pairing in neutron matter for realisticnucleon-nucleon interactions such as the Argonne $v_6$ and the Reid $v_6$potentials. It is shown that diagrammatic contributions that are outside theparquet class play an important role. These are, in variational theories,identified as so-called "commutator contributions". Moreover, using aparticle-hole propagator appropriate for a superfluid system results in thesuppression of the spin-channel contribution to the induced interaction.Applying these corrections to the pairing interaction, our results agree quitewell with Quantum Monte Carlo data.

Variational and parquet-diagram calculations for neutron matter. III. S-wave pairing