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

Abstract

We apply parquet-diagram summation methods for the calculation of the superfluid gap in S-wave pairing in neutron matter for realistic nucleon-nucleon interactions such as the Argonne v6 and the Reid v6 potentials. It is shown that diagrammatic contributions that are outside the parquet class play an important role. These are, in variational theories, identified as so-called "commutator contributions". Moreover, using a particle-hole propagator appropriate for a superfluid system results in the suppression of the spin-channel contribution to the induced interaction. Applying these corrections to the pairing interaction, our results agree quite well with Quantum Monte Carlo data.

Triplet Pairing in Neutron Matter

“…Our results of Krotscheck & Wang (2021) agree quite well with these calculations; whether the extension of Monte Carlo methods for systems where complicated tensor-and spin-orbit components of the interaction are essential remains to be seen.…”

“…For our calculations we have used the v 8 form of the nucleonnucleon interaction for the Reid interaction (Reid 1968) as formulated in Day (1981), as well as the Argonne potential (Wiringa et al 1995) as represented in Equations ( 5)-( 6). We have calculated the pairing interaction as described in Krotscheck & Wang (2021). In addition, we have included the spin-orbit term, which is necessary for triplet pairing but plays no role for pairing in the 1 S 0 channel.…”

Variational and parquet-diagram calculations for neutron matter: Structure and energetics

“…and its logical generalization to multiparticle correlation functions has been extremely successful. Here Φ 0 is a model state describing the statistics and, when appropriate, the geometry of the system; for fermions it is normally taken as a Slater determinant but Bardeen-Cooper-Schrieffer (BCS) states have also been used [23][24][25][26][27][28][29].…”

“…We stress, of course, that the dynamic interaction Ŵ (q, ω) is replaced by the the static Ŵ (q) only for the ground state correlations. In both the calculation of the dynamic structure function to be discussed below, as well as in the calculation of pairing phenomena [28,29] we keep the full energy dependence.…”

“…We also stress that, in this case, neither of the the local approximations discussed in Sec. II A 4 is necessary; in fact it is more appropriate to calculate the effective interaction for ω = 0 [29].…”