Three-Nucleon Forces and Triplet Pairing in Neutron Matter

The existence of superfluidity of the neutron component in the core of a neutron star, associated specifically with triplet P-wave pairing, is currently an open question that is central to interpretation of the observed cooling curves and other neutron-star observables. Ab initio theoretical calculations aimed at resolving this issue face unique challenges in the relevant high-density domain, which reaches beyond the saturation density of symmetrical nuclear matter. These issues include uncertainties in the three-nucleon (3N) interaction and in the effects of strong short-range correlations—and more generally of in-medium modification of nucleonic self-energies and interactions. A survey of existing solutions of the gap equations in the triplet channel demonstrates that the net impact on the gap magnitude of 3N forces, coupled channels, and mass renormalization shows extreme variation dependent on specific theoretical inputs, in some cases even pointing to the absence of a triplet gap, thus motivating a detailed analysis of competing effects within a well-controlled model. In the present study, we track the effects of the 3N force and in-medium modifications in the representative case of the ^3P_2 channel, based on the Argonne v_{18} two-nucleon (2N) interaction supplemented by 3N interactions of the Urbana IX family. Sensitivity of the results to the input interaction is clearly demonstrated. We point out consistency issues with respect to the simultaneous treatment of 3N forces and in-medium effects, which warrant further investigation. We consider this pilot study as the first step toward a systematic and comprehensive exploration of coupled-channel ^3P F_2 pairing using a broad range of 2N and 3N interactions from the current generation of refined semi-phenomenological models and models derived from chiral effective field theory.