3P2–3F2 pairing in dense neutron matter: the spectrum of solutions Original Research Article

The 3P2–3F2 pairing model is generally considered to provide an adequate description of the superfluid states of neutron matter at densities some 2–3 times that of saturated symmetrical nuclear matter. The problem of solving the system of BCS gap equations expressing the 3P2–3F2 model is attacked with the aid of the separation approach. This method, developed originally for quantitative study of S-wave pairing in the presence of strong short-range repulsions, serves effectively to reduce the coupled, singular, nonlinear BCS integral equations to a set of coupled algebraic equations. For the first time, sufficient precision becomes accessible to resolve small energy splittings between the different pairing states. Adopting a perturbative strategy, we are able to identify and characterize the full repertoire of real solutions of the 3P2–3F2 pairing model, in the limiting regime of small tensor-coupling strength. The P–F channel coupling is seen to lift the striking parametric degeneracies revealed by a earlier separation treatment of the pure, uncoupled 3P2 pairing problem. Remarkably, incisive and robust results are obtained solely on the basis of analytic arguments. Unlike the traditional Ginzburg–Landau approach, the analysis is not restricted to the immediate vicinity of the critical temperature, but is equally reliable at zero temperature. Interesting connections and contrasts are drawn between triplet pairing in dense neutron matter and triplet pairing in liquid 3He.