New method in bardeen-cooper-schrieffer theory: Tiplet pairing in superfluid dense neutron matter

On the basis of the method outlined in the first part of this review, the properties of superfluid dense neutron matter are analyzed in the density region where the spin of a Cooper pair and its total angular momentum are S=1 and J=2, respectively. An analytic solution to the problem of 3P2 pairing in neutron matter is presented. Basic features of the structure and of the energy spectrum of superfluid phases are discussed. Degeneracy that is absolutely dissimilar to that which is associated with the phase transformation of the order parameter in the S-pairing problem is a distinct feature of the structure of the aforementioned phases. It appears that one or even a few numbers characterizing the weight of components associated with different values of the projection M of the total angular momentum J=2 of a Cooper pair can be chosen arbitrarily, while the others adjust to them in accordance with universal laws. As a result, the structure of any phase depends neither on the density, nor on the temperature, nor on any other input parameter. The phases found here form two groups degenerate in energy. One of these groups comprises phases for which the sign of the order parameter remains unchanged over the entire Fermi surface, while the other consists of phases whose order parameter has a zero. The energy splitting between the phases from the different groups is calculated analytically as a function of temperature. The relative magnitude of this splitting changes from approximately 3% at T=0 to zero in the vicinity of the critical point Tc. The role of tensor forces in dense neutron matter is analyzed. It is shown that the mixing of the orbital angular momenta L=1 and L=3 of Cooper pairs that is induced by tensor forces completely removes degeneracy peculiar to the 3P2-pairing problem—the number of phases and their structure at a given temperature are tightly fixed, while the energy spectrum of the phases splits completely.