Nuclear matter and finite nuclei exhibit the property of superfluidity by forming Cooper pairs. We review the microscopic theories and methods that are being employed to understand the basic properties of superfluid nuclear systems, with emphasis on the spatially extended matter encountered in neutron stars, supernova envelopes, and nuclear collisions. Our survey of quantum many-body methods includes techniques that employ Green functions, correlated basis functions, and Monte Carlo sampling of quantum states. With respect to empirical realizations of nucleonic and hadronic superfluids, this review is focused on progress that has been made toward quantitative understanding of their properties at the level of microscopic theories of pairing, with emphasis on the condensates that exist under conditions prevailing in neutron-star interiors. These include singlet S-wave pairing of neutrons in the inner crust, and, in the quantum fluid interior, singlet-S proton pairing and triplet coupled P -F -wave neutron pairing. Additionally, calculations of weak-interaction rates in neutron-star superfluids within the Green function formalism are examined in detail. We close with a discussion of quantum vortex states in nuclear systems and their dynamics in neutron-star superfluid interiors. PACS. 97.60.Jd Neutron stars -21.65.+f Nuclear matter -47.37.+q Hydrodynamic aspects of superfluidity; quantum fluids -67.85.+d Ultracold gases, trapped gases -74.25.Dw Superconductivity phase diagrams Contents arXiv:1802.00017v4 [nucl-th] 26 Sep 2019 emerge in the interaction part of the Hamiltonian when evaluating Eq. (5) in terms of Bogolyubov operators vanish. Such terms would account for fluctuations in the system, but are beyond the scope of the present mean-field treatment. 4 Note that the variation δ(E − µN )/δn p,↑ , with up and vp held constant, yields the quantity Ep, confirming its interpretation. Armen Sedrakian, John W. Clark: Superfluidity in nuclear systems and neutron stars 5

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We show that homogeneous superconductors with broken spin/isospin symmetry lower their energy via a transition to a novel superconducting state where the Fermi surfaces are deformed to a quasiellipsoidal form at zero total momentum of Cooper pairs. In this state, the gain in the condensation energy of the pairs dominates over the loss in the kinetic energy caused by the lowest order (quadrupole) deformation of Fermi surfaces from the spherically symmetric form. The phase transition from the spherically symmetric state to the superconducting state with broken rotational symmetry is first order.

Various nuclear structure observables are evaluated employing low-momentum nucleonnucleon (NN) potentials V low−k derived from the CD-Bonn and Nijmegen NN interactions V N N . By construction, the high momentum modes of the original V N N are integrated out in V low−k , with the requirement that the deuteron binding energy and low energy phase shifts of V N N are exactly reproduced. Using this interaction, we evaluate the bulk properties (binding energy and saturation density) of nuclear matter and finite nuclei, in particular their dependence on the cut-off parameter. We also study the pairing gap and the residual interaction in nuclear matter in terms of the Landau parametrization. At low and medium densities, the HF and BHF binding energies for nuclear matter calculated with the V low−k 's derived from the CD-Bonn and Nijmegen potentials are nearly identical. The pairing gaps and Landau parameters derived from V low−k are remarkably close to those given by the full-space V N N . The V low−k interactions, however, fail to reproduce the saturation property of nuclear matter at higher densities if the cut-off for the high momentum modes is assumed density independent.

The hypernuclear matter is studied within the relativistic Hartree-Fock theory employing several parametrizations of the hypernuclear density functional with density dependent couplings. The equations of state and compositions of hypernuclear matter are determined for each parametrization and compact stars are constructed by solving their structure equations in spherical symmetry. We quantify the softening effect of Fock terms on the equation of state, as well as discuss the impact of tensor interactions, which are absent in the Hartree theories. Starting from models of density functionals which are fixed in the nuclear sector to the nuclear phenomenology, we vary the couplings in the hyperonic sector around the central values which are fitted to the hyperon potentials in nuclear matter. We use the SU(6) spin-flavor and SU(3) flavor symmetric quark models to relate the hyperonic couplings to the nucleonic ones. We find, consistent with previous Hartree studies, that for the SU(6) model the maximal masses of compact stars are below the two-solar mass limit. In the SU(3) model we find sufficiently massive compact stars with cores composed predominantly of Λ and Ξ hyperons and a low fraction of leptons (mostly electrons). The parameter space of the SU(3) model is identified where simultaneously hypernuclear compact stars obey the astrophysical limits on pulsar masses and the empirical hypernuclear potentials in nuclear matter are reproduced. arXiv:1801.07084v2 [nucl-th]