Mean Field Calculation of Thermal Properties of Simple Nucleon Matter on a Lattice

Thermal properties of single species nucleon matter are investigated assuming a simple form of the nucleon-nucleon interaction. The nucleons are placed on a cubic lattice, hopping from site to site and interacting through a spin-dependent force, as in the extended, attractive Hubbard model. A mean field calculation in the Hartree-Fock Bogoliubov approximation suggests that the superfluid ground state generated by strong nucleon pairing undergoes a second-order phase transition to a normal state as the temperature increases. The calculation is shown to lead to a promising description of the thermal properties of low-density neutron matter. A possibility of a density wave phase is also examined.Comment: 30 pages, 8 figures, to appear in Physical Review

Possibility of \Lambda\Lambda pairing and its dependence on background density in relativistic Hartree-Bogoliubov model

We calculate a \Lambda\Lambda pairing gap in binary mixed matter of nucleons and \Lambda hyperons within the relativistic Hartree-Bogoliubov model. Lambda hyperons to be paired up are immersed in background nucleons in a normal state. The gap is calculated with a one-boson-exchange interaction obtained from a relativistic Lagrangian. It is found that at background density \rho_{N}=2.5\rho_{0} the \Lambda\Lambda pairing gap is very small, and that denser background makes it rapidly suppressed. This result suggests a mechanism, specific to mixed matter dealt with relativistic models, of its dependence on the nucleon density. An effect of weaker \Lambda\Lambda attraction on the gap is also examined in connection with revised information of the \Lambda\Lambda interaction.Comment: 8 pages, 6 figures, REVTeX 4; substantially rewritten, emphasis is put on the LL pairing in pure neutron matte

Superfluidity of Σ−\Sigma^- hyperons in β\beta-stable neutron star matter

In this work we evaluate the $^1S_0$ energy gap of $\Sigma^-$ hyperons in $\beta$-stable neutron star matter. We solve the BCS gap equation for an effective $\Sigma^-\Sigma^-$ pairing interaction derived from the most recent parametrization of the hyperon-hyperon interaction constructed by the Nijmegen group. We find that the $\Sigma^-$ hyperons are in a $^1S_0$ superfluid state in the density region $\sim 0.27-0.7$ fm$^{-3}$, with a maximum energy gap of order 8 MeV at a total baryon number density of $\sim 0.37$ fm$^{-3}$ and a $\Sigma^-$ fraction of about 8%. We examine the implications on neutron star cooling.Comment: 4 pages, double column, 4 figures. Accepted in PR

Extended-soft-core Baryon-Baryon Model II. Hyperon-Nucleon Interaction

The YN results are presented from the Extended-soft-core (ESC) interactions. They consist of local- and non-local-potentials due to (i) One-boson-exchange (OBE), with pseudoscalar-, vector-, scalar-, and axial-vector-nonets, (ii) Diffractive exchanges, (iii) Two-pseudoscalar exchange, and (iv) Meson-pair-exchange (MPE). This model, called ESC04, describes NN and YN in a unified way using broken flavor SU(3)-symmetry. Novel ingredients are the inclusion of (i) the axial-vector-mesons, (ii) a zero in the scalar- and axial-vector meson form factors. We describe simultaneous fits to the NN- and YN-data, using four options in the ESC-model. Very good fits were obtained. G-matrix calculations with these four options are also reported. The obtained well depths (U_\Lambda, U_\Sigma, U_\Xi) reveal distinct features of ESC04a-d. The \Lambda\Lambda-interactions are demonstrated to be consistent with the observed data of_{\Lambda\Lambda}^6He. The possible three-body effects are investigated by considering phenomenologically the changes of the vector-meson masses in a nuclear medium.Comment: preprint vesion 66 pages, two-column version 27 pages, 17 figure

Superfluid Phase Transitions in Dense Neutron Matter

The phase transitions in a realistic system with triplet pairing, dense neutron matter, have been investigated. The spectrum of phases of the $^3P_2-^3F_2$ model, which adequately describes pairing in this system, is analytically constructed with the aid of a separation method for solving BCS gap equation in states of arbitrary angular momentum. In addition to solutions involving a single value of the magnetic quantum number (and its negative), there exist ten real multicomponent solutions. Five of the corresponding angle-dependent order parameters have nodes, and five do not. In contrast to the case of superfluid $^3$He, transitions occur between phases with nodeless order parameters. The temperature dependence of the competition between the various phases is studied.Comment: 11 pages, 2 figure

Quark description of the Nambu-Goldstone bosons in the color-flavor locked phase

We investigate the color-singlet order parameters and the quark description of the Nambu-Goldstone (NG) bosons in the color-flavor locked (CFL) phase. We put emphasis on the NG boson (phason) called ``H'' associated with the $\mathrm{U_B(1)}$ symmetry breaking. We qualitatively argue the nature of H as the second sound in the hydrodynamic regime. We articulate, based on a diquark picture, how the structural change of the condensates and the associated NG bosons occurs continuously from hadronic to CFL quark matter if the quark-hadron continuity is realized. We sharpen the qualitative difference between the flavor octet pions and the singlet phason. We propose a conjecture that superfluid H matter undergoes a crossover to a superconductor with tightly-bound diquarks, and then a crossover to superconducting matter with diquarks dissociated.Comment: 14 pages, 1 table, 1 figure and confusing statements are correcte

S-wave Pairing of Λ\Lambda Hyperons in Dense Matter

In this work we calculate the $^1S_0$ gap energies of $\Lambda$ hyperons in neutron star matter. The calculation is based on a solution of the BCS gap equation for an effective G-matrix parameterization of the $\Lambda-\Lambda$ interaction with a nuclear matter background, presented recently by Lanskoy and Yamamoto. We find that a gap energy of a few tenths of MeV is expected for $\Lambda$ Fermi momenta up to about 1.3 fm$^{-1}$. Implications for neutron star matter are examined, and suggest the existence of a $\Lambda$ $^1S_0$ superfluid between the threshold baryon density for $\Lambda$ formation and the baryon density where the $\Lambda$ fraction reaches $15-20$.Comment: 16 pages, Revtex, 9 figures, 33 reference

Pairing properties of nucleonic matter employing dressed nucleons

A survey of pairing properties of nucleonic matter is presented that includes the off-shell propagation associated with short-range and tensor correlations. For this purpose, the gap equation has been solved in its most general form employing the complete energy and momentum dependence of the normal self-energy contributions. The latter correlations include the self-consistent calculation of the nucleon self-energy that is generated by the summation of ladder diagrams. This treatment preserves the conservation of particle number unlike approaches in which the self-energy is based on the Brueckner-Hartree-Fock approximation. A huge reduction in the strength as well as temperature and density range of ${}^3S_1$-${}^3D_1$ pairing is obtained for nuclear matter as compared to the standard BCS treatment. Similar dramatic results pertain to ${}^1S_0$ pairing of neutrons in neutron matter.Comment: 15 pages, 10 figure

Pair condensation and bound states in fermionic systems

We study the finite temperature-density phase diagram of an attractive fermionic system that supports two-body (dimer) and three-body (trimer) bound states in free space. Using interactions characteristic for nuclear systems, we obtain the critical temperature T_c2 for the superfluid phase transition and the limiting temperature T_c3 for the extinction of trimers. The phase diagram features a Cooper-pair condensate in the high-density, low-temperature domain which, with decreasing density, crosses over to a Bose condensate of strongly bound dimers. The high-temperature, low-density domain is populated by trimers whose binding energy decreases toward the density-temperature domain occupied by the superfluid and vanishes at a critical temperature T_c3 > T_c2.Comment: 11 pages, 4 figures, uses RevTex; v2: 12 pages, 4 figures, matches published versio

Effect of hyperon bulk viscosity on neutron-star r-modes

Neutron stars are expected to contain a significant number of hyperons in addition to protons and neutrons in the highest density portions of their cores. Following the work of Jones, we calculate the coefficient of bulk viscosity due to nonleptonic weak interactions involving hyperons in neutron-star cores, including new relativistic and superfluid effects. We evaluate the influence of this new bulk viscosity on the gravitational radiation driven instability in the r-modes. We find that the instability is completely suppressed in stars with cores cooler than a few times 10^9 K, but that stars rotating more rapidly than 10-30% of maximum are unstable for temperatures around 10^10 K. Since neutron-star cores are expected to cool to a few times 10^9 K within seconds (much shorter than the r-mode instability growth time) due to direct Urca processes, we conclude that the gravitational radiation instability will be suppressed in young neutron stars before it can significantly change the angular momentum of the star.Comment: final PRD version, minor typos etc correcte