Microscopic calculation of a pairing gap in semi-infinite nuclear matter

The pairing gap in semi-infinite nuclear matter has been calculated microscopically by solving the gap equation for a nonlocal interaction with the aid of the method proposed by V.A. Khodel, A.V. Khodel, and J.W. Clark [Nucl. Phys. A 598, 390 (1996)] for the case of infinite nuclear matter. The calculation employs the effective pairing interaction obtained previously for semi-infinite geometry on the basis of the separable 3×3 representation of the Paris nucleon-nucleon potential. The gap found in this way changes sharply in the surface region, where it has a pronounced maximum. The dependence of the surface effect on the chemical potential of nuclear matter has been investigated.     

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 ³ P ₂ 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 T _c. 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 ³ P ₂-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.     

非对称核物质中质子和中子的1S0态超流性

利用Brueckner-Hartree-Fock和BCS理论方法,计算了非对称核物质中处于1S0态的质子和中子的对关联能隙,着重研究和讨论了能隙的同位旋依赖性和三体核力的影响.结果表明:随核物质的同位旋非对称度增大,中子1S0态超流相存在的密度范围逐渐缩小而且对关联能隙峰值稍有升高;质子1S0态超流相存在的密度范围迅速扩大而且对关联能隙峰值显著降低.三体核力对非对称核物质中1S0态中子超流性及其同位旋依赖性的影响相对较小,但对1S0态质子超流性具有重要影响,而且其效应随核子数密度增大而迅速增强.三体核力的主要作用是强烈地抑制了具有高非对称度的核物质中高密度区域的1S0态质子超流性,导致质子超流相存在的密度范围显著缩小.     

Bridging the gap by squeezing superfluid matter

Cooper pairing between fermions in dense matter leads to the formation of a gap in the fermionic excitation spectrum and typically exponentially suppresses transport properties. However, we show here that reactions involving conversion between different fermion species, such as Urca reactions in nuclear matter, become strongly enhanced and approach their ungapped level when the matter undergoes density oscillations of sufficiently large amplitude. We study both the neutrino emissivity and the bulk viscosity due to direct Urca processes in hadronic, hyperonic, and quark matter and discuss different superfluid and superconducting pairing patterns.     

Equation of state for pion condensed neutron star matter

We include the effect of the Δ-isobar resonance in the equation of state for neutron star matter in the presence of a pion condensate. We find matter undergoing a first order phase transition after a seconf order phase transition at a much lower density.     

Specific heat of the superfluid neutron matter in neutron star crusts

By means of X-γ andγ-γ coincidence measurements of the³⁵Cl+⁵⁸Ni reaction products, 38γ lines have been identified to be in coincidence with KX(Tc)-rays and assigned to the decay of⁹⁰Ru. Its half-life of 11±3 s has been deduced from the 154.6 keVγ-decay. The result supports our previous identification of⁹⁰Ru produced in the same reactions.     

Equation of state for pion-condensed neutron matter at finite temperature

The equation of state for neutron matter in the presence of a pion condensate is investigated at finite, but small temperature within the σ model. It is found that a transition of van der Waals type takes place at low temperature for sufficiently strong effective p-wave interaction, which disappears however beyond a critical temperature T_c. Within a wide variety of model assumptions, an upper limit of about 50 MeV is found for T_c.     

Equation of state for neutron matter in the Quark Compound Bag model

The equation of state for neutron matter is derived in the framework of the Quark Compound Bag model, in which the nucleon–nucleon interaction is generated by the s-channel exchange of six-quark Jaffe–Low primitives.     

Equation of state of asymmetric nuclear matter and the tidal deformability of neutron star

The European Physical Journal A - In recent years there has been much progress on the investigation of the QCD phase diagram with lattice QCD simulations. In this review we focus on the...     

Equation of state for neutron matter in the presence of a pion condensate

The energy density for neutron matter including a pion condensed phase is studied, with particular emphasis on the role of Δ-isobars. Relativistic corrections to vertex functions involving isobars are considered and turn out to be important in the high density region. We arrive at a simple schematic model in which the inclusion of isobars leads to an effective enhancement of the axial vector coupling constant, which competes with an effective reduction due to the Lorentz-Lorenz correction. In the equation of state, inclusion of a pion condensed phase can lead to an appreciable reduction of total pressure.     

Equation of state of nuclear matter and neutron stars in a hadron mass scaling frame

The equation of state for nuclear matter at finite temperature and the properties of neutron stars are studied starting from an effective Lagrangian in the framework of the relativistic mean field theory. We find that the empirical properties of nuclear matter can be reproduced if the medium effects are mainly described in terms of the Brown-Rho mass scaling on top of the Bonn potential used as the underlying bare nucleon-nucleon interaction. In particular a correct symmetry energy at saturation density is obtained. The extrapolation of the equation of state to neutron matter and some predictions for the neutron-star masses are finally discussed and compared with other nucleonic many-body approaches.PACS: 21.65. + f Nuclear matter - 21.30.Fe Forces in hadronic systems and effective interactions - 97.60.Jd Neutron stars     

1S0 Superfluid phase transition in neutron matter with realistic nuclear potentials and modern many-body theories

The 1S0 pairing in neutron matter is studied using realistic two- and three-nucleon interactions. The auxiliary field diffusion Monte Carlo method and correlated basis function theory are employed to get quantitative and reliable estimates of the gap. The two methods are in good agreement up to the maximum gap density and both point to a slight reduction with respect to the standard BCS value. In fact, the maximum gap is about 2.5 MeV at kF approximately 0.8 fm(-1) in BCS and 2.2-2.4 MeV at kF approximately 0.6 fm(-1)in correlated matter. In general, the computed medium polarization effects are much smaller than those previously estimated within all theories. Truncations of Argonne to simpler forms give the same gaps in BCS, provided the truncated potentials have been refitted to the same data set. The three-nucleon interaction provides an additional increase of the gap of about 0.35 MeV.     

Superfluidity of neutron matter: (II). Triplet pairing

The possibility of neutron triplet pairing and superfluidity in neutron star matter is investigated, and the energy gap and corresponding critical temperature is calculated or estimated as a function of Fermi momentum or density. The calculations are performed for a “one-pion-exchange gaussian” potential, and compared with the results for neutron and proton singlet pairing and superfluidity calculated earlier.The results indicate that neutron superfluidity, corresponding specifically to ³P₂ state pairing, may exist in a high-density shell in the nuclear-matter region of a neutron star, i.e. for 1.6 × 10¹⁴g/cm³ < ρ < 1.4 × 10¹⁵g/cm³, and the maximum self-consistent energy gap is Δ⁰₁k_F ≈ 0.6 MeV and Δ⁰₃(k_F) ≈ 0.1 MeV for an effective mass $\text{m}{}^1\text{≈ 0.75}\text{and}\text{k}{}_{\mathrm{<mtext>F</mtext>}}\text{≈ 2.1}\text{fm}{}^{\mathrm{?1}}$, i.e. for a mas ? ≈ 5.2 × 10¹⁴g/cm³. For $\text{m}{}^1\text{= 1.0}$ we get correspondingly Δ⁰₁(k_F) ≈ 3.3 MeV and Δ⁰₃(k_F) ≈ 0.6 MeV for k_F ≈ 2.2 fm^?1.     

Two quasiparticle scattering and pairing in neutron matter with Skyrme interactions

Pairing matrix elements in neutron matter are computed employing Skyrme interactions under different approaches. We compare the pairing strengths calculated from the exact scattering amplitudes to those obtained as one neglects the integral kernel of the Bethe-Salpeter equation, and to the matrix element of the bare particle-particle interaction with and without rearrangement contribution. The effect upon the gap is analyzed in the frame of the simple weak coupling approximation, in order to indicate possible outcomes of more refined treatments of the pairing problem.     

Surface behaviour of the pairing gap in a slab of nuclear matter

The surface behavior of the pairing gap previously studied for semi-infinite nuclear matter is analyzed in the slab geometry. The gap-shape function is calculated in two cases: a) pairing with the Gogny force in a hard-wall potential and b) pairing with the separable Paris interaction in a Saxon-Woods mean-field potential. It is shown that the surface features are preserved in the case of slab geometry, being almost independent of the width of the slab. It is also demonstrated that the surface enhancement is strengthened as the absolute value of chemical potential decreases which simulates the approach to the nucleon drip line.-1Received: 3 March 2003, Published online: 30 September 2003PACS: 21.30.-x Nuclear forces - 21.60.-n Nuclear structure models and methods - 21.65.+f Nuclear matter - 26.60.+c Nuclear matter aspects of neutron stars