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. 关键词： 同位旋非对称核物质 质子和中子超流性 三体核力 BCS理论     

Superfluid states in β-stable nuclear matter

Two superfluid states of nuclear matter, which are supposed to play an important role in neutron stars, are discussed: the first one due to the proton-proton ¹ S ₀ pairing in β-equilibrium nuclear matter; the second one due to the anisotropic neutron-neutron ³ PF ₂ pairing in neutron matter. Since the two phases appear at high density of nuclear matter, the three-body forces were added to the pairing interaction and the strong correlation effects in the single-paricle spectrum. The energy gaps, obtained solving the extended BCS equations, significantly deviate from the values without medium effects so as to limit the role of these two superfluid states in the interpretation of phenomena occurring in the neutron-star core.     

利用密度相关的相对论平均场理论对核物质与中子星的研究(英文)

研究和详细地比较了RMF理论中不同的有效相互作用强度的密度依赖性, 并且讨论了这种密度依赖性对于核物质和中子星性质的影响. 对于核物质, 不同的参数组给出的对称核物质的饱和点非常接近, 基本都在经验值的范围内. 对于中子星, 考虑超子后不同参数组给出的质量极限的范围为1.52—2.06 M☉, 半径为10.24—11.38 km.The density dependencies of various effective interaction strengths in the relativistic mean field and their influences on the properties of nuclear matter and neutron stars are studied and carefully compared. The differences of saturation properties given by various effective interactions are subtle in symmetric nuclear matter. The Oppenheimer Volkoff mass limits of neutron stars calculated from different equations of state are 1.52—2.06 M☉, and the radii are 10.24—11.38 km with hyperons included.     

核物质的对称能与中子皮厚度(英文)

在现有的平均场模型中引入同位旋相关的高阶修正项．研究了核物质对称能的密度依赖性和。^208Pb的中子皮厚度。采用新提出的PK1相互作用以及NL3．S271和Z271相互作用．得到核物质饱和点对称能的范围为29-38MeV以及相应的^208Pb中子皮厚度为0．17—0.28fm．在所有相互作用中，核物质饱和点的对称能与^208Pb的中子皮厚度近似呈线性关系。After adding isospin dependent high order correction terms to existing relativistic mean field models (RMF), the density dependence of symmetry energy and the neutron skin thickness S for 208Pb are studied. Using the new effective interaction PK1, together with NL3, S271 and Z271, a range of 29—38 MeV for the symmetry energy for nuclear matter at saturation point and the corresponding neutron skin thickness S = 0.14—0.28 fm for 208Pb are obtained. For all effective interactions, a linear relation between the symmetry energy at saturation point and the neutron skin thickness for 208Pb is observed.     

Medium polarization and pairing in asymmetric nuclear matter

The many-body theory of asymmetric nuclear matter is developed beyond the Brueckner–Hartree–Fock approximation to incorporate the medium polarization effects. The extension is performed within the Babu–Brown induced interaction theory. After deriving the particle–hole interaction in the form of Landau–Migdal parameters, the effects of the induced component on the symmetry energy are investigated along with the screening of ¹ S ₀ proton–proton and ³ PF ₂ neutron–neutron pairing, which are relevant for the neutron-star cooling. The crossover from repulsive (screening) to attractive (anti-screening) interaction going from pure neutron matter to symmetric nuclear matter is discussed.     

Isovector Scalar Field Effects in Asymmetric Nuclear Matter

Density-dependent parametrization models of the nucleon-meson coupfing constants, including the isovector scalar δ-field, are applied to asymmetric nuclear matter. The nuclear equation of state （EOS） and the neutron star properties are studied in a relativistic Lagrangian density, using the relativistic mean field （RMF） hadron theory. It is known that the δ-field in the constant coupling scheme leads to a larger repulsion in dense neutron-rich matter and to a definite splitting of proton and neutron effective masses, finally influences the stability of the neutron stars. We use density-dependent models of the nucleon-meson couplings to study the properties of neutron star matter and to reexamine the （~-field effects in asymmetric nuclear matter. Our calculation shows that the stability conditions of the neutron star matter can be improved in presence of the δ-meson in the density-dependent models of the coupling constants. The EOS of nuclear matter strongly depends on the density dependence of the interactions.     

基于相对论平均场有效对力的中子物质BCS-BEC渡越

基于核物质的相对论Hartree-Bogoliubov（RHB）理论,采用相对论平均场单玻色子交换形式的有效对相互作用,研究了不同对力强度下双中子关联及其中的BCS-BEC渡越现象。通过引入有效衰减因子χ调节对力强度,定量分析费米面处中子对能隙和单粒子动能比值△_Fn/e_Fn及无量纲参数1/（k_Fna）随费米动量k_Fn的演化行为,发现双中子对在χ=0.51时进入BCS-BEC渡越区域,在χ=0.67时可达到幺正极限。进而分析了中子对能隙、中子对波函数及相干长度等物理量在相应临界点处的特征,并给出渡越时双中子短程关联概率的定量判据。发现当配对中子处于平均中子间距以内的概率P（d_n）?0.80时,双中子对从纯BCS耦合过渡到BCS-BEC渡越区域。Based on the relativistic Hartree-Bogoliubov theory in nuclear matter, the dineutron correlations and the crossover from Bardeen-Cooper-Schrieffer (BCS) region of neutron Cooper pairs to Bose-Einstein condensation (BEC) are investigated with the one-boson-exchange type of pairing force generated from the relativistic mean field (RMF) model. By introducing an effective factor χ in the RMF effective pairing interaction, the density dependence of the ratios between neutron pairing gap at Fermi surface and neutron Fermi kinetic energy △_Fn/e_Fn and the dimensionless parameter 1/(k_Fna) are analyzed quantitatively. Then the criteria where dineutron correlations exactly reach the threshold of BCS-BEC crossover or unitary limit are determined to be χ=0.51 or 0.67, respectively. In addition, features of neutron pairing gap, Cooper pair wave function and dineutron coherence length are illustrated, and the value of the probability for partner neutrons correlated within the average inter-neutron distance, namely P (d_n) ?0.80, is obtained as a criterion of BCS-BEC crossover.     

Some Aspects of Nuclear Structure in Relativistic Approach

The nucleon effective interaction in the nuclear medium is investigated in the framework of the DiracBrueckner-Hartree-Fock (DBHF) approach. A new decomposition of the Dirac structure of nucleon self-energy in the DBHF is adopted for asymmetric nuclear matter. The properties of finite nuclei are investigated with the nucleon effective interaction. The agreement with the experimental data is satisfactory. The relativistic microscopic optical potential in asymmetric nuclear matter is investigated in the DBHF approach. The proton scattering from nuclei is calculated and compared with the experimental data. A proper treatment of the resonant continuum for exotic nuclei is studied. The width effect of the resonant continuum on the pairing correlation is discussed. The quasiparticle relativistic random phase approximation based on the relativistic mean-field ground state in the response function formalism is also addressed.     

Some Aspects of Nuclear Structure in Relativistic Approach

The nucleon effective interaction in the nuclear medium is investigated in the framework of the DiracBrueckner-Hartree-Fock (DBHF) approach. A new decomposition of the Dirac structure of nucleon self-energy in the DBHF is adopted for asymmetric nuclear matter. The properties of finite nuclei are investigated with the nucleon effective interaction. The agreement with the experimental data is satisfactory. The relativistic microscopic optical potential in asymmetric nuclear matter is investigated in the DBHF approach. The proton scattering from nuclei is calculated and compared with the experimental data. A proper treatment of the resonant continuum for exotic nuclei is studied. The width effect of the resonant continuum on the pairing correlation is discussed. The quasiparticle relativistic random phase approximation based on the relativistic mean-field ground state in the response function formalism is also addressed.     

Non-empirical pairing energy density functional

We perform systematic calculations of pairing gaps in semi-magic nuclei across the nuclear chart using the Energy Density Functional method and a non-empirical pairing functional derived, without further approximation, at lowest order in the two-nucleon vacuum interaction, including the Coulomb force. The correlated single-particle motion is accounted for by the SLy4 semi-empirical functional. Rather unexpectedly, both neutron and proton pairing gaps thus generated are systematically close to experimental data. Such a result further suggests that missing effects, i.e. higher partial waves of the NN interaction, the NNN interaction and the coupling to collective fluctuations, provide an overall contribution that is sub-leading as for generating pairing gaps in nuclei. We find that including the Coulomb interaction is essential as it reduces proton pairing gaps by up to 40%.     

A Separable Pairing Force in Nuclear Matter

The method introduced by Duguet is adopted to derive a separable form of the pairing interaction in the ^1So channel from a bare or an effective nucleon-nucleon （NN） interaction in nuclear matter. With this approach the separable pairing interaction reproduces the pairing properties provided by its corresponding NN interaction. In this work, separable forms of pairing interactions in the ^1So channel for the bare NN interaction, Bonn potential and the Gogny effective interaction are obtained. It is found that the separable force of the Gogny effective interaction in the 1So channel has a clear link with the bare NN interaction. With such a simple separable form pairing properties provided by the Gogny force in nuclear matter can be reproduced.     

The skyrme-plus-pairing effective interaction and the global neutron-excess dependence of the pairing gap

The neutron and proton pairing gaps were recently found to have a global dependence on neutron excess. We investigate whether the couplings necessary to obtain this behaviour can be provided by a mean field associated with a Skyrme-type plus usual pairing effective interaction. The parameters of this effective interaction are constrained by nuclear-matter properties, such as binding energy, saturation density, effective mass and values of the second derivatives of the energy with respect to the four densities (neutron and proton with spin-up and spin-down), together with the surface energy. The pairing gaps are then calculated as a function of neutron excess for various parameter sets for very large systems and for finite nuclei in the local-density approximation. We find that the empirical results cannot be reproduced by this procedure. We put forward therefore the hypothesis that, to account for this failure, the usual phenomenology of effective interactions in nuclei ought to be modified; we propose a simple residual neutron-proton interaction that can do that, yet maintains all the previous successes.     

The Landau-Migdal parameters from the Brueckner theory

The zero-order Landau-Migdal parameters are discussed in the framework of the Brueckner-Hartree-Fock approximation with realistic two- and three-body forces. Their usefulness is proved in two applications. First, the structure functions in high-density nuclear matter are calculated within the linear response theory to weak probes and the neutrino mean free path is predicted for neutron stars. Second, the screening of the low-density neutron matter to the neutron pairing is calculated in the RPA without and with induced interaction. The extension of the calculation to symmetric nuclear matter reveals the anti-screening effect of the proton medium polarization.     

Landau parameters and pairing-on the shores of the nuclear Fermi sea

We present a systematic scheme for calculating the ground-state energy, single-particle energies and the effective mass, Fermi-liquid parameters, and pairing matrix elements for nuclear and neutron matter with realistic state-dependent interactions. The method retains much of the clarity of more conventional treatments while permitting reliable numerical calculations. Deficiencies in the central Jastrow correlation operator ansatz are largely overcome by low-order perturbation theory in the correlated basis generated by the Jastrow operator. Calculations of these quantities are presented for the Reid and Bethe-Johnson interactions. An analysis of the results emphasizes the importance of state-dependent correlations arising directly from the interaction or indirectly through many-body effects. The numerical results provide insight into the actual structure of the self-energy operator in nuclear and neutron matter and into the usefulness of sum rules for the quasiparticle interaction and the Landau parameters.     

核势和核子有效质量的同位旋相关性

在Dirac Brueckner Hartree-Fock (DBHF)理论框架下研究了核子光学势和核子有效质量的同位旋相关性. 非对称核物质的计算采用了DBHF的核子自能的Dirac结构的新的分解方法, 核子自能的实部是用G矩阵在Hartree-Fock近似下计算得到, 而虚部从极化图得到. 用核子的薛定谔等价势可以得到核子矢量有效质量. 研究表明考虑了核势的能量相关性在丰中子核物质情况下核子矢量有效质量比质子的大.     

Investigation of the Mg isotopes using the shell-model-like approach in relativistic mean field theory

Ground state properties for Mg isotopes, including binding energies, one- and two-neutron separation energies, pairing energies, nuclear matter radii and quadrupole deformation parameters, are obtained from the self-consistent relativistic mean field (RMF) model with the pairing correlations treated by a shell-mode-like approach (SLAP), in which the particle-number is conserved and the blocking effects are treated exactly. The experimental data, including the binding energies and the one- and two-neutron separation energies, which are sensitive to the treatment of pairing correlations and block effects, are well reproduced by the RMF+SLAP calculations.     

Neutral color-spin-locking phase in neutron stars

We present results for the spin-1 color-spin-locking (CSL) phase using a NJL-type model in two-flavor quark matter for compact stars applications. The CSL condensate is flavor symmetric and therefore charge and color neutrality can easily be satisfied. We find small energy gaps ≃ 1MeV, which make the CSL matter composition and the EoS not very different from the normal quark matter phase. We keep finite quark masses in our calculations and obtain no gapless modes that could have strong consequences in the late cooling of neutron stars. Finally, we show that the region of the phase diagram relevant for neutron star cores, when asymmetric flavor pairing is suppressed, could be covered by the CSL phase.     

Incompressibility and single-particle potential for asymmetric nuclear matter with Skyrme potential

The incompressibility and the single-particle potential of asymmetric nuclear matter have been investigated in the framework of the Skyrme interaction. These parameters have been studied as functions of the nuclear density, the neutron excess parameter, and the temperature. The ratio of the isothermal incompressibility of hot nuclear matter to the incompressibility of cold nuclear matter for different values of neutron excess as a function of temperature is calculated. It is observed that this ratio decreases with temperature increasing apart from pure neutron matter when the growth of temperature leads to the growth of incompressibility. The symmetry incompressibility has been calculated as a function of density for different values of temperature. The text was submitted by the authors in English.