The Brueckner-Hartree-Fock Equation of State for Nuclear Matter and Neutron Skin

The equation of state for nuclear matter is presented within the Brueckner Hartree-Fock （BHF） scheme, by using the realistic Argonne VI8 or Bonn B two-nucleon potentials plus their corresponding microscopic three-nucleon forces. It is then applied to calculate the properties of finite nuclei within a simple liquid-drop model, and we compare the calculated volume, surface, and Coulomb parameters with the empirical ones from the liquid drop model. Nuclear density distributions and charge radii in good agreement with the experimental data are obtained~ and we predict the neutron skin thickness of various nuclei.

Extraction of Nuclear Matter Properties from Nuclear Masses by a Model of Equation of State

The extraction of nuclear matter properties from measured nuclear masses is investigated in the energy density functional formalism of nuclei.It is shown that the volume energy a1 and the nuclear incompressibility Ko depend essentially on μnN -+- pZ - 2EN,whereas the symmetry energy J and the density symmetry coefficient L as well as symmetry incompressibility Ks depend essentially on μn - μp,where μp ＝μp - Ec/ Z,μn and μp are the neutron and proton chemical potentials respectively,EN the nuclear energy,and Ec the Coulomb energy.The obtained symmetry energy is J ＝ 28.5 MeV,while other coefficients are uncertain within ranges depending on the model of nuclear equation of state.

The Equation of State of Nuclear Matter and Neutron Stars Properties

The equation of state (EOS) of symmetric nuclear and pure neutron matter has been investigated extensively by adopting the non-relativistic Brueckner-Hartree-Fock (BHF). For more comparison, the extended BHF approaches using the self-consistent Green’s function approach or by including a three-body force will be done. The EOS will be studied for different approaches at zero temperature. We can calculate the total mass and radius of neutron stars using various equations of state. A comparison with relativistic BHF calculations will be done. Relativistic effects are known to be important at high densities, giving an increased repulsion. This leads to a stiffer EOS compared to the EOS derived with a non-relativistic approach.

Temperature Effects on the Equation of State and Symmetry Energy: A Critique

The investigation of strongly interacting systems ranges from matter inside atomic nuclei to matter under extreme conditions in astrophysics. These systems require the introduction of nuclear forces and a systematic many-body approach to solve the strong interaction particles. Understanding the behavior of infinite nuclear matter provides a path to predict the properties of neutron stars and gives insights to astrophysical phenomena. Three-nucleon forces have to be considered when studying nuclear systems, because their impact is necessary to reproduce properties of nuclei and to correctly obtain the neutron drip line. Moreover, they are needed to predict the empirical saturation properties of infinite nuclear matter. The self-consistent Green’s Function approach paves the way for an improved Ab initio analysis of nuclear matter, thereby providing the basis for the equation of state of neutron stars and supernova explosions.

A phenomenological equation of state for isospin asymmetric nuclear matter

A phenomenological momentum-independent(MID) model is constructed to describe the equation of state(EOS) for isospin asymmetric nuclear matter,especially the density dependence of the nuclear symmetry energy Esym(ρ).This model can reasonably describe the general properties of the EOS for symmetric nuclear matter and the symmetry energy predicted by both the sophisticated isospin and momentum dependent MDI model and the Skyrme-Hartree-Fock approach.We find that there exists a nicely linear correlation between Ksym and L as well as between J0/K0 and K0,where L and Ksym represent,respectively,the slope and curvature parameters of the symmetry energy at the normal nuclear density ρ0,while K0 and J0 are,respectively,the incompressibility and the third-order derivative parameter of symmetric nuclear matter at ρ0.These correlations together with the empirical constraints on K0,L and Esym(ρ0) lead to an estimation of -477 MeV Ksat,2 -241 MeV for the second-order isospin asymmetry expansion coefficient for the incompressibility of asymmetric nuclear matter at the saturation point.

Decomposition of the equation of state of asymmetric nuclear matter into different spin-isospin channels

We investigate the equation of state of asymmetric nuclear matter and its isospin dependence in various spin-isospin ST channels within the framework of the Brueckner-Hartree-Fock approach extended to include a microscopic three-body force（TBF） . It is shown that the potential energy per nucleon in the isospinsinglet T = 0 channel is mainly determined by the contribution from the tensor SD coupled channel. At high densities,the TBF effect on the isospin-triplet T = 1 channel contribution turns out to be much larger than that on the T =0 channel contribution. At low densities around and below the normal nuclear matter density,the isospin dependence is found to come essentially from the isospin-singlet SD channel and the isospin-triplet T = 1 component is almost independent of isospin asymmetry. As the density increases,the T = 1 channel contribution becomes sensitive to the isospin asymmetry and at high enough densities its isospin dependence may even become more pronounced than that of the T = 0 contribution. The present results may provide some microscopic constraints for improving effective nucleon-nucleon interactions in a nuclear medium and for constructing new functionals of effective nucleon-nucleon interaction based on microscopic many-body theories.

Influence of Density-Dependent Coupling Constants on Equation of State of Infinite Symmetric Nuclear Matter

In the mean field approximation of nonlinear relativistic a-ω-p model, we have studied the influence of density-dependent coupling constants between nucleons and mesons on the equation of state （EOS） of infinite symmetric nuclear matter in different conditions. We find that the EOS of nuclear matter will become stiffer as e, d in the self- interaction of σ meson increase when the coeffcients except aω in Гω, in which the opposite occurs, are fixed. On the other hand, greater values of aσ, bσ, cσ, aω, dω and smaller values of dσ, bω, cω will lead to stiffer EOS ifc and d are fixed. Besides, greater values of Гω lead to stiffer EOS in high density region for the EOS with same incompressibility coefficient at saturation density.

Constraints on the skewness coefficient of symmetric nuclear matter within the nonlinear relativistic mean field model

Within the nonlinear relativistic mean field(NLRMF) model, we show that both the pressure of symmetric nuclear matter at supra-saturation densities and the maximum mass of neutron stars are sensitive to the skewness coefficient, J_0, of symmetric nuclear matter. Using experimental constraints on the pressure of symmetric nuclear matter at supra-saturation densities from flow data in heavy-ion collisions and the astrophysical observation of a large mass neutron star PSR J0348+0432, with the former favoring a smaller J_0 while the latter favors a larger J_0, we extract a constraint of -494 MeV≤J_0≤-10 MeV based on the NL-RMF model. This constraint is compared with the results obtained in other analyses.

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.

Finite Temperature Asymmetric Nuclear Matter Using Pion Dressing

We study the asymmetric nuclear matter in a nonperturvative manner at finite temperatures using thermofield dynamics method. The nucleon-meson interaction is taken to examine the binding energy (EB), pressure (P) for various proton fractions.

Bulk Properties of Symmetric Nuclear and Pure Neutron Matter

We study the equation of state (EOS) of symmetric nuclear and neutron matter within the framework of the Brueckner-Hartree-Fock (BHF) approach which is extended by including a density-dependent contact interaction to achieve the empirical saturation property of symmetric nuclear matter. This method is shown to affect significantly the nuclear matter EOS and the density dependence of nuclear symmetry energy at high densities above the normal nuclear matter density, and it is necessary for reproducing the empirical saturation property of symmetric nuclear matter in a nonrelativistic microscopic framework. Realistic nucleon-nucleon interactions which reproduce the nucleon-nucleon phase shifts are used in the present calculations.

CHEMICAL POTENTIAL-DENSITY EQUATIONS OF STATE IN FINITE ASYMMETRIC NUCLEAR MATTER WITH SKYRME INTERACTIONS

Using the method of finite temperature real time Green’s function, the equations of stateof the chemical potential-density for finite asymmetric nuclear matter are derived. The ef-fects of the Coulomb potential and the rearrangement potential on liquid-gas phase transitionin the nuclear matter with Skyrme interactions are discussed.

How tightly is the nuclear symmetry energy constrained by a unitary Fermi gas?

We examine critically how tightly the density dependence of nuclear symmetry energy E_(sym)(q) is constrained by the universal equation of state of the unitary Fermi gas EUG(q) considering currently known uncertainties of higher order parameters describing the density dependence of the equation of state of isospin asymmetric nuclear matter. We found that E_(UG)(q) does provide a useful lower boundary for the E_(sym)(q). However, it doesnot tightly constrain the correlation between the magnitude E_(sym)(q_0) and slope L unless the curvature K_(sym)of the symmetry energy at saturation density q_0 is more precisely known. The large uncertainty in the skewness parameters affects the E_(sym)(q_0) versus L correlation by the same almost as significantly as the uncertainty in K_(sym).

Bayesian Inference of Nucleus Resonance and Neutron Skin

In this proceeding,some highlight results on the constraints of the nuclear matter equation of state(EOS)from the data of nucleus resonance and neutron-skin thickness using the Bayesian approach based on the Skyrme-Hartree-Fock model and its extension have been presented.Typically,the anti-correlation and positive correlations between the slope parameter and the value of the symmetry energy at the saturation density under the constraint of the neutron-skin thickness and the isovector giant dipole resonance have been discussed respectively.It’s shown that the Bayesian analysis can help to find a compromise for the“PREXII puzzle”and the“soft Tin puzzle”.The possible modifications on the constraints of lower-order EOS parameters as well as the relevant correlation when higher-order EOS parameters are incorporated as independent variables have been further illustrated.For a given model and parameter space,the Bayesian approach serves as a good analysis tool suitable for multi-messengers versus multi-variables,and is helpful for constraining quantitatively the model parameters as well as their correlations.

中子皮结构及其在核反应中的效应

中子皮是不稳定原子核中存在的一种奇特结构,在核反应过程中会产生各种效应。不同理论模型研究发现,中子皮厚度会影响核-核碰撞中的中子擦去截面、轻粒子产额比、重碎片产额比、光子产生截面等物理量,也与原子核的集团结构、表面宽度、温度等存在密切关系。在高能重离子碰撞中研究发现,中子皮同样存在明确的效应。实验上,基于放射性核束装置可以产生具有中子皮结构的不稳定核,通过测量其与稳定核发生反应后与中子皮敏感的观测量,能提取或确定中子皮厚度。结合核理论模型,可以进一步约束非对称核物质的状态方程及核天体的相关性质。

非均匀核物质状态方程研究

在相对论平均场理论框架下研究非均匀核物质,自洽的Thomas-Fermi近似是一种有效的方法。这种方法假设了非均匀核物质是由原子核及核外中子气和质子气构成。在温度T、质子分支比Yp以及重子密度ρB确定的情况下,通过改变Wigner-Seitz原胞半径,对系统的每重子自由能进行最小化,从而得到热力学稳定态,原胞内的重子分布也可以自洽地得到。由自洽的Thomas-Fermi近似得到的结果可以与之前工作所得到的结果进行详细比较,之前的工作所采用的是参数化的Thomas-Fermi近似方法。

原子核的中子皮厚度与非对称核物质态方程

挑选47组常用的Skyrme参数，采用Skyrme能量密度泛函结合拓展的Thomas-Fermi展开，用约束的密度变分法，我们计算了208^Pb、112-124^Sn、48^Ca、96^Zr、18^O等丰中子核的中子皮厚度并与实验数据分析抽取的中子皮厚度比较，研究了中子皮厚度与非对称核物质态方程中同位旋相关的对称能项之间的关系．我们发现中子皮厚度随对称能系数α,以及对称能在饱和密度附近的斜率L、曲率Ksym的增大呈现近似的线性增大的趋势，对称能越硬的核势确定的中子皮越厚．以反质子湮灭法拟合的参考实验值作为标准，我们给出对称能系数，对称能在饱和密度附近的斜率和曲率的参考范围分别为：αs=30～35MeV，L=20-100MeV，Ksym=256-70MeV。满足这个条件的Skyrme参数有：SLy0-SLy10、SkM^＊、SkP、SLy230a、SkMP、SKT1—3、Ski3、MSk1-2、SⅡ．

对称核物质状态方程

有关热核物质性质的研究一直是核物理、天体物理和宇宙学的一个十分活跃的前沿领域，而其中核物质状态方程的研究又占有相当重要的地位。

核物质热力学性质的扩展Skyrme力研究

从有限温度有限核的扩展Skyrme力自由能密度,熵密度和内能密度出发,计算了对称核物质和非对称核物质的一系列热力学性质,包括每核子内能、熵、核物质状态方程及不可压缩系数.

中子星性质的模型依赖性

采用相对论平均场理论(RMFT)下的GL85,GL92,TM1和TM2等核物质参数组,研究了这些参数组对中子星的粒子数密度分布、状态方程及质量-半径关系的影响.结果表明,在不同的参数组下,超子出现的密度、顺序和种类均不同;状态方程的软硬情况也较大不同;中子星的引力质量和相应的半径有明显不同.计算结果也表明,采用GL85,TM1和TM2等参数组得到的中子星质量和半径均在脉冲星的观测数据范围内,而采用GL92参数组得到的中子星质量小于中子星质量下限1.4M⊙(M⊙=1.99×1030kg为太阳质量).