Calculation of Quark Condensate in Nuclear Matter with the Chiral Symmetry Spontaneous Breaking Lagrangian

Using the chiral symmetry spontaneous breaking Lagrangian with mean-field approximation, we investigate the in-medium quark condensate 〈qq〉. It is found that the condensate decreases as the nuclear matter density ρ increases. Meanwhile, the desent deviates from the linear decrease and becomes remarkably slow as the density of the nuclear matter further increases. It shows that the chiral symmetry spontaneous breaking is only partially restored in densed nuclear matter.     

The cloudy bag model

We review recent developments in the bag model, in which the constraints of chiral symmetry are explicitly included. The model has profound implications for nuclear, medium energy and high energy physics.     

重离子碰撞中阈能附近超子产生机制

在量子分子动力学输运模型LQMD(Lanzhou quantum molecular dynamics transport model)框架下,研究了不同重离子反应系统中同位旋和核介质效应对超子产生以及动能谱的影响.基于手征有效场理论,引入了动量和密度相关的排斥超子-核子光学势,并且考虑了该势对超子产生截面阈能的修正....     

A phenomenological approach to pion condensation

The threshold of π-condensation in isospin symmetric nuclear matter is studied with a field theoretic model which reproduces the low energy πN data. We find a critical density around normal nuclear matter density. Besides the role of the nucleon-nucleon correlations we investigate the effect of the s-wave πN interaction on- and off-mass-shell. The chiral symmetry breaking Σ-term may impede pion condensation.     

Nuclear energy density functionals constrained by low-energy QCD

A microscopic framework of nuclear energy density functionals is reviewed, which establishes a direct relation between low-energy QCD and nuclear structure, synthesizing effective field theory methods and principles of density functional theory. Guided by two closely related features of QCD in the low-energy limit: a) in-medium changes of vacuum condensates, and b) spontaneous breaking of chiral symmetry; a relativistic energy density functional is developed and applied in studies of ground-state properties of spherical and deformed nuclei.     

核物质四阶对称能中的交换项相关物理

基于协变密度泛函（CDF）理论,核物质四阶对称能可以被分解为动能部分,同位旋单态势能部分以及同位旋三重态势能部分。交换项的引入明显改变了同位旋单态势能部分和同位旋三重态势能部分的密度行为,特别是来自同位旋标量介子-核子耦合道的交换项贡献提供了一个压制作用。作为一种有益的尝试,引入广义的对称能,可以更直观地统一描述核物质各阶对称能效应。The density dependence of nuclear fourth-order symmetry energy S₄ is studied within the covariant density functional (CDF) theory in terms of the kinetic energy, isospin-singlet, and isospin-triplet potential energy parts of the energy density functional. When the Fock diagram is introduced, it is found that both isospin-singlet and isospin-triplet components of the potential energy plays important roles in determining the fourth-order symmetry energy. Especially, an extra suppression, which comes from the Fock terms via isoscalar meson-nucleon coupling channels, is revealed in the isospin-triplet potential part of the fourth-order symmetry energy. As an useful attempt, the generalized symmetry energy is introduced to describe the various orders of nuclear symmetry energies in a visual and self-consistent way.     

基于有限核性质确定核物质对称能的密度依赖性

密度依赖的对称能作为核物质状态方程的同位旋相关部分,是当前核物理和天体物理两个领域共同关注的重要热点问题之一。人们在实验和理论两方面对此进行了大量的探索,然而由于问题的困难性,对其研究尚未达成共识。目前,研究对称能的方法有很多,其中包括微观和唯像核多体理论、重离子碰撞、原子核的巨共振等。近年来,低密对称能的研究已经取得了重要进展。本文综述了利用有限核的信息来约束核物质对称能的密度依赖性方面的研究工作,这一研究途径尽可能地降低了理论分析的模型依赖性。研究表明,208Pb对称能(系数)asym(A)等于参考密度ρA=0.55ρ0处的核物质对称能(系数)。这个关系将有限核与核物质的对称能联系了起来,借此可以探究亚饱和密度核物质对称能的密度依赖性,因此核心目标是准确确定208Pb对称能(系数)。我们通过重核β-衰变能和质量差来提取208Pb对称能(系数),进而约束亚饱和密度下核物质对称能的密度依赖行为。     

Temperature Effects on the Equation of State and Symmetry Energy at Low and High Densities

Thermal properties of symmetric nuclear matter and pure neutron matter are studied in a selfconsistent Green’s function and Brueckner–Hartree–Fock approaches with the inclusion of the contact interaction using CDBONN potential. Also we investigate the temperature dependence of the symmetry energy. The symmetry energy at fixed density is found to generally decrease with temperature. The temperature effects on the nuclear matter symmetry energy are found to be stronger at lower densities while become much weaker at higher densities. The results of several microscopic approaches are compared. Also the results are compared with recent experimental data. There is good agreement between the experimental symmetry energy and those calculated in the Brueckner–Hartree–Fock approach.     

Systematic Study on System Size Dependence of Global Stopping: Role of Momentum-Dependent Interactions and Symmetry Energy

Using the isospin-dependent quantum molecular dynamical model, we systematically study the role of symme- try energy with and without momentum-dependent interactions on the global nuclear stopping. We simulate the reactions by varying the total mass of the system from 80 to 394 at different beam energies from 30 to 1000 Me V/nucleon over central and semi-central geometries. The nuclear stopping is found to be sensitive towards the momentum-dependent interactions and symmetry energy at low incident energies. The momentum-dependent interactions are found to weaken the finite size effects in nuclear stopping.     

Phase Transition in the Chiral Quark Soliton

Chiral symmetry phase transition is studied by making use of the finite temperature Green's function and the path integral approach in the chiral soliton model. The temperature-dependent effective potential is obtained in the one-loop approximation, including quark and σ-, π-meson loop. The critical temperature-versus the nuclear density is calculated. At zero baryop density the critical temperature is 172 MeV. In nuclear medium it is found that the critical temperature decreases fast when the nuclear density is increasing.     

Relationship between the symmetry energy and the single-nucleon potential in isospin-asymmetric nucleonic matter

When skyrmions representing nucleons are put on crystal lattice and compressed to simulate high density, there is a transition above the normal nuclear matter density (n₀) from a matter consisting of skyrmions with integer baryon charge to a state of half-skyrmions with half-integer baryon charge. We exploit this observation in an effective field theory framework to access dense baryonic system. We find that the topology change involved in the transition implies changeover from a Fermi liquid structure to a non-Fermi liquid with the chiral condensate in the “melted-off” nucleon. The ～ 80% of the nucleon mass that remains “unmelted”, invariant under chiral transformation, points to the possible origin of the (bulk of) proton mass that is not encoded in the standard mechanism of spontaneously broken chiral symmetry. The topology change engenders a drastic modification of the nuclear tensor forces, thereby non-trivially affecting the EoS, in particular, the symmetry energy, for compact star matter. It brings in stiffening of the EoS needed to accommodate a neutron star of ～ 2 solar mass. The strong effect on the EoS in general and in the tensor force structure in particular will also have impact on processes that could be measured at RIB-type accelerators.     

The nuclear symmetry energy from relativistic Brueckner-Hartree-Fock model

The microscopic mechanisms of the symmetry energy in nuclear matter are investigated in the framework of the relativistic Brueckner-Hartree-Fock (RBHF) model with a high-precision realistic nuclear potential, pvCDBonn A. The kinetic energy and potential contributions to symmetry energy are decomposed. They are explicitly expressed by the nucleon self-energies, which are obtained through projecting the G-matrices from the RBHF model into the terms of Lorentz covariants. The nuclear medium effects on the nucleon self-energy and nucleon-nucleon interaction in symmetry energy are discussed by comparing the results from the RBHF model and those from Hartree-Fock and relativistic Hartree-Fock models. It is found that the nucleon self-energy including the nuclear medium effect on the single-nucleon wave function provides a largely positive contribution to the symmetry energy, while the nuclear medium effect on the nucleon-nucleon interaction, i.e., the effective G-matrices provides a negative contribution. The tensor force plays an essential role in the symmetry energy around the density. The scalar and vector covariant amplitudes of nucleon-nucleon interaction dominate the potential component of the symmetry energy. Furthermore, the isoscalar and isovector terms in the optical potential are extracted from the RBHF model. The isoscalar part is consistent with the results from the analysis of global optical potential, while the isovector one has obvious differences at higher incident energy due to the relativistic effect.     

A^80核区在束γ谱学研究进展

为深入研究原子核手征对称性自发破缺等重要的科学问题,山东大学(威海)核物理研究团队利用在束γ谱学实验技术,系统研究了A^80核区一系列原子核的能级结构,丰富了这个区域原子核的谱学信息,并对这些原子核的对称性、形状和运动模式等问题进行了探讨。研究结果表明,在A^80核区存在包括奇奇核和奇A核在内的多例候选手性原子核,能级寿命测量支持80Br的手性解释。此外,本文也讨论了随着中子数的增加,手征几何和八极关联效应的演化情况以及这个核区近球形核的中子跨壳激发现象。     

清华大学物理系原子核物理研究的新进展

在清华大学物理系成立80周年之际,对近年来清华大学物理系原子核物理研究的主要进展情况作一介绍,包括原子核高自旋态的实验研究,原子核结构的理论研究,高能核物理的理论研究.在高自旋态研究方面,内容包括在A～100丰中子核区核的集体振动转动带结构、新的准粒子带特性、新手征二重带等特性研究;在A～140丰中子核区核的八极形变及八级关联等特性研究;在A～130缺中子核区核的形状驱动效应,包括扁椭形变带、形状共存等特性研究.在原子核结构理论研究方面,内容包括用相互作用玻色子模型、推转壳模型、投影壳模型以及相对论平均场对原子核特性的研究;对原子核结构或其他量子系统的各种对称性和代数方法的研究,如动力学对称性、超对称性、势代数方法等;与对称性紧密联系的普通李代数和非线性李代数的表示,如普通李代数、李超代数、平方根型非线性李代数、多项式型非线性李代数等.在高能核物理研究方面,内容主要包括量子色动力学（QCD）在高温高密条件下的相变以及在相对论重离子碰撞中相变信号的研究.     

Constraints on the symmetry energy using the mass-radius relation of neutron stars

The nuclear symmetry energy is intimately connected with nuclear astrophysics. This contribution focuses on the estimation of the symmetry energy from experiment and how it is related to the structure of neutron stars. The most important connection is between the radii of neutron stars and the pressure of neutron star matter in the vicinity of the nuclear saturation density n_s. This pressure is essentially controlled by the nuclear symmetry energy parameters S_v and L , the first two coefficients of a Taylor expansion of the symmetry energy around n_s. We discuss constraints on these parameters that can be found from nuclear experiments. We demonstrate that these constraints are largely model-independent by deriving them qualitatively from a simple nuclear model. We also summarize how recent theoretical studies of pure neutron matter can reinforce these constraints. To date, several different astrophysical measurements of neutron star radii have been attempted. Attention is focused on photospheric radius expansion bursts and on thermal emissions from quiescent low-mass X-ray binaries. While none of these observations can, at the present time, determine individual neutron star radii to better than 20% accuracy, the body of observations can be used with Bayesian techniques to effectively constrain them to higher precision. These techniques invert the structure equations and obtain estimates of the pressure-density relation of neutron star matter, not only near n_s, but up to the highest densities found in neutron star interiors. The estimates we derive for neutron star radii are in concordance with predictions from nuclear experiment and theory.     

Effects of the Three-Nucleon Forces from Different Meson Exchanges on the Triton Binding Energy

Effects of the three-nucleon forces on the triton binding energy are investigated using different models for which the xN scattering amplitudes for the off-mass-shell pions are extrapolated from the on-mass-shell data. In the independent model potential, the threenucleon forces are constructed using the chiral symmetry through partial conservation of the axial current vectors and current algebra. On the other hand, the three-nucleon forces in the dependent model potential are derived from an effective Lagrangian which is constrained by chiral and gauge symmetry. The effect of the long range 2π and the repulsive ap-exchange three-nucleon forces on the triton binding energy are investigated. The bound state triton binding energies are then calculated by solving the Faddeev equations with a Hamiltonian including the three-nucleon forces, using different nucleon-nucleon interactions. The pionic form factors are considered with different sets of the form factor cutoff,parameter Λ. The 2π-exchange forces with S- and P-wave amplitudes are found to overbind the triton binding energy by about 0.4～Y 1.6 MeV. However, xp-exchange forces are found to reduce the 2π exchange forces by about 18% of its contribution, to the triton binding energy.     

Dynamical mass function of quark and effective potential in QCD

Direct variational method is applied to the problem of the dynamical breaking of chiral symmetry in QCD. The minimum of the effective potential corresponding to the phase with spontaneous chiral symmetry breaking is found.     

Chiral thermodynamics of dense hadronic matter

We discuss phases of hot and dense hadronic matter using chiral Lagrangians. A two-flavored parity doublet model constrained by the nuclear matter ground state predicts chiral symmetry restoration. The model thermodynamics is shown within the mean-field approximation. A field-theoretical constraint on possible phases from the anomaly matching is also discussed.