Ground-State Properties of Ca Isotopes and the Density Dependence of the Symmetry Energy

A relativistic mean field model is used to study the ground-state properties of neutron-rich nuclei in Ca isotopes. An additional isoscalar and isovector nonlinear coupling has been introduced in the relativistic mean field model, which could soften the symmetry energy, while keep the agreement with the experimental data. The sensitivity of proton and neutron density distributions and single particle states in Ca isotopes to the additional isoscalarisovector nonlinear coupling term is investigated. We found that the binding energies, the density distributions of single particle levels are strongly correlated with the density dependence of the symmetric energy in nuclear matter.     

Nuclear symmetry energy effects in finite nuclei and neutron star

Within a relativistic mean-field model with nonlinear isoscalar–isovector coupling, we explore the possibility of constraining the density dependence of nuclear symmetry energy from a systematic study of the neutron skin thickness of finite nuclei and neutron star properties. We find the present skin data supports a rather stiff symmetry energy at subsaturation densities that corresponds to a soft symmetry energy at supranormal densities. Correlation between the skin of ²⁰⁸Pb and the neutron star masses and radii with kaon condensation has been studied. We find that ²⁰⁸Pb skin estimate suggest star radii that reveals considerable model dependence. Thus precise measurements of neutron star radii in conjunction with skin thickness of heavy nuclei could provide significant constraint on the density dependence of symmetry energy.     

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。     

Disentangling the Effects of Thickness of the Neutron Skin and Symmetry Potential in Nucleon Induced Reactions on Sn Isotopes

The effects of density dependence of symmetry energy and the thickness of the neutron skin in proton （neutron） induced reactions on Sn isotopes are investigated by means of the improved molecular dynamics model. The investigation shows that the target size dependence of the reaction cross sections for proton induced reactions on Sn isotopes is sensitive to the density dependence of the symmetry energy and less sensitive to the thickness of the neutron skin of the target nuclei, but that, for neutron induced reactions on Sn isotopes, it is less sensitive to the density dependence of the symmetry energy and sensitive to the thickness of the neutron skin of the target nucleus.     

Dependence of flow observables in heavy-ion collisions on the symmetry energy and the in-medium nucleon-nucleon interaction

We employ a QMD transport model to study the influence of the isospin dependent part of the nuclear matter equation of state on the dynamics of heavy-ion collisions at intermediate energies. Parametrization of the in-medium dependence of the nucleon-nucleon elastic cross-sections, as predicted by microscopical models, are used. The sensitivity of flow observables to various parametrizations of the isospin dependent part of the equation of state (symmetry energy) is studied. The experimentally observed splitting of the elliptic flow values in Ru+Zr and Zr+Ru at incident energies of 400 MeV is shown to be due to, to an equal extent, density dependence of the microscopic nucleon-nucleon cross-section and symmetry energy.     

Symmetry energy,unstable nuclei and neutron star crusts

We present an upgraded review of our microscopic investigation on the single-particle properties and the EOS of isospin asymmetric nuclear matter within the framework of the Brueckner theory extended to include a microscopic three-body force. We pay special attention to the discussion of the three-body force effect and the comparison of our results with the predictions by other ab initio approaches. Three-body force is shown to be necessary for reproducing the empirical saturation properties of symmetric nuclear matter within nonrelativistic microscopic frameworks, and also for extending the hole-line expansion to a wide density range. The three-body force effect on nuclear symmetry energy is repulsive, and it leads to a significant stiffening of the density dependence of symmetry energy at supra-saturation densities. Within the Brueckner approach, the three-body force affects the nucleon s.p. potentials primarily via its rearrangement contribution which is strongly repulsive and momentum-dependent at high densities and high momenta. Both the rearrangement contribution induced by the three-body force and the effect of ground-state correlations are crucial for predicting reliably the single-particle properties within the Brueckner framework.     

原子核对称能对中子星壳层结构的影响

中子星内壳层中存在原子核、中子、电子等非均匀分布的物质。在Wigner-Seitz近似下,共存相方法和自洽Thomas-Fermi近似方法是描述这种非均匀物质的有效方法。中子在非均匀物质所占的比例远远大于其他组分,因此原子核的对称能对非均匀物质的性质会产生十分重要的影响,而原子核对称能的密度依赖关系在核物质饱和密度附近有较大的不确定性。采用相对论平均场理论描述核子间相互作用,研究原子核对称能对中子星内壳层的密度范围、pasta相结构、壳核相变密度等性质的影响,探寻其中可能存在的关联。计算结果表明,原子核对称能及其密度依赖性在决定中子星内壳层非均匀物质的性质中起着重要作用,这与之前相关研究中得到的结论基本相符。Within Wigner-Seitz approximation, both the coexisting phases method and the self-consistent Thomas-Fermi approximation can be used to describe the nonuniform matter consisting of nuclei, neutrons, and electrons, which may coexist in the inner crust of neutron star. Since the neutron fraction is very large, nuclear symmetry energy may have an important impact on the properties of nonuniform matter. However, the density dependence of nuclear symmetry energy around saturation density is still rather uncertain. This paper focuses on the influence of nuclear symmetry energy on the density range of inner crust, pasta phase structure, and crust-core transition density of neutron star, where the relativistic mean field theory is adopted to describe the nucleon-nucleon interaction. It is turned out that the nuclear symmetry energy and its density dependence play an import role in determining the properties of nonuniform matter in the inner crust of neutron star, which is consistent with the former related studies.     

Systematics of nuclear matter and finite nuclei properties in a non-linear relativistic mean field approach

A phenomenological non-linear relativistic mean field approach is used to investigate primarily the properties of nuclear matter. The dimensionless parameters are adjusted using different empirical quantities which are discussed in detail: saturation conditions, the incompressibility parameter, symmetry energy and surface energy. Particular attention is paid to the cubic and quartic terms in the self-interaction part of the scalar field. The effective parameters are then used to study doubly magic finite nuclei in the Dirac-Hartree approximation. Different ground-state properties, binding energies, rms radii, density distributions, are then systematically analyzed and discussed. A remarkable agreement with experimental quantities is found and further possibilities are suggested.     

Exploration of Pseudospin Symmetry in the Resonant States

Taking ^120Sn as an example, we discuss the pseudospin symmetry in the single proton resonant states by examining the energies, widths and the wavefunctions. The information of the single proton resonant states in spherical nuclei are extracted from an analytic continuation in the coupling constant method within the framework of the self-consistent relativistic mean field theory under the relativistic boundary condition. We find small energy splitting in a pair of pseudospin partners in the resonant states. The lower components of the Dirac wavefunctions of a pseudospin doublet agree well in the region where nuclear potential dominates. It is concluded that the pseudospin symmetry is also well conserved for the resonant states in realistic nuclei.     

Probing the nuclear symmetry energy with heavy-ion reactions induced by neutron-rich nuclei

Heavy-ion reactions induced by neutron-rich nuclei provide a unique means to investigate the equation of state of isospin-asymmetric nuclear matter, especially the density dependence of the nuclear symmetry energy. In particular, recent analyses of the isospin diffusion data in heavy-ion reactions have already put a stringent constraint on the nuclear symmetry energy around the nuclear matter saturation density. We review this exciting result and discuss its implications on nuclear effective interactions and the neutron skin thickness of heavy nuclei. In addition, we also review the theoretical progress on probing the high density behaviors of the nuclear symmetry energy in heavy-ion reactions induced by high energy radioactive beams.      

Probing the density content of the nuclear symmetry energy

The nature of equation of state for the neutron star matter is crucially governed by the density dependence of the nuclear symmetry energy. We attempt to probe the behaviour of the nuclear symmetry energy around the saturation density by exploiting the empirical values for volume and surface symmetry energy coefficients extracted from the precise data on the nuclear masses.     

Flow probe of symmetry energy in relativistic heavy-ion reactions

Various definitions of the symmetry energy are introduced for nuclei, dilute nuclear matter below saturation density and stellar matter, which is found in compact stars or core-collapse supernovae. The resulting differences are exemplified by calculations in a theoretical approach based on a generalized relativistic density functional for dense matter. It contains nucleonic clusters as explicit degrees of freedom with medium-dependent properties that are derived for light clusters from a quantum statistical approach. With such a model the dissolution of clusters at high densities can be described. The effects of the liquid-gas phase transition in nuclear matter and of cluster formation in stellar matter on the density dependence of the symmetry energy are studied for different temperatures. It is observed that correlations and the formation of inhomogeneous matter at low densities and temperatures causes an increase of the symmetry energy as compared to calculations assuming a uniform uncorrelated spatial distribution of constituent baryons and leptons.     

Effects of symmetry energy on two-nucleon correlation functions in heavy-ion collisions induced by neutron-rich nuclei

Using an isospin-dependent transport model, we study the effects of nuclear symmetry energy on two-nucleon correlation functions in heavy-ion collisions induced by neutron-rich nuclei. We find that the density dependence of the nuclear symmetry energy affects significantly the nucleon emission times in these collisions, leading to larger values of two-nucleon correlation functions for a symmetry energy that has a stronger density dependence. Two-nucleon correlation functions are thus useful tools for extracting information about the nuclear symmetry energy from heavy-ion collisions.     

Probing Nuclear Symmetry Energy with Giant Dipole Resonances in Finite Nuclei

The relationship between the centroid energies of the isovector giant dipole resonance of finite nuclei and the symmetry energy has been studied.It is found the excitation energies of the dipole resonance in finite nuclei are correlated linearly with the symmetry energy at and below the saturation density.This linear correlation leads to the symmetry energy at the saturation density at the interval 33.0 MeV ≤ S(ρ_0) ≤ 37.0 MeV,and the symmetry energy at ρ=0.1 fm~(-3) at the interval 21.2-22.5 MeV.It is proposed that a precise measurement of the dipole mode in nuclei could set up an important constraint on the equation of state for nuclear matter.     

核物质对称能的高密行为研究

同位旋物理的主要任务之一是通过放射性核束引起的核反应来探索介质中有效核子-核子相互作用的同位旋依赖性,尤其是同位旋相关的核物质状态方程, 即密度依赖的核物质对称能。由于对称能,尤其是其高密行为,对核物理学和天体物理学具有重要意义,密度依赖的对称能在过去10年一直是中能重离子物理研究领域的主要焦点之一。近年来,低密对称能的研究已经取得了重要进展, 而对称能的高密行为仍然很不确定。在理论方面,人们提出了许多对高密对称能敏感的观测量。 实验方面, 关于对称能高密行为研究的实验计划已经展开,世界各地正在建造的放射性核束装置为对称能的高密行为研究提供了新的机遇。基于IBUU输运模型综述了研究对称能高密行为的一些敏感观测量及其最新进展, 以及所面临的挑战与机遇。One of the major tasks of studying isospin physics via heavy ion collisions with neutron rich nuclei, is to explore the isospin dependence of in medium nuclear effective interactions and the equation of state of neutron rich nuclear matter, i.e., the density dependence of nuclear symmetry energy. Because of its great importance for understanding many phenomena in both nuclear physics and astrophysics, the study of the density dependence of nuclear symmetry energy has been the main focus of the intermediate energy heavy ion physics community during the last decade. Nowadays significant progress has been achieved in studying the low density behavior of nuclear symmetry energy, but the high density behavior of nuclear symmetry energy is still very uncertain. Theoretically, a number of observables have been proposed as sensitive probes to the high density behavior of nuclear symmetry energy. With new opportunities provided by the various radioactive beam facilities being constructed around the world, studies of the high density behavior of nuclear symmetry energy is expected to be one of the main forefront research areas in nuclear physics in the near future. In this report, based on the transport model IBUU we have reviewed the major progress achieved in studying the high density behavior of nuclear symmetry energy and discussed future challenges in this field.     

Recent progress and new challenges in isospin physics with heavy-ion reactions

The ultimate goal of studying isospin physics via heavy-ion reactions with neutron-rich, stable and/or radioactive nuclei is to explore the isospin dependence of in-medium nuclear effective interactions and the equation of state of neutron-rich nuclear matter, particularly the isospin-dependent term in the equation of state, i.e., the density dependence of the symmetry energy. Because of its great importance for understanding many phenomena in both nuclear physics and astrophysics, the study of the density dependence of the nuclear symmetry energy has been the main focus of the intermediate-energy heavy-ion physics community during the last decade, and significant progress has been achieved both experimentally and theoretically. In particular, a number of phenomena or observables have been identified as sensitive probes to the density dependence of nuclear symmetry energy. Experimental studies have confirmed some of these interesting isospin-dependent effects and allowed us to constrain relatively stringently the symmetry energy at sub-saturation densities. The impact of this constrained density dependence of the symmetry energy on the properties of neutron stars have also been studied, and they were found to be very useful for the astrophysical community. With new opportunities provided by the various radioactive beam facilities being constructed around the world, the study of isospin physics is expected to remain one of the forefront research areas in nuclear physics. In this report, we review the major progress achieved during the last decade in isospin physics with heavy ion reactions and discuss future challenges to the most important issues in this field.     

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.     

Isotope analysis in central heavy ion collisions at intermediate energies

Symmetry energy is a key quantity in the study of the equation of state of asymmetric nuclear matter. Heavy ion collisions at low and intermediate energies, performed at Laboratori Nazionali di Legnaro and Laboratori Nazionali del Sud, can be used to extract information on the symmetry energy coefficient C_sym, which is currently poorly known but relevant both for astrophysics and for deeper knowledge of the structure of exotic nuclei.     

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.