Effects of isospin and momentum dependent interactions on liquid–gas phase transition in hot asymmetric nuclear matter

The liquid–gas phase transition in hot neutron-rich nuclear matter is investigated within a self-consistent thermal model using an isospin and momentum dependent interaction (MDI) constrained by the isospin diffusion data in heavy-ion collisions, a momentum-independent interaction (MID), and an isoscalar momentum-dependent interaction (eMDYI). The boundary of the phase-coexistence region is shown to be sensitive to the density dependence of the nuclear symmetry energy with a softer symmetry energy giving a higher critical pressure and a larger area of phase-coexistence region. Compared with the momentum-independent MID interaction, the isospin and momentum-dependent MDI interaction is found to increase the critical pressure and enlarge the area of phase-coexistence region. For the isoscalar momentum-dependent eMDYI interaction, a limiting pressure above which the liquid–gas phase transition cannot take place has been found and it is shown to be sensitive to the stiffness of the 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。     

中能重离子碰撞中的中子(质子)发射的同位旋效应

利用同位旋相关的量子分子动力学,对中能重离子碰撞过程中的中子和质子发射的同位旋效应进行了分析.计算结果表明在有动量相关作用条件下,在很宽的能量和碰撞参数范围内,缺中子碰撞系统的中子(质子)发射数强烈地依赖于同位旋相关的核子–核子碰撞截面,而较弱地依赖于对称势.在对丰中子碰撞系统的研究中,上述规律减弱.这样就可以通过实验上对缺中子碰撞系统的中子(质子)发射数的探测,来提取介质中同位旋相关核子–核子碰撞截面的知识.     

Nuclear symmetry energy in terms of single-nucleon potential and its effect on the proton fraction of <Emphasis Type="Italic">β</Emphasis>-stable <Emphasis Type="Italic">npeμ</Emphasis> matter

Momentum and density dependence of single-nucleon potential u_τ (k, ρ, β) is analyzed using a density dependent finite range effective interaction of the Yukawa form. Depending on the choice of the strength parameters of exchange interaction, two different trends of the momentum dependence of nuclear symmetry potential are noticed which lead to two opposite types of neutron and proton effective mass splitting. The 2nd-order and 4th-order symmetry energy of isospin asymmetric nuclear matter are expressed analytically in terms of the single-nucleon potential. Two distinct behavior of the density dependence of 2nd-order and 4th-order symmetry energy are observed depending on neutron and proton effective mass splitting. It is also found that the 4th-order symmetry energy has a significant contribution towards the proton fraction of β-stable npeμ matter at high densities.     

Effects of the density dependence of the symmetry energy on neutron stars

In this paper,we include the density dependence behavior of the symmetry energy in the improved quark mass density dependent (IQMDD) model.Under the mean field approximation,this model is applied to investigate neutron star matter and neutron stars successfully.Effects of the density dependence of the symmetry energy on neutron stars are described.     

Neck fragmentation reaction mechanism

Based on a microscopic transport model, we study the origin of nonstatistical intermediate mass fragment (IMF) production in semicentral heavy ion collisions at the Fermi energies. We show that a fast, dynamical IMF formation process, the neck fragmentation mechanism, can explain the experimentally observed features: deviations from Viola systematics and anisotropic, narrow angular distributions. It may be regarded as the continuation of the multifragmentation mechanism towards intermediate impact parameters. Its relation to other dynamical mechanisms, the induced fission and the abrasion of the spectator zones, that can also contribute to mid-rapidity IMF production, is discussed. The dependence on beam energy and centrality of the collision is carefully analysed. The competition between volume and surface instabilities makes this mechanism very sensitive to the in-medium nucleon-nucleon interactions, from the cross sections for hard collisions to the compressibility and other equation of state (EOS) properties.

For charge asymmetric collisions the sensitivity of various observables to the symmetry energy is investigated. Of particular interest appears the isospin diffusion dynamics with no signal of isospin equilibration. However, in spite of the short time scales and of the dynamical aspects, we notice isoscaling features of the neck mechanism. We observe that isospin enrichment of the neck zone as well as the isoscaling parameters are sensitive to the density dependence of asymmetry term of EOS around and below saturation value.     

Analyzing fragment production in mass-asymmetric reactions as a function of density dependent part of symmetry energy

We performed a theoretical investigation of different mass-asymmetric reactions to access the direct impact of the density-dependent part of symmetry energy on multifragmentation. The simulations are performed for a specific set of reactions having same system mass and N/Z content, using isospin-dependent quantum molecular dynamics model to estimate the quantitative dependence of fragment production on themass-asymmetry factor (τ) for various symmetry energy forms. The dynamics associated with different mass-asymmetric reactions is explored and the direct role of symmetry energy is checked. Also a comparison with the experimental data (asymmetric reaction) is presented for a different equation of states (symmetry energy forms).     

Impact of density-dependent symmetry energy and Coulomb interactions on the evolution of intermediate mass fragments

Within the framework of isospin-dependent quantum molecular dynamics (IQMD) model, we demonstrate the evolution of intermediate mass fragments in heavy-ion collisions. In this paper, we study the time evolution, impact parameter, and excitation energy dependence of IMF production for the different forms of density-dependent symmetry energy. The IMF production and charge distribution show a minor but considerable sensitivity towards various forms of density-dependent symmetry energy. The Coulomb interactions affect the IMF production significantly at peripheral collisions. The IMF production increases with the stiffness of symmetry energy.     

用改进的量子分子动力学研究中能重离子碰撞中多重碎裂

本文利用改进的量子分子动力学模型(MQMD)研究中能重离子碰撞中的多重碎裂过程.在MQMD的基础上通过模拟计算发现:MQMD由于考虑了动量相关势和Pauli势,极大地改善了多重碎裂产额的计算结果与实验数据的比较.同时研究了二者对碰撞动力学的不同影响.最后,讨论了理论计算与实验结果仍有矛盾的原因,并提出了进一步改进的方案.     

Multifragmentation Process in HIC Simulated by Modified Quantum Molecular Dynamics

The collision dynamics and yields of the multifragmentation in intermediate energy heavy ion collisions are simulated within the frame of the modified quantum molecular dynamics(MQMD ).With this new MQMD,it is found that the obvious improvements about the agreements between the experimental data and the simulating results for the fragment production by means of MDI and Pauli potential are achieved.Meanwhile the different influences of MDI and Pauli potential on the collision dynamics of intermediate energy heavy ion collisions are obtained.Finally the possible reasons for the discrepancies between the experimental data and the present simulating results and remedies of these deficiencies are discussed in detail.     

The dynamical ingredients governing the multifragmentation process and collision dynamics in heavy ion collisions

By simulating numerically the reaction dynamics of heavy ion collisions within the modified quantum molecular dynamics (MQMD), we have studied the influences of the nucleon-nucleon (n-n) collision cross section with and without medium effect, momentum dependent interactions (MDI), equation of state (EOS) and the aggregating method of fragments on the multifragmentation process of heavy ion collisions with different beam energies. It is found that multifragmentation patterns of the final fragment distributions, the collective flows of fragments and single particles, collision number and nuclear matter density depend strongly on then-n cross section and momentum dependent interactions and the nuclear equation of state, especially these dependences are associated with beam energies. But the fragment multiplicity distribution patterns depend very weakly on the equation of state.     

质子椭圆流与对称能的密度依赖性

基于同位旋和动量依赖的强子输运IBUU04模型, 研究了¹³²Sn+¹²⁴Sn碰撞系统中的质子椭圆流对对称能的敏感关系. 研究发现入射能量从每核子400MeV到800MeV时质子椭圆流在低横动量端对对称能的敏感性高于高横动量端, 同时发现随着入射能量的增大, 质子椭圆流对对称能的敏感性在降低. 在研究入射能量范围内, 当入射能量为每核子400MeV左右时质子椭圆流对对称能最为敏感.     

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.     

核物质和夸克物质的对称能（英文）

对称能表征了同位旋非对称强相互作用物质状态方程的同位旋相关部分,它对于理解核物理和天体物理中的许多问题有重要意义。简要总结了关于核物质和夸克物质对称能研究的最新进展。对于核物质对称能,通过对核结构,核反应以及中子星的研究,目前对其亚饱和密度的行为已有比较清楚的认识,同时,对饱和密度附近对称能的约束也取得了很好的研究进展。但如何确定核物质对称能的高密行为仍然是一个挑战。另一方面,在极端高重子数密度条件下,强相互作用物质将以退禁闭的夸克物质状态存在。同位旋非对称夸克物质可能存在于致密星内部,也可能产生于极端相对论重离子碰撞中。对最近关于夸克物质对称能对夸克星性质的影响以及重夸克星的存在对夸克物质对称能的约束的研究工作进行了介绍,结果表明同位旋非对称夸克物质中上夸克和下夸克可能感受到很不一样的相互作用,这对于研究极端相对论重离子碰撞中部分子动力学的同位旋效应有重要启发。The symmetry energy characterizes the isospin dependent part of the equation of state of isospin asymmetric strong interaction matter and it plays a critical role in many issues of nuclear physics and astrophysics. In this talk, we briefly review the current status on the determination of the symmetry energy in nucleon (nuclear) and quark matter. For nuclear matter, while the subsaturation density behaviors of the symmetry energy are relatively well-determined and significant progress has been made on the symmetry energy around saturation density, the determination of the suprasaturation density behaviors of the symmetry energy remains a big challenge. For quark matter, which is expected to appear in dense matter at high baryon densities, we briefly review the recent work about the effects of quark matter symmetry energy on the properties of quark stars and the constraint of possible existence of heavy quark stars on quark matter symmetry energy. The results indicate that the u and d quarks could feel very different interactions in isospin asymmetric quark matter, which may have important implications on the isospin effects of partonic dynamics in relativistic heavy-ion collisions.     

Crust-core properties of neutron stars in the Nambu–Jona-Lasinio model

We adopt the Nambu–Jona-Lasinio(NJL) model to study the crust-core transition properties in neutron stars(NSs). For a given momentum cutoff and symmetry energy of saturation density in the NJL model, decreasing the slope of the symmetry energy gives rise to an increase in the crust-core transition density and transition pressure.Given the slope of the symmetry energy at saturation density, the transition density and corresponding transition pressure increase with increasing symmetry energy. The increasing trend between the fraction of the crustal moment of inertia and the slope of symmetry energy at saturation density indicates that a relatively large momentum cutoff of the NJL model is preferred. For a momentum cutoff of 500 Me V, the fraction of the crustal moment of inertia clearly increases with the slope of symmetry energy at saturation density. Thus, at the required fraction(7%) of the crustal moment of inertia, the NJL model with momentum cutoff of 500 Me V and a large slope of the symmetry energy of saturation density can give the upper limit of the mass of the Vela pulsar to be above 1.40 M_⊙.     

Time evolution of the fields associated with a cosmic string

The time development of the fields associated with a straight cosmic string in the localU(1) model is studied numerically in an expanding universe. The effective potential is time dependent due to the cooling of the universe. After the spontaneous breaking of theU(1) symmetry the fields start to oscillate as the system tends towards the static state of the stable Nielsen-Olesen string. It is shown that energy flows out of the comoving cylinder in the form of electromagnetic waves. Due to Hubble damping and energy outflow the oscillation amplitudes decrease but static fields are not obtained without additional damping terms originating, e.g., from particle production.     

对称能密度依赖的输运理论模型研究中的一些问题的讨论

本文非常简要地介绍了目前通过重离子碰撞中的对称能敏感观测量获取对称能密度依赖的研究现状,讨论了在输运理论模型计算中可能引起计算结果的不确定性的几个问题。特别与目前广泛采用的输运理论模型计算相关的3个方面的问题,即对称势动量依赖项和中子、质子有效质量劈裂;不同电荷态△产生的阈能和相关截面的介质修正;输运理论模型中的多体关联和涨落等的处理等问题。     

Nuclear compression moduli and density-dependent forces

Density-dependent zero-range forces of the form of the modified delta interaction (MDI) are generalized (MDI3, MDI4) in order to yield reasonable values of the compression modulus in nuclear matter (K_N = 200 MeV). This low value can be fitted by introducing two terms with different density dependence in the force. The four free parameters of MDI3 are adjusted to reproduce the nuclear matter values of the binding energy, density and compression modulus, and to fulfil the condition that the total energy of ¹⁶O in harmonic oscillator wave functions has a minimum at the oscillator length b = 1.75 fm, corresponding to the correct rms radius. MDI4 contains in addition a two-body spin-orbit interaction. The five parameters of MDI4 are fitted to the above three nuclear matter data and by requiring that Hartree-Fock (HF) calculations in ²⁰⁸Pb yield the experimental charge rms radius and reasonable values of certain single-particle spin-orbit splittings. The quality of MDI4 is checked by comparing calculated rms radii, binding energies, and elastic electron scattering cross sections with available experimental data for doubly closed shell nuclei. As a test the energy levels and the nuclear monopole polarization of muonic ²⁰⁸Pb are calculated self-consistently yielding impressive agreement with experiment.     

重离子碰撞中同位旋分馏对碰撞系统同位旋的依赖性

利用同位旋相关的量子分子动力学模型，研究了中能重离子碰撞过程中同位旋分馏现象及其对于碰撞系统同位旋的依赖性.计算结果表明:在碰撞系统膨胀的低密度区, 气相(发射核子)与液相(碎片)的中子-质子比出现不均等分配现象,即同位旋分馏. 同位旋分馏的强弱明显地依赖于碰撞系统的中子-质子比,其强度随着系统中子-质子比的增大而增大. 丰中子碰撞系统产生丰中子的气相和缺中子的液相,而缺中子碰撞系统产生缺中子的气相和丰中子的液相.在丰中子的碰撞系统中同位旋分馏强度敏感地依赖于对称势,而对于两体碰撞的同位旋效应并不敏感，但对于缺中子的碰撞系统,同位旋分馏强度对于对称势不敏感， 同时发现动量相关作用对于同位旋分馏过程的作用不明显. 关键词： 中能重离子碰撞 同位旋分馏 同位旋效应 对称势     

Plan for nuclear symmetry energy experiments using the LAMPS system at the RIB facility RAON in Korea

We review the calculation of the equation of state of pure neutron matter using quantum Monte Carlo (QMC) methods. QMC algorithms permit the study of many-body nuclear systems using realistic two- and three-body forces in a non-perturbative framework. We present the results for the equation of state of neutron matter, and focus on the role of three-neutron forces at supranuclear density. We discuss the correlation between the symmetry energy, the neutron star radius and the symmetry energy. We also combine QMC and theoretical models of the three-nucleon interactions, and recent neutron star observations to constrain the value of the symmetry energy and its density dependence.