Effect of entrance-channel asymmetry on the isospin dependence of nucleon emission in heavy ion collisions

Using the isospin- and momentum-dependent hadronic transport model IBUU04, we have in-vestigated the influence of the entrance-channel isospin asymmetry on the sensitivity of the pre-equilibrium neutron/proton ratio to symmetry energy in central heavy-ion collisions induced by high-energy radioactive beams. Our analysis and discussion are based on the dynamical simulations of the three isotopic reaction systems 132Sn+124Sn, 124Sn+112Sn and 112Sn+112Sn which are of the same total proton number but different isospin asymmetry. We find that the kinetic-energy distributions of the pre-equilibrium neutron/proton ratio are quite sensitive to the density-dependence of symmetry energy at incident beam energy E/A = 400 MeV,and the sensitivity increases as the isospin asymmetry of the reaction system increases.     

Exploring nuclear symmetry energy with isospin dependence in neutron skin thickness of nuclei

We propose an alternative way to constrain the density dependence of the symmetry energy from the neutron skin thickness of nuclei which shows a linear relation to both the isospin asymmetry and the nuclear charge with a form of Z^2/3. The relation of the neutron skin thickness to the nuclear charge and isospin asymmetry is systematically studied with the data from antiprotonic atom measurement, and with the extended Thomas-Fermi approach incorporating the Skyrme energy density functional. An obviously linear relationship between the slope parameter L of the nuclear symmetry energy and the isospin asymmetry dependent parameter of the neutron skin thickness can be found, by adopting 70 Skyrme interactions in the calculations. Combining the available experimental data, the constraint of -20 MeV L 82 MeV on the slope parameter of the symmetry energy is obtained. The Skyrme interactions satisfying the constraint are selected.     

Probing the medium effect and isospin dependence of the in-medium nucleon--nucleon cross section in heavy ion collisions

Probing in-medium nucleon-nucleon （NN） cross section σ1/NN（α） in heavy ion collisions has been investigated by means of the isospin-dependent quantum molecular dynamics （IQMD） with the isospin- and momentum-dependent interaction （IMDI（T））. It is found that there are the very obvious medium effect and the sensitive isospin-dependence of nuclear stopping R on the in-medium NN cross section α1/NN（α） in the nuclear reactions induced by halo-neutron projectile and the same-mass stable projectile. However, R induced by the neutron-halo projectile is obviously lower than that induced by the corresponding stable projectile. In particular, there is a very obvious dependence of R on the medium effect of σ1/NN（α） in the whole beam energy region for the above two kinds of projectiles. Therefore, the comparison between the results of R＇s in the reactions induced by the neutron-halo projectile and the corresponding same-mass stable projectile is a more favourable probe for extracting the information of σ1/NN（α） because of adding a new judgement.[第一段]     

核物质对称能和重离子碰撞中径向流阈能的同位旋效应

基于同位旋相关的量子分子动力学模型，采用三种不同形式的对称势，研究了¹²⁴Sn+¹²⁴Sn和¹²⁴Ba+¹²⁴Ba对心碰撞时在三种不同对称势下的径向膨胀流，发现径向膨胀流阈能与所采用的对称能形式密切相关，表现出明显同位旋效应，预示着径向膨胀流阈能的同位旋相关性可作为对称能的灵敏探针. 关键词： 径向膨胀流阈能 同位旋效应 重离子碰撞 同位旋相关的量子分子动力学模型     

同位旋依赖的动量相关作用对同位旋分馏的影响随入射道条件的演化

由量子分子动力学通常应用的动量相关作用公式出发，引入同位旋自由度后得到了在量子分子动力学中可用于数值计算的同位旋依赖的动量相关作用.并用这个公式较系统地研究了在它的作用下，同位旋分馏比的入射道效应和它们的动力学机理.结果表明所有入射道能量、碰撞参数以及所有的丰中子碰撞系统中子-质子比和质量条件下动量相关作用的同位旋依赖性对同位旋分馏过程产生了重要的同位旋效应，然而它没有明显改变同位旋分馏比对于对称势灵敏的依赖性，即在考虑动量相关作用的同位旋自由度后同位旋分馏比仍是提取同位旋非对称核物质状态方程的灵敏探针. 关键词： 同位旋分馏比 动量相关作用 重离子碰撞     

同位旋依赖的动量相关作用对同位旋分馏过程的影响和机理

在同位旋相关的量子分子动力学理论的基础上，引入同位旋自由度，将同位旋无关的动量相 关作用改造成为在同位旋相关的量子分子动力学中可用的同位旋依赖的动量相关作用．研究 了它在中能重离子碰撞中的作用和机理．研究结果表明，考虑同位旋依赖的动量相关作用后 ，对同位旋分馏过程有很大的影响，使同位旋分馏强度降低．降低的幅度随入射能量的增加 而迅速增加.特别是动量相关作用的同位旋效应与对称势的同位旋效应具有大体相同数量级 ．但两者具有完全不同的动力学机理．所以同位旋依赖的动量相关作用的研究对于定量的研 究同位旋非对称核物质状态方程是重要的. 关键词： 同位旋依赖的动量相关作用 同位旋分馏强度 重离子碰撞     

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     

放射性束引起的重离子碰撞中敏感于对称能的几个观测量

利用同位旋与动量相关的强子输运模型，我们研究了放射性束引起的中能重离子碰撞中几个观测量的对称能效应。我们发现自由核子发射的非对称度的快度分布，中快度中－质比的横动量分布，的动能分布，以及同位旋相分化（fractionation）的时间演化都敏感于对称能。     

Isospin effects of the Skyrme potential and the momentum dependent interaction at intermediate energy heavy ion collisions

We improve the isospin dependent quantum molecular dynamical model by including isospin effects in the Skyrme potential and the momentum dependent interaction to obtain an isospin dependent Skyrme potential and an isospin dependent momentum interaction. We investigate the isospin effects of Skyrme potential and momentum dependent interaction on the isospin fractionation ratio and the dynamical mechanism in intermediate energy heavy ion collisions. It is found that the isospin dependent Skyrme potential and the isospin dependent momentum interaction produce some important isospin effects in the isospin fractionation ratio.     

Application of microscopic transport model in the study of nuclear equation of state from heavy ion collisions at intermediate energies

The equation of state (EOS) of nuclear matter, i.e., the thermodynamic relationship between the binding energy per nucleon, temperature, density, as well as the isospin asymmetry, has been a hot topic in nuclear physics and astrophysics for a long time. The knowledge of the nuclear EOS is essential for studying the properties of nuclei, the structure of neutron stars, the dynamics of heavy ion collision (HIC), as well as neutron star mergers. HIC offers a unique way to create nuclear matter with high density and isospin asymmetry in terrestrial laboratory, but the formed dense nuclear matter exists only for a very short period, one cannot measure the nuclear EOS directly in experiments. Practically, transport models which often incorporate phenomenological potentials as an input are utilized to deduce the EOS from the comparison with the observables measured in laboratory. The ultrarelativistic quantum molecular dynamics (UrQMD) model has been widely employed for investigating HIC from the Fermi energy (40 MeV per nucleon) up to the CERN Large Hadron Collider energies (TeV). With further improvement in the nuclear mean-field potential term, the collision term, and the cluster recognition term of the UrQMD model, the newly measured collective flow and nuclear stopping data of light charged particles by the FOPI Collaboration can be reproduced. In this article we highlight our recent results on the studies of the nuclear EOS and the nuclear symmetry energy with the UrQMD model. New opportunities and challenges in the extraction of the nuclear EOS from transport models and HIC experiments are discussed.     

Bayesian inference on isospin splitting of nucleon effective mass from giant resonances in ~(208)Pb

From a Bayesian analysis of the electric dipole polarizability,the constrained energy of isovector giant dipole resonance,the peak energy of isocalar giant quadrupole resonance,and the constrained energy of isocalar giant monopole resonance in ~(208)Pb,we extract the iso scalar and isovector effective masses in nuclear matter at saturation density p_0 as m_(s,0)~*/m=0.87_(-0.04)~(+0.04) and m_(v,0)~*/m=0.78_(-0.05)~(+0.06),respectively,at 90% confidence level.The constraints obtained on m_(s,0)~* and m_(v,0)~* lead to a positive iso spin splitting of nucleon effective mass in asymmetric nuclear matter of iso spin asymmetry δ at p_0 as m_(n-p)~*/m=(0.20_(-0.14)~(+0.15))δ.In addition,the symmetry energy at the subsaturation density p~*=0.05 fm~(-3) is determined to be E_(sym)(p~*)=16.7±1.3 MeV at 90% confidence level.     

Isospin effects of the Skyrme potential and the momentum dependent interaction at intermediate energy heavy ion collisions

We improve the isospin dependent quantum molecular dynamical model by including isospin effects in the Skyrme potential and the momentum dependent interaction to obtain an isospin dependent Skyrme potential and an isospin dependent momentum interaction. We investigate the isospin effects of Skyrme potential and momentum dependent interaction on the isospin fractionation ratio and the dynamical mechanism in intermediate energy heavy ion collisions. It is found that the isospin dependent Skyrme potential and the isospin dependent momentum interaction produce some important isospin effects in the isospin fractionation ratio.     

Isospin splitting of nucleon effective mass and symmetry energy in isotopic nuclear reactions

Within an isospin and momentum dependent transport model, the dynamics of isospin particles(nucleons and light clusters) in Fermi-energy heavy-ion collisions are investigated for constraining the isospin splitting of nucleon effective mass and the symmetry energy at subsaturation densities. The impacts of the isoscalar and isovector parts of the momentum dependent interaction on the emissions of isospin particles are explored, i.e., the mass splittings of m_n~*=m_p~* and m_n~* m_p~*(m_n~* m_p~*). The single and double neutron to proton ratios of free nucleons and light particles are thoroughly investigated in the isotopic nuclear reactions of ~(112)Sn+~(112)Sn and ~(124)Sn+~(124)Sn at incident energies of 50 and 120 MeV/nucleon, respectively. It is found that both the effective mass splitting and symmetry energy impact the kinetic energy spectra of the single ratios, in particular at the high energy tail(larger than 20 Me V). The isospin splitting of nucleon effective mass slightly impacts the double ratio spectra at the energy of 50 MeV/nucleon. A soft symmetry energy with stiffness coefficient of γ_s =0.5 is constrained from the experimental data with the Fermi-energy heavy-ion collisions.     

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.     

从晕中子核引起核反应中提取对称势

利用同位旋相关量子分子动力学理论研究了中子晕核引起核反应机制中重要的同位旋效应以提取对称势. 因为同位旋相关量子分子动力学理论中的相互作用和介质中核子-核子碰撞截面都灵敏地依赖于碰撞系统的密度分布, 本项研究工作基于中子晕核扩展的密度分布. 该密度分布包含了反应机制中同位旋效应和疏散内部结构的平均特征. 为了弄清楚晕核引起核反应机制的同位旋效应, 在完全相同的入射道条件下, 比较了由中子晕核炮弹引起的同位旋效应和由相等质量的稳定核炮弹引起同位旋效应. 结果发现中子晕核炮弹引起的发射中子-质子比和同位旋分馏比明显大于相等质量稳定弹核产生的结果. 因而可以通过理论结果与实验数据的系统比较提取对称势.     

Isospin effect in peripheral heavy-ion collisions at Fermi energies

The isospin effect in peripheral heavy-ion collisions was thoroughly investigated within the framework of the Lanzhou quantum molecular dynamics (LQMD) transport model. A coalescence approach was used to recognize the primary fragments formed in nucleus-nucleus collisions. The secondary decay process of these fragments was described using the statistical code GEMINI. The production mechanism and isospin effect of the projectile-like and target-like fragments were analyzed using the combined approach. It was found that the isospin migration from the high-isospin density to the low-density matter occurred in the neutron-rich nuclear reactions, i.e., ⁴⁸Ca+²⁰⁸Pb, ⁸⁶Kr+⁴⁸Ca/²⁰⁸Pb/¹²⁴Sn, ¹³⁶Xe+²⁰⁸Pb, ¹²⁴Sn+¹²⁴Sn, and ¹³⁶Xe+¹³⁶Xe. A hard symmetry energy was available for creating the neutron-rich fragments, particularly in the medium-mass region. The isospin effect of the neutron-to-proton (n/p) ratio of the complex fragments was reduced when the secondary decay process was included. However, a soft symmetry energy enhanced the n/p ratio of the light particles, particularly at kinetic energies greater than 15 MeV/nucleon.     

Investigation of neutron emission from relativistic heavy ion interactions by nuclear tracks

Fast neutrons produced in 44 and 22 GeV ¹²C+Cu interactions have been recorded and analysed with a CR-39 detector stack. The irradiation of the CR-39 stack to fast neutrons was carried out at the accelerator Synchrophasotron, Joint Institute for Nuclear Research, Dubna, Russia. Areal and volume densities of tracks induced by fast neutrons in the CR-39 at different positions and for different etching time have been measured. The neutron production ratio of 44 GeV to 22 GeV ¹²C+Cu interactions has been obtained, which is 2.17 ± 0.30 by areal track density, or 2. 12±0.33 by step etch technique, or 2.03±0.34 by volume track density measurement. These results confirm that the production rate at 44 GeV ¹²C+Cu interactions is more than theoretical estimation.     

Nucleon effective mass splitting and density-dependent symmetry energy effects on elliptic flow in heavy ion collisions at E_(lab)= 0.09 ～ 1.5 GeV/nucleon

By incorporating an iso spin-dependent form of the momentum-dependent potential in the ultra-relativistic quantum molecular dynamics(UrQMD) model,we systematically investigate effects of the neutron-proton effective mass splitting m*_(n-p)=m*_n-m*_p/m and the density-dependent nuclear symmetry energy E_(sym)(ρ) on the elliptic flow v_2 in~(197)Au+~(197) Au collisions at beam energies from 0.09 to 1.5 GeV/nucleon.It is found that at higher beam energies(≥0.25 GeV/nucleon) with the approximately 75 MeV difference in slopes of the two different E_(sym)(ρ),and the variation of m*_(n-p) ranging from-0.03 to 0.03 at saturation density with isospin asymmetry δ=(ρ_n-ρ_p)/ρ-0.2,the E_(sym)(ρ) has a stronger influence on the difference in v_2 between neutrons and protons,i.e.,v_2~n-v_2~p,than m*_(n-p) has.Meanwhile,at lower beam energies(≤0.25 GeV/nucleon),v_2~n-v_2~p is sensitive to both the E_(sym)(ρ) and the m*_(n-p).Moreover,the influence of m*_(n-p) on v_2~n-v_2~p is more evident with the parameters of this study when using the soft,rather than stiff,symmetry energy.