利用自由中-质比研究对称能的高密行为

基于同位旋和动量依赖的强子输运模型IBUU04, 采用两种具有不同密度依赖的对称能研究了¹³²Sn+¹²⁴Sn反应系统在400MeV/A, 600MeV/A, 800MeV/A三种不同碰撞能量下中快度发射核子中-质比随横动量的变化关系. 发现发射核子中--质比在低横动量端非常敏感于对称能, 发射核子中--质比的强度随碰撞能量的降低而增强. 并且发射核子中-质比对对称能的敏感性随着碰撞能量的增大而降低, 在高横动量端尤为明显, 在碰撞能量为400MeV/A时, 自由核子中-质比对对称能的敏感性最为明显.     

基于中能重离子碰撞研究高密对称能

用于描述核物质中子质子单粒子能量之差的对称能,最近20年得到了核物理学界的广泛关注。在饱和核密度附近,对称能的数值及斜率基本得到约束,然而其高密行为至今仍具有很大的不确定性。当前,探测对称能的研究计划正在世界范围内能够提供放射性束流的实验室展开。伴随着对称能相关实验的规划、进行,发展更加先进的同位旋依赖的输运理论模型变得非常必要。我们将核子-核子短程关联及介质中同位旋依赖的重子-重子非弹性散射截面等研究的新进展融入到了同位旋依赖的输运模型里面;探索了新的敏感于高密对称能的可观测量,比如挤出核子的中质比、光子、轻碎片,以及包含奇异隐奇异夸克的介子产生等;提出了高密对称能探测盲点的问题并给出解决办法;对于常见的对称能敏感观测量的模型预言的不确定性进行了彻底细致的研究;提出采用定性观测量,比如高能出射粒子的中质比,将高密对称能进行定性约束;率先提出并研究了对称能敏感观测量的探测密度区间问题,指出对称能敏感观测量的探测密度往往小于核反应最大压缩密度;发现核子-核子短程关联明显削弱观测量的对称能效应;考虑到饱和点处对称能斜率的约束范围,基于输运模型,提出通过探测对称能的曲率来约束高密对称能。除了利用重离子碰撞约束高密对称能之外,人们也可以通过与中子星相关的大量天体观测来间接约束高密对称能。     

利用π－/π+探测对称能的高密行为

利用同位旋和动量相关的IBUU相对论强子输运模型,以¹³²Sn+¹²⁴Sn碰撞在E/A=400MeV，b=1fm时为例,研究了在3种不同的对称能作用下发射粒子谱中π－/π＋的比率随时间和横动量的演化. 计算结果表明，π－/π＋的比率与核物质对称能的硬度有一个反向变化关系. 由于π介子主要来自于核反应形成的高密区,因此π－/π＋的比率可以作为精确研究核物质对称能高密行为的一个探针. 通过与实验数据的比较，就能够得出比以往更精确的关于对称能高密行为的重要信息.     

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.     

重离子碰撞中的对称势翻转

利用同位旋和动量相关的输运模型IBUU，以Sn,Sn同位素在低能与高能碰撞为例，在两种不同的对称势作用下，研究了重离子碰撞中的对称势翻转现象.我们发现从低能到高能在同位旋相分化、发射核子的中-质比、发射核子的双n/p比，中-质微分横向流观测量中均存在对称势翻转现象.对称势翻转效应的研究有利于确定对称能的密度依赖性. 关键词： 重离子碰撞 对称势翻转 对称能     

中能Ca+Ca反应中的对称能效应

采用把重离子碰撞的动力学和统计衰变过程相结合的一个两步模型,再现了INDRA Collaborations 对入射能为35 AMeV40Ca+40Ca 和48Ca+48Ca 反应的实验结果。进而得到了反应碎块同位素分布的Isoscaling 参数α(Z) 和β(N),约化对称能系数ζ(Z) 及与平均场中的对称能强度系数Cs 之间的关系。结果表明,Isoscaling 参数强烈依赖于系统的丰中子程度。随着质子数的增大,ζ(Z) 在动力学阶段呈现平缓趋势但在衰变之后呈现上升趋势,且该结果不依赖于所选取的反应系统。对称能效应在统计衰变过程之后的末级碎块分布中有明显表现。A two-step model for combining the dynamical and statistical decay processes in heavy-ion collisions is used to reproduce the experimental results of the INDRA Collaborations on 40Ca+40Ca and 48Ca+48Ca reactions at 35 AMeV. We obtain the isoscaling parameters α(Z) and β(N) of isotopic distributions of the fragments, the reduced symmetry energy coefficient ζ(Z) and its dependence on the symmetry energy strength coefficient Cs in the mean field. Our results suggest that Isoscaling parameters strongly depend on the degree of neutron-rich. With the increasing atomic number, ζ(Z) represents a smoothly flat tendency during the dynamical process but shows the increasing tendency after decay, and such results are independent on the selected reaction systems. The effect of symmetry energy shows evidently in the isotopic distributions of fragments after statistical decay process.     

利用同质异位素产额比提取对称能的近似方法

在修改的Fisher模型框架下, 利用同质异位素产额比和结合能方程中对称能系数与温度比率的关联, 可以提取对称能系数与温度的比值。 利用3种不同的近似方法得到了重离子核反应产生丰中子余核的对称能系数与温度比（a_sym/T）,并研究了相关物理量对a_sym/T的影响。结果表明, 库仑能对提取丰中子余核的a_sym/T影响较小,且参考核的选取对a_sym/T的提取也有一定的影响。 In the framework of the modified Fisher model, correlations between the symmetry energy coefficient in semi classical mass formula to temperature (a_sym/T) and the isobaric yield ratio in Heavy ion collisions are established. a_sym/Tof neutron rich fragments are extracted using these correlations. It is found that the Coulomb energy term has little effect on a_sym/T of fragments, while the reference isobars adopted have great influence on the extracted a sym/T of fragments.     

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。     

核物质对称能和对称自由能的温度相关性

基于同位旋和动量相关的MDI相互作用, 研究了核物质对称能和对称自由能的温度相关性. 利用得到的密度和温度相关的对称能, 分析了同位旋标度实验的数据.     

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.     

Probing the high density behavior of the nuclear symmetry energy with high energy heavy-ion collisions

High energy heavy-ion collisions are proposed as a novel means to constrain stringently the high density (HD) behavior of nuclear symmetry energy. Within an isospin-dependent hadronic transport model, it is shown for the first time that the isospin asymmetry of the HD nuclear matter formed in high energy heavy-ion collisions is uniquely determined by the HD behavior of the nuclear symmetry energy. Experimental signatures in two sensitive probes, i.e., pi(-) to pi(+) ratio and neutron-proton differential collective flow, are also investigated.     

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     

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     

The spin-isospin decomposition of the nuclear symmetry energy from low to high density

The energy per particle BA in nuclear matter is calculated up to high baryon density in the whole isospin asymmetry range from symmetric matter to pure neutron matter.The results,obtained in the framework of the Brueckner-Hartree-Fock approximation with two-and three-body forces,confirm the well-known parabolic dependence on the asymmetry parameterβ=(N?Z)/A(β^2 law)that is valid in a wide density range.To investigate the extent to which this behavior can be traced back to the properties of the underlying interaction,aside from the mean field approximation,the spin-isospin decomposition of BA is performed.Theoretical indications suggest that theβ^2 law could be violated at higher densities as a consequence of the three-body forces.This raises the problem that the symmetry energy,calculated according to theβ^2 law as a difference between BA in pure neutron matter and symmetric nuclear matter,cannot be applied to neutron stars.One should return to the proper definition of the nuclear symmetry energy as a response of the nuclear system to small isospin imbalance from the Z=N nuclei and pure neutron matter.     

Symmetry energy from elliptic flow in Au + Au

The elliptic-flow ratio of neutrons with respect to protons or light complex particles in reactions of neutron-rich systems at relativistic energies is proposed as an observable sensitive to the strength of the symmetry term in the equation of state at supra-normal densities. The results obtained from the existing FOPI/LAND data for ¹⁹⁷Au + ¹⁹⁷Au collisions at 400 MeV/nucleon in comparison with the UrQMD model favor a moderately soft symmetry term with a density dependence of the potential term proportional to γ(ρ/ρ₀)${(\rho /{\rho }_0)}^{\gamma }$ with γ=0.9±0.4$\gamma =0.9\pm 0.4$.     

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。     

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.      

Studies of K-shell x-ray energy shifts induced by MeV/u heavy ions

This paper reports that the K x-ray spectra of the thin target 47Ag, 48Cd, 49In and 50Sn were measured by an HPGe semi-conductor detector in collisions with 84.5 MeV 6C4+ ions. Our experiment revealed the Kα x-ray energy shifts were not obvious and the Kβ1 x-ray energy shifts were about 90～110 eV. The simple model of Burch et al has been previously used to calculate the K x-ray energy shifts due to an additional vacancy in 2p orbit. The present work extends the model of Burch to calculate the x-ray energy shifts of multiple ionized atoms induced by heavy ions with kinetic energy of MeV/u. In addition to our experimental results, many other experimental results are compared with the calculated values by using the model.