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Constraints on the density dependence of symmetry energy

Constraints on the density dependence of symmetry energy. 十三届全国中高能核物理大会暨第七届全国中高能核物理专题研讨会 USTC ， 合肥， 11/6/2009. Outline. Yingxun Zhang 张英逊. Motivation and Strategies on Study the density dependence of symmetry energy Brief introduction on ImQMD model

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Constraints on the density dependence of symmetry energy

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  1. Constraints on the density dependence of symmetry energy 十三届全国中高能核物理大会暨第七届全国中高能核物理专题研讨会 USTC， 合肥， 11/6/2009 Outline Yingxun Zhang 张英逊 • Motivation and Strategies on Study the density dependence of symmetry energy • Brief introduction on ImQMD model • Constraints on the density dependence of symmetry energy from the ImQMD model • Summary and outlook 合作者： Zhuxia Li（李祝霞）, M.B.Tsang , P.Danielewicz, W.G.Lynch • China Institute of Atomic Energy, 中国原子能科学研究院 • JINA, NSCL/MSU

  2. Motivation and strategies on study the density dependence of symmetry energy • Symmetry energy and the density dependence of symmetry energy In asymmetric nuclear matter, the EOS E/A(,) = E/A(,0) + Esym(r)d2＋O(d4) ; d = (n- p)/ (n+ p) = (N-Z)/A Esym(r):the density dependence of symmetry energy • It is a fundamental properties of nuclear matter, and is very important for understanding • neutron-rich HICs process • nuclear structure • thickness of the neutron skins,.. • properties of NS, …. (Lie-Wen’s Talk)

  3. Equation of State of Nuclear Matter E/A(,) = E/A(,0) + d2Esym(r) ; d = (n- p)/ (n+ p) = (N-Z)/A 集体流以及Kaon凝聚的实验数据对于1～5r0的对称核物质状态方程给出了约束 对称能密度依赖形式有很大的不确定性 ！ 因此非对称核物质状态方程的确定依赖于对称能密度依赖形式的确定 Danielewicz, Lacey, Lynch, Science 298,1592 (2002)

  4. 我们的工作主要是利用丰中子核中能重离子碰撞的方法对于低密区对称能密度依赖形式的约束我们的工作主要是利用丰中子核中能重离子碰撞的方法对于低密区对称能密度依赖形式的约束 Why HICs ? Observables to probe Esym(r) • Low densities (<0): • Isoscaling of fragments • Isospin diffusion • n/p spectra and flows; R(n/p), R(t/3He) • Fragment isotopic distributions, R(N/Z) • Correlation function, C(q) • Neutron, proton radii, E1 collective modes. • High densities (>0) • Neutron/proton, t/3He spectra and flows; C(q) • + vs. - production (Z.G.Xiao talk), k, hyperon production. (BA Li, Tsang, Danielewciz, LW Chen, QFLi, YX Zhang, ZG Xiao…… )

  5. data ImQMD 而对于中能重离子碰撞：包含各种复杂碎块的产生。 ImQMD能够较好的重现中能区重离子碰撞的特点。 T.X.Liu.et.al., PRC76,034603 • 利用ImQMD模型的计算结果与MSU/NSCL的Sn+Sn@50AMeV中心以及擦边碰撞下的实验数据比较，获取低于饱和密度时对称能密度依赖形式的信息；研究碎块发射对于观测量的影响

  6. Brief introduction on the ImQMD model • Microscopic dynamics n-body transport model, • nucleon is represented by a Gauss WF 主要改进与发展： • the mean fields acting on nucleon wavepackets are derived fromSkyrme potential energy density functional potential energy density functional: • Change the symmetry potential in the transport model by varying the g

  7. Parameters in Vloc are obtained from standard Skyrme interactionsparameters Energy density functional from Momentum dependent interaction • Phase space constraint for considering Pauli principle The occupation number in cubic of h3 should be small than1(Pauli principle) • Isospin dependent nucleon-nucleon cross sections • are adopted, the medium corrections are Cugnon, et al., Nucl.Instr.Meth.Phys. B111, 215(1996)

  8. 成功的描述中能重离子碰撞的一些基本特点描述成功的描述中能重离子碰撞的一些基本特点描述 1) multifragmentation Zhang, Li, PRC71(2005)24606 不同反应系统 不同入射能量下 （<400AMeV)

  9. ImQMD ImQMD 2) Stopping and flow observables Zhang, Li, PRC74,014602 集体流与直接流的激发函数 Zhang, Li, PRC74,014602 阻止能力

  10. ImQMD Constraints on the density dependence of symmetry energy with multi-observables from ImQMD model 1), the density dependence of symmetry energy with the interaction in ImQMD 对称能密度依赖形式

  11. 2) The n/p ratios of emitted nucleons and the influence of cluster emission • 对称势特点： • 中子排斥 • 质子吸引 • n/p ratio is related to the stiffness of symmetry potential at subsaturation density (BALi, PRL(1997)) YX Zhang, et al, PLB664(2008)145 • more pre-equilibrium neutrons get emitted from the neutron rich 124Sn+124Sn system • relatively more pre-equilibrium neutrons are also emitted in the calculations with softer symmetry energy b=2fm

  12. DR(n/p)=Rn/p(124)/Rn/p(112) • Significant cluster and sequential decay effects are at low energy! • Over the whole energy range for both free and coalescence-invariant DR(n/p) the data seem closer to the gi=0.5 calculation Detailed comparison with data by varying gi YX Zhang, P.Danielewicz, et al, PLB664(2008)145 • For very small gi, the system completely disintegrated, DR decreases and approaches the limit of reaction system. the double ratio values peak around gi~0.7. • By comparing with data, the gi=[0.4,1.05] within c2<2s MBTsang,YXZhang et.al., PRL102(2009)

  13. 124 112 Ri = -1 124 112 124 112 Ri = 1 3) The isospin transport ratio and isospin diffusion and the influence of cluster emission Isospin diffusion occurs only in asymmetric systems A+B, and diffusion ability depends on the symmetry energy. No isospin diffusion between symmetric systems 同位旋扩散的能力由同位旋转移之比来量度 In absence of isospin diffusion R=1 or R=-1, R~0 for isospin equilibrium Ri=(2X-XAA-XBB)/(XAA-XBB) • Theory: X is the d, the isospin asymmetry of projectile residues • Exp: X is the isoscaling parameter a, • There is linear relationship between d and a, So, Ri(d)=Ri(a)

  14. X=d: from projectile residues with relevant rapidity X=d: from heaviest fragments with Z>20 Tsang,YX Zhang, et.al., PRL102,122701(2009) • Cluster emission effects make Ri larger for Ri (d(Zmax>20)) • The differences between Ri(d) and Ri(d(Zmax>20)) reflect the isospin diffusion mechanism for peripheral collisions. Isospin diffusion mainly occurs around neck region. • Fast equilibration occurs for soft symmetry energy • within 2s uncertainties, gamma_i=[0.4,1.0]

  15. 4) The rapidity distribution of R7 • Ri increase with rapidity increasing • with 2s uncertainties, gamma_i=[0.45,0.95] 利用ImQMD分析三种观测量，确定出在2s的不确定度内gi的范围是 [0.45,0.95], Cs=35.2MeV

  16. Summary and Outlook • The cluster emission play important roles on the isospin sensitive observables at intermediate energy HICs. • The consistent constraints on the density dependence of symmetry energy at subsaturation density can be obtained from three observables, DR(n/p) ratios, Ri and R7 with ImQMD model. • more observables and accurate data are needed in future in order to reduce the uncertainties on constraints on the density dependence of symmetry energy and reduce the uncertainties of the transport model.

  17. 与其他模型的比较 The results overlap with recent constraints obtained from giant dipole resonances, pygmy dipole resonance, and mass data. SMF, Wotler, arXiv:0712.2187

  18. 中低能重离子输运理论中不确定性的来源： • 平均场、动量相关势，核子有效质量 • 介质中核子－核子散射截面 • 泡里阻塞的处理 • ……

  19. International workshop on simulations of low and intermediate energy HICs ECT*, Italy, 2009 Same EOS, Same cross section different results!

  20. 输运模型计算上的一些技术细节同样会导致很大的不确定性输运模型计算上的一些技术细节同样会导致很大的不确定性 • 如：test part 波包宽度、如何抽取初始核，…… • 需要更多、精确的实验数据来减少输运理论的不确定型。 • 输运模型本身还需进一步的发展。 谢谢！

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