Recent progress on the determination of the symmetry Energy Lie-Wen Chen (陈列文) INPAC, Department of Physics, Shanghai Jiao Tong University lwchen@sjtu.edu.cn Collaborators： Wei-Zhou Jiang (SEU) Che Ming Ko (TAMU) Bao-An Li and Jun Xu (TAMU-Commerce) De-Hua Wen (SCUT) Zhi-Gang Xiao (Tsinghua) Chang Xu (NJU) Gao-Chan Yong (IMP) Xin Wang, Xiao-Hua Li, Bao-Jun Cai, Rong Chen, Peng-Cheng Chu, Zhen Zhang , Kai-Jia Sun, Hao Zheng, Rui Wang (SJTU) “第十四届全国核结构大会暨第十次全国核结构专题讨论会”, 湖州，浙江，2012年4月12-16日

核物质的状态方程与对称能 约束核物质的对称能: 对称能的效应： 总结和展望 目录 (1) 饱和密度附近的行为 (2) 低密行为 (3) 高密行为 对称能的效应： (1) 核的有效相互作用 (2) 原子核的“中子皮” (3) 中子星的“壳-芯”边界(见郑皓报告) (4) “第五种力”(见郑皓报告) 总结和展望

核物质的状态方程与对称能 约束核物质的对称能: 对称能的效应： 总结和展望 目录 (1) 饱和密度附近的行为 (2) 低密行为 (3) 高密行为 对称能的效应： (1) 核的有效相互作用 (2) 原子核的“中子皮” (3) 中子星的“壳-芯”边界(见郑皓报告) (4) “第五种力”(见郑皓报告) 总结和展望

状态方程(Equation of State): a relationship among several state variables 物质的状态方程 状态方程(Equation of State): a relationship among several state variables Van der Waals EOS: The EOS depends on the interactions and properties of the particles in the matter. It describes how the state of the matter changes under different conditions

核物质的状态方程

Symmetric Nuclear Matter (relatively well-determined) 核物质的对称能 EOS of Isospin Asymmetric Nuclear Matter (Parabolic law) Symmetric Nuclear Matter (relatively well-determined) Symmetry energy term (poorly known) Isospin asymmetry The Nuclear Symmetry Energy

Astrophysics and Cosmology 为什么研究对称能？ The multifaceted influence of the nuclear symmetry energy A.W. Steiner, M. Prakash, J.M. Lattimer and P.J. Ellis, Phys. Rep. 411, 325 (2005). Nuclear Physics on the Earth Symmetry Energy Astrophysics and Cosmology in Heaven The symmetry energy is also related to some issues of fundamental physics: 1. The precision tests of the SM through atomic parity violation observables (Sil et al., PRC05) 2. Possible time variation of the gravitational constant (Jofre et al. PRL06; Krastev/Li, PRC07) 3. Non-Newtonian gravity proposed in the grand unified theories (Wen/Li/Chen, PRL09)

强相互作用物质相图 Holy Grail of Nuclear Physics QCD Phase Diagram in 3D: density, temperature, and isospin V.E. Fortov, Extreme States of Matter – on Earth and in the Cosmos, Springer-Verlag Berlin Heidelberg 2011 夸克胶子等离子体物理 Holy Grail of Nuclear Physics 同位旋核物理 致密星体物理 理解极端条件下强相互作用物质的性质，尤其是它的状态方程 放射性核结构及重离子碰撞(地球上加速器实验); 2. 致密星体(天文观测); …

Nuclear Matter EOS: Many-Body Approaches The nuclear EOS cannot be measured experimentally, its determination thus depends on theoretical approaches Microscopic Many-Body Approaches Non-relativistic Brueckner-Bethe-Goldstone (BBG) Theory Relativistic Dirac-Brueckner-Hartree-Fock (DBHF) approach Self-Consistent Green’s Function (SCGF) Theory Variational Many-Body (VMB) approach Green’s Function Monte Carlo Calculation Vlowk + Renormalization Group Effective Field Theory Density Functional Theory (DFT) Chiral Perturbation Theory (ChPT) QCD-based theory Phenomenological Approaches Relativistic mean-field (RMF) theory Quark Meson Coupling (QMC) Model Relativistic Hartree-Fock (RHF) Non-relativistic Hartree-Fock (Skyrme-Hartree-Fock) Thomas-Fermi (TF) approximations

核物质的对称能 Z.H. Li et al., PRC74, 047304(2006) Dieperink et al., PRC68, 064307(2003) BHF Chen/Ko/Li, PRC72, 064309(2005) Chen/Ko/Li, PRC76, 054316(2007) 10

Nuclear Matter EOS: Transport Theory Transport Models Ni + Au, E/A = 45 MeV/A Transport Models for HIC’s at intermediate energies: N-body approaches CMD, QMD,IQMD,IDQMD, ImQMD,ImIQMD,AMD,FMD One-body approaches BUU/VUU, BNV, LV, IBL Relativistic covariant approaches RVUU/RBUU,RQMD… Central collisions Broad applications of transport models in astrophysics, plasma physics, electron transport in semiconductor and nanostructures, particle and nuclear physics, ……

放射性核束装置 Cooling Storage Ring (CSR) Facility at HIRFL/Lanzhou in China (2008) up to 500 MeV/A for 238U http://www.impcas.ac.cn/zhuye/en/htm/247.htm Beijing Radioactive Ion Facility (BRIF-II) at CIAE in China (2012) http://www.ciae.ac.cn/ Radioactive Ion Beam Factory (RIBF) at RIKEN in Japan (2007) http://www.riken.jp/engn/index.html Facility for Antiproton and Ion Research (FAIR)/GSI in Germany (2016) up to 2 GeV/A for 132Sn (NUSTAR - NUclear STructure, Astrophysics and Reactions ) http://www.gsi.de/fair/index_e.html SPIRAL2/GANIL in France (2013) http://pro.ganil-spiral2.eu/spiral2 Selective Production of Exotic Species (SPES)/INFN in Italy (2015) http://web.infn.it/spes Facility for Rare Isotope Beams (FRIB)/MSU in USA (2018) up to 400(200) MeV/A for 132Sn http://www.frib.msu.edu/ The Korean Rare Isotope Accelerator (KoRIA) (Planning) up to 250 MeV/A for 132Sn, up to 109 pps

核物质的状态方程与对称能 约束核物质的对称能: 对称能的效应： 总结和展望 目录 (1) 饱和密度附近的行为 (2) 低密行为 (3) 高密行为 对称能的效应： (1) 核的有效相互作用 (2) 原子核的“中子皮” (3) 中子星的“壳-芯”边界(见郑皓报告) (4) “第五种力”(见郑皓报告) 总结和展望

“对称核物质”的状态方程 (1) EOS of symmetric matter around the saturation density ρ0 Giant Monopole Resonance K0=231±5 MeV Yongblood/Clark/Lui, PRL82, 691 (1999) Recent results: K0=240±20 MeV G. Colo et al. U. Garg et al. S. Shlomo et al. Uncertainty of the extracted K0 is mainly due to the uncertainty of L (slope parameter of the symmetry energy) and m*0 (isoscalar nucleon effective mass) (See, e.g., L.W. Chen/J.Z. Gu, JPG39, 035104(2012))

See also: C. Hartnack, H. Oeschler, “对称核物质”的状态方程 (2) EOS of symmetric matter for 1ρ0< ρ < 3ρ0 from K+ production in HIC’s J. Aichelin and C.M. Ko, PRL55, (1985) 2661 C. Fuchs, Prog. Part. Nucl. Phys. 56, (2006) 1 C. Fuchs et al, PRL86, (2001) 1974 Transport calculations indicate that “results for the K+ excitation function in Au + Au over C + C reactions as measured by the KaoS Collaboration strongly support the scenario with a soft EOS.” See also: C. Hartnack, H. Oeschler, and J. Aichelin, PRL96, 012302 (2006)

“对称核物质”的状态方程 (3) Present constraints on the EOS of symmetric nuclear matter for 2ρ0< ρ < 5ρ0 using flow data from BEVALAC, SIS/GSI and AGS P. Danielewicz, R. Lacey and W.G. Lynch, Science 298, 1592 (2002) The highest pressure recorded under laboratory controlled conditions in nucleus-nucleus collisions High density nuclear matter 2 to 5ρ0 Use constrained mean fields to predict the EOS for symmetric matter Width of pressure domain reflects uncertainties in comparison and of assumed momentum dependence.

Promising Probes of the Esym(ρ) (an incomplete list !) 对称能的实验探针 Promising Probes of the Esym(ρ) (an incomplete list !) Pigmy/Giant resonances Nucleon optical potential B.A. Li, L.W. Chen, C.M. Ko Phys. Rep. 464, 113(2008)

已成为目前国际上关于对称能研究的标准参考文献之一 “同位旋核物理”的综述性文章 已成为目前国际上关于对称能研究的标准参考文献之一 被引用: >248 (SCIE) 在SPIRES数据库“The 100 most highly cited papers during 2010 in the nucl-th archive )”排名第5 入选“ESI 高被引用论文”(Most Cited Papers in Essential Science Indicators)

PRL papers about Esym in 2010-2012 2010: 1 2011: 4 2012: 4 (2009: 7) J.B. Natowitz et al, Symmetry Energy of Dilute Warm Nuclear Matter, PRL104, 202501 (2010) J. Dong, W. Zuo, and W. Scheid, Correlation between -Decay Energies of Superheavy Nuclei Involving the Effects of Symmetry Energy, PRL 107, 012501 (2011) S. S. Henshaw et al., New Method for Precise Determination of the Isovector Giant Quadrupole Resonances in Nuclei, PRL 107, 222501 (2011) X. Roca-Maza et al., Neutron Skin of 208Pb, Nuclear Symmetry Energy, and the Parity Radius Experiment, PRL 106, 252501 (2011) A. Tamii et al., Complete Electric Dipole Response and the Neutron Skin in 208Pb, PRL 107, 062502 (2011) P. Moller et al., New Finite-Range Droplet Mass Model and Equation-of-State Parameters, PRL 108, 052501 (2012) F.L.Roberts et al., Protoneutron Star Cooling with Convection: The Effect of the Symmetry Energy, PRL 108, 061103 (2012) A.W. Steiner and S. Gandolfi, Connecting Neutron Star Observations to Three-Body Forces in Neutron Matter and to the Nuclear Symmetry Energy, PRL 108, 081102 (2012) L. Qin et al., Laboratory Tests of Low Density Astrophysical Equations of State, PRL (2012), in press

(1) Esym: Isospin Diffusion in HIC’s Isospin Diffusion/Transport ______________________________________ How to measure Isospin Diffusion? PRL84, 1120 (2000) A+A,B+B,A+B X: isospin tracer

(1) Esym: Isospin Diffusion in HIC’s Symmetry energy, isospin diffusion, in-medium cross section Chen/Ko/Li, PRL94,032701 (2005) Chen/Ko/Li, PRC72,064309 (2005) Li/ Chen, PRC72, 064611(2005) Isospin Diffusion Data  Esym(ρ0)=31.6 MeV L=88±25 MeV

(2) Esym: Isoscaling in HIC’s Isoscaling observed in many reactions M.B. Tsang et al. PRL86, 5023 (2001)

(2) Esym: Isoscaling in HIC’s Consistent with isospin diffusion data! Constraining Symmetry Energy by Isocaling: TAMU Data Shetty/Yennello/Souliotis, PRC75,034602(2007); PRC76, 024606 (2007) Isoscaling Data  Esym(ρ0)=31.6 MeV L=65 MeV Consistent with isospin diffusion data!

(3) Esym: Isospin diffusion and double n/p ratio in HIC’s ImQMD: n/p ratios and two isospin diffusion measurements Tsang/Zhang/Danielewicz/Famiano/Li/Lynch/Steiner, PRL 102, 122701 (2009) ImQMD: Isospin Diffusion and double n/p ratio  Esym(ρ0)~28 - 34 MeV? L=38 - 103 MeV

(4) Esym: Nuclear Mass in Thomas-Fermi Model Myers/Swiatecki, NPA 601, 141 (1996) Thomas-Fermi Model analysis of 1654 ground state mass of nuclei with N,Z≥8 Thomas-Fermi Model + Nuclear Mass  Esym(ρ0)=32 .65 MeV L=49.9 MeV

(5) Esym: Droplet Model Analysis on Neutron Skin N-Skin data measured in antiprotonic atoms Droplet Model + N-skin  Esym(ρ0)=28 - 35 MeV, L=55 ± 25 MeV

(6) Esym: Skyrme-HF Analysis on Neutron Skin Chen/Ko/Li/Xu PRC82, 024321(2010) N-Skin data of Sn isotopes Esym(ρ0)=30 MeV Neutron skin constraints on L and Esym(ρ0) are insensitive to the variations of other macroscopic quantities.

(7)、(8) Esym: Pygmy Dipole Resonances Electric dipole strength in atomic nuclei By Deniz Savran

(7)、(8) Esym: Pygmy Dipole Resonances Pygmy Dipole Resonances of 130,132Sn  Esym(ρ0)=32 ± 1.8 MeV L=43.125 ± 15 MeV Pygmy Dipole Resonances of 68Ni and 132Sn  Esym(ρ0)=32.3 ± 1.3 MeV, L=64.8 ± 15.7 MeV

(9) Esym: IAS+LDM Danielewicz/Lee, NPA 818, 36 (2009) Esym from Isobaric Analog States + Liquid Drop model with surface symmetry energy IAS+Liquid Drop Model with Surface Esym  Esym(ρ0)=32.5 ± 1 MeV L=94.5 ± 16.5 MeV

Esym from Liquid Drop model with surface symmetry energy (10) Esym: LDM Esym from Liquid Drop model with surface symmetry energy Liquid Drop Model with Surface Esym  Esym(ρ0)=31.1 ± 1.7 MeV L=66.0 ± 13 MeV

(11) Esym: Global nucleon optical potential Xu/Li/Chen, PRC82, 054607 (2010) =26.11 MeV

(11) Esym: Global nucleon optical potential Xu/Li/Chen, PRC82, 054607 (2010)

Esym from FRDM-2011 + Nuclear Mass (AME2003) (12) Esym: FRDM Esym from FRDM-2011 + Nuclear Mass (AME2003) FRDM+Nuclear Mass (AME2003)  Esym(ρ0)=32.5 ± 0.5 MeV L=70 ± 15 MeV

Nuclear matter symmetry energy aroundρ0 Current constraints on Esym (ρ0) and L from nuclear reactions and structures (1) TF+Nucl. Mass (1996) Myers/Swiatecki, NPA 601, 141 (1996) (2) Iso. Diff. (IBUU04, 2005) L.W. Chen et al., PRL94, 032701 (2005); B.A. Li/L.W. Chen, PRC72, 064611(2005) (3) Isoscaling (2007) D. Shetty et al., PRC76, 024606 (2007) (4) PDR in 130,132Sn (2007) (LAND/GSI) A. Klimkiewicz et al., PRC76, 051603(R)(2007) (5) Iso. Diff. & double n/p (ImQMD, 2009) M.B. Tsang et al., PRL102, 122701 (2009); (6) IAS+LDM (2009) Danielewicz/J. Lee, NPA818, 36 (2009) (7) DM+N-Skin (2009) M. Centelles et al., PRL102, 122502 (2009); M. Warda et al., PRC80, 024316 (2009) (10) Opt. Pot. (2010) C. Xu et al., PRC82, 054607 (2010) (8) PDR in 68Ni and 132Sn (2010) A. Carbon et al., PRC81, 041301(R)(2010) (11) Nucl. Mass (2010) M. Liu et al., PRC82, 064306 (2010) (9) SHF+N-Skin (2010) L.W. Chen et al., PRC82, 024321 (2010) (12) FRDM (2012) P. Moller et al., PRL108, 052501 (2012)

对称能：饱和密度附近行为 Current constraints on Esym (ρ0) and L from nuclear reactions and structures Chen/Ko/Li/Xu, PRC82, 024321(2010) Esym(ρ0)=30±5 MeV L=58±18 MeV Esym(ρ0)=27 - 36 MeV L=30 - 90 MeV More accurate data are needed to obtain more stringent constraints!

Esym: Neutron Skin + Esym(ρ=0.1 fm-3) L.W. Chen, PRC83, 044308(2011) Linear L-Esym corr. IVGDR of 208Pb/SHF: Trippa/Colo/Vigezzi, PRC77, 061304(R)(2008) IVGDR of 132Sn/RMF: Cao/Ma, CPL25, 1625(2008) Nuclear Mass: Liu/Wang/Li/Zhang, PRC82, 064306(2010) Neutron-Skin of Tin isotopes Chen/Ko/Li/Xu, PRC82, 024321(2010) Based on the same SHF approach! 一种新的思路???基于同样的理论框架，使用不同的实验探针:交叉约束！ Esym(ρ0) = 30.5±3 MeV L = 52.5±20 MeV

核物质的状态方程与对称能 约束核物质的对称能: 对称能的效应： 总结和展望 目录 (1) 饱和密度附近的行为 (2) 低密行为 (3) 高密行为 对称能的效应： (1) 核的有效相互作用 (2) 原子核的“中子皮” (3) 中子星的“壳-芯”边界(见郑皓报告) (4) “第五种力”(见郑皓报告) 总结和展望

极端低密时的对称能：结团效应 Horowitz and Schwenk, Nucl. Phys. A 776 (2006) 55 S. Kowalski, et al., PRC 75 (2007) 014601. 39

极端低密时的对称能：结团效应 40

核物质的状态方程与对称能 约束核物质的对称能: 对称能的效应： 总结和展望 目录 (1) 饱和密度附近的行为 (2) 低密行为 (3) 高密行为 对称能的效应： (1) 核的有效相互作用 (2) 原子核的“中子皮” (3) 中子星的“壳-芯”边界(见郑皓报告) (4) “第五种力”(见郑皓报告) 总结和展望

Isospin fractionation! 对称能的高密行为：重离子碰撞 Heavy-Ion Collisions at Higher Energies IBUU simu. n/p ratio of the high density region Isospin fractionation! Xu/Tsang et al. PRL85, 716 (2000)

粒子产生阈能 实验发现在低于阈能时，重离子碰撞中仍能产生以上粒子， 称为阈下产生。重离子碰撞中粒子的阈下产生为研究高温高 密核介质中强子的性质以及核介质的性质提供了实验基础。

A Quite Soft Esym at supra-saturation densities ??? 对称能高密探针:pion比率 A Quite Soft Esym at supra-saturation densities ??? IBUU04, Xiao/Li/Chen/Yong/Zhang, PRL102,062502(2009) Zhang et al.,PRC80,034616(2009) Softer Stiffer Pion Medium Effects? Xu/Ko/Oh PRC81, 024910(2010) Threshold effects? Δ resonances? …… ImIQMD, Feng/Jin, PLB683, 140(2010)

对称能高密探针:n/p椭圆流v2 A Soft or Stiff Esym at supra-saturation densities ??? P. Russotto,W. Trauntmann, Q.F. Li et al., PLB697, 471(2011)

对称能高密行为:Ksym参数？ L.W. Chen, Sci. China Phys. Mech. Astron. 54, suppl. 1, s124 (2011) [arXiv:1101.2384]

对称能高密行为:Ksym参数？ L.W. Chen, PRC83, 044308(2011) L.W. Chen, Sci. China Phys. Mech. Astron. 54, suppl. 1, s124 (2011) [arXiv:1101.2384]

The Skyrme HF Energy Density Functional Standard Skyrme Interaction: There are more than 120 sets of Skyrme- like Interactions in the literature _________ Agrawal/Shlomo/Kim Au PRC72, 014310 (2005) Yoshida/Sagawa PRC73, 044320 (2006) Chen/Ko/Li/Xu PRC82, 024321(2010) 9 Skyrme parameters: 9 macroscopic nuclear properties:

核物质的状态方程与对称能 约束核物质的对称能: 对称能的效应： 总结和展望 目录 (1) 饱和密度附近的行为 (2) 低密行为 (3) 高密行为 对称能的效应： (1) 核的有效相互作用 (2) 原子核的“中子皮” (3) 中子星的“壳-芯”边界(见郑皓报告) (4) “第五种力”(见郑皓报告) 总结和展望

对称能与核的有效相互作用 Chen/Ko/Li, PRC76, 054316(2007) Esym(ρ0)= 31.5 ±4.5 MeV and L=55 ± 25 MeV: only 55/118 Esym(ρ0)= 31.5 ±4.5 MeV and L=55 ± 25 MeV: only 8/23

核物质的状态方程与对称能 约束核物质的对称能: 对称能的效应： 总结和展望 目录 (1) 饱和密度附近的行为 (2) 低密行为 (3) 高密行为 对称能的效应： (1) 核的有效相互作用 (2) 原子核的“中子皮” (3) 中子星的“壳-芯”边界(见郑皓报告) (4) “第五种力”(见郑皓报告) 总结和展望

(5) Esym: Droplet Model Analysis on Neutron Skin Chen/Ko/Li, PRC72,064309 (2005) Good linear Correlation: S-L Oyamatsu et al., NPA634, 3 (1998); Brown, PRL85,5296 (2000); Horowitz/Piekarewicz, PRL86, 5647 (2001); Furnstahl, NPA706, 85 (2002); Yoshida/Sagawa, PRC73, 044320 (2006) 52

208Pb Radius EXperiments - PREX Chen/Ko/Li/Xu, PRC82, 024321 (2010) Jefferson Lab (JLab): 208Pb Radius EXperiments - PREX The Lead Radius Experiment ("PREX"), experiment number E06002, uses the parity violating weak neutral interaction to probe the neutron distribution in a heavy nucleus, namely 208Pb, thus measuring the RMS neutron radius to 1% accuracy, which has an important impact on nuclear theory.   PRL108, 112502(2012): A quite stringent constraint on Δrnp of 208Pb:

核物质的状态方程与对称能 约束核物质的对称能: 对称能的效应： 总结和展望 目录 (1) 饱和密度附近的行为 (2) 低密行为 (3) 高密行为 对称能的效应： (1) 核的有效相互作用 (2) 原子核的“中子皮” (3) 中子星的“壳-芯”边界(见郑皓报告) (4) “第五种力”(见郑皓报告) 总结和展望

总结和展望 通过重离子碰撞，原子核结构性质(mass, neutron skin, GR/PG…), 以及核子光学势的研究，我们对饱和密度附近及低密核物质对称能 的行为有了一定的认识: Esym(ρ0) =31±3 MeV and L=60±30 MeV 更精确的约束需要更精确的实验数据和更可靠的理论方法! 对称能对于理解核的有效相互作用、丰中子核的中子皮结构、 中子星的结构性质以及引力的短距离行为有重要意义 决定对称能的高密行为依然是一个巨大的挑战 (Many-body forces, Short range tensor forces, Short range NN correlations(许昌报告), Model cross check, more data,……).丰中子核引起的高能重离子碰 撞的实验数据将变得非常重要! 对称能高阶系数(Ksym,Jsym,…)？ 直接由QCD出发计算对称能？QCD sum rule → Lorentz Covariant Nucleon Self-Energies → Esym (蔡宝军 报告)

重离子碰撞物理@SJTU Dr. Lie-Wen Chen (陈列文) Dr. Xin Wang(王欣) Dr. Xiao-Hua Li (李小华) Mr. Bao-Jun Cai (蔡宝军) Mr. Peng-Cheng Chu (初鹏程) Mr. Rong Chen (陈融) Mr. Zhen Zhang (张振) Mr. Kai-Jia Sun (孙开佳) Mr. Hao Zheng (郑皓)

谢 谢！ Thanks!