从原子核到中子星－谈核物质的对称能

从原子核到中子星－谈核物质的对称能 陈列文上海交通大学物理系/粒子物理宇宙学研究所(INPAC) lwchen@sjtu.edu.cn 交叉学科理论研究中心，中国科学技术大学，合肥， 2013年4月11日

目录 • 核物质的状态方程与对称能 • 约束核物质的对称能: (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 (4) “第五种力” • 总结和展望

物质的状态方程 状态方程(EOS-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) The Nuclear Symmetry Energy Symmetry energy term (poorly known) 核物质的对称能 EOS of Isospin Asymmetric Nuclear Matter (Parabolic law) Isospin asymmetry

Symmetry energy term Symmetry energy including surface diffusion effects (ys=Sv/Ss) 核的对称能原子核的液滴模型(Liquid-drop model) W. D. Myers, W.J. Swiatecki, P. Danielewicz, P. Van Isacker, A. E. L. Dieperink,……

为什么研究对称能？ The multifaceted influence of the nuclear symmetry energyA.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) 4. Dark Matter Direct Detection (Hao Zheng, Zhen Zhang, and Lie-Wen Chen, in preparation)

夸克胶子等离子体物理 致密星体物理同位旋核物理强相互作用物质相图 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 Holy Grail of Nuclear Physics HIC’s 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 1. 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

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

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, ……

Transport model for HIC’s Isospin-dependent BUU (IBUU) model • Solve the Boltzmann equation using test particle method (C.Y. Wong) • Isospin-dependent initialization • Isospin- (momentum-) dependent mean field potential • Isospin-dependent N-N cross sections • a. Experimental free space N-N cross section σexp • b. In-medium N-N cross section from the Dirac-Brueckner • approach based on Bonn A potential σin-medium • c. Mean-field consistent cross section due to m* • Isospin-dependent Pauli Blocking EOS

Facilities of Radioactive Beams • 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 • Texas A&M Facility for Rare Exotic Beams -T-REX (2013) • http://cyclotron.tamu.edu • 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-RAON(RISP Accelerator Complex) (Planning) • up to 250 MeV/A for 132Sn, up to 109 pps • ……

极端同位旋条件下的核物理 12 12 12 18 18 3 Studied extensively Symmetric matter ρn=ρp density ρ=ρn+ρp Very small isospin asymmetry A new dimension ??? Isospin asymmetryδ=(ρn-ρp)/ρ

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

Nuclear matter symmetry energy around ρ0 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)

Why is the Esym(ρ) still so uncertain even at saturation density? • Is there a general principle at some level, independent of the interaction and many-body theory, telling us what determines the Esym(ρ0) and L? • If possible, how to constrain separately each component of Esym(ρ0) and L?

Decomposition of the Esym and L according to the Hugenholtz-Van Hove (HVH) theorem C. Xu, B.A. Li, L.W. Chen and C.M. Ko, NPA 865, 1 (2011) R. Chen, B.J. Cai. L.W. Chen, B.A. Li, X.H. Li, and C. Xu, PRC85, 024305 (2012). The Lane potential Higher order in isospin asymmetry

Constraining symmetry potentials from neutron-nucleus scattering data Providing a boundary condition on Usym,1(ρ,p) and Usym,2(ρ,p) at saturation density from global neutron-nucleus scattering optical potentials using the latest and most complete data base for n+A elastic angular distributions X.H. Li, B.J. Cai. L.W. Chen, R. Chen, B.A. Li, and C. Xu, PLB721, 101 (2013)

Constraining symmetry potentials from neutron-nucleus scattering data X.H. Li, B.J. Cai. L.W. Chen, R. Chen, B.A. Li, and C. Xu, PLB721, 101 (2013)

Constraints on Ln from n+A elastic scatterings X.H. Li, B.J. Cai. L.W. Chen, R. Chen, B.A. Li, and C. Xu, PLB721, 101 (2013)

Applying the constraints from neutron-nucleus scattering

Lorentz Covariant Self-energy Decomposition of the Esym and L B.J. Cai and L.W. Chen, PLB711, 104 (2012) Lorentz covarinat nucleon self-energy can be obtained from QCD sum rules!

Esym：Around saturation density Current constraints (totally 24) on Esym (ρ0) and L from terrestrial experiments and astrophysical observations All constraints are essentially consistent with Esym(ρ0)=31±2 MeV and L=50±20 MeV More accurate data and more reliable theoretical models/methods are needed to obtain more stringent constraints!

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

极端低密时的对称能：结团效应

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 Xu/Tsang et al. PRL85, 716 (2000) B.A. Li, PRL88, 192701(2002) Isospin fractionation!

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。

对称能高密探针:pion比率 A Quite Soft Esym at supra-saturation densities ??? ImIBLE, Xie/Su/Zhu/Zhang, PLB718,1510(2009) IBUU04, Xiao/Li/Chen/Yong/Zhang, PRL102,062502(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)

High density Esym: Ksymparameter？ L.W. Chen, Sci. China Phys. Mech. Astron. 54, suppl. 1, s124 (2011) [arXiv:1101.2384]

High density Esym: Ksymparameter？ L.W. Chen, in preparation This conclusion is also valid for other energy density functionals (SHF, Gogny-HF, RMF,BHF) !!! Model independent!

Ksym: Symmetry energy of finite nuclei Symmetry energy coefficient of finite nuclei in mass formula Q: neutron-skin stiffness coefficient in the droplet model, it is also related to the surface symmetry energy, and can be obtained from asymmetric semi-infinite nuclear matter (ASINM) calculations As a good approximation (Treiner/Krivine, Ann. Phys. 170, 406(86), and L.W. Chen, PRC83, 044308 (2011)), we have M. Liu et al., PRC82, 064306 (2010)

High density Esym : Esym(2ρ0)？ Iso. Diff. & double n/p (ImQMD, 2009) M.B. Tsang et al., PRL102, 122701 (2009) SHF+N-Skin (2010) L.W. Chen et al., PRC82, 024321 (2010) Nucl. Mass+Nskin (2003): Danielewicz, NPA727, 233 (2003) IAS (2009): Danielewicz/Lee, NPA818, 36 (2009) Nucl. Mass (2010): M. Liu et al., PRC82, 064306 (2010) L.W. Chen, in preparation

High density Esym : Esym(2ρ0)？ L.W. Chen, in preparation P. Russotto,W. Trauntmann, Q.F. Li et al., PLB697, 471(2011)

核子-核子势 拟合核子-核子散射数据，氘核的性质等

Cross interaction between isovector and isoscalar mesons _________ 核的有效相互作用 Relativistic Mean Field Model: Standard Skyrme Interaction: 9 Skyrme parameters: There are about 120 sets of Skyrme-like Interactions in the literature There are about few tens sets of interactions in the literature 这些参数都能较好符合原子核的质量和电荷半径等实验数据！

对称能与核的有效相互作用 Chen/Ko/Li, PRC76, 054316(2007) Chen/Ko/Li, PRC72,064309 (2005) 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

原子核的“中子皮” Bodmer, Nucl. Phys. 17, 388 (1960) Sprung/Vallieres/Campi/Ko, NPA253, 1(1975) Shlomo/Friedman, PRL39, 1180 (1977) …… For heavier stable nuclei: N>Z Neutron Skin Thickness:

208Pb的“中子皮” 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:

中子星 中子星被认为是宇宙中一类最神秘的客体，它是恒星走完一生的最终归宿之一。研究表明，一颗典型的中子星的质量大约为1.4倍太阳的质量，但它的半径却只有10公里左右，所以中子星一般是极端致密的星体。由于强大的引力约束，中子星内部的密度可以达到甚至超过5-6倍正常核物质密度(正常核物质密度和重原子核中心的密度相当，大约是水的密度的一百万亿倍)。乒乓球大小的中子星物质的质量大概与地球上一座高山的质量相当。中子星的内部通常由电中性的处于beta平衡(弱相互作用平衡)的均匀的致密核物质组成，其主要成分为中子，另外含有少量的质子和轻子等。中子星的核芯还可能由夸克物质或其它奇特物质形态组成。随着半径向外延，均匀的致密核物质密度降低，开始出现结团(clustering)不稳定性，进入中子星的壳层部分，即发生中子星的壳-芯转变(core-crust transition)。 Gravity Weak E&M Strong Stable Neutron Stars @beta equilibrium Determined by the 4 forces together

对称能与中子星 Lattimer/Prakash, Science 304, 536 (2004) core-crust transition • Neutron star has solid crust over liquid core. • Rotational glitches: small changes in period from sudden unpinning of superfluid vortices. • Evidence for solid crust. • 1.4% of Vela moment of inertia glitches. • Needs to know the transition density to calculate the fractional moment of inertia of the crust Link et al., PRL83,3362(99)

pasta Significantly less than their fiducial values: ρt=0.07-0.08 fm-3 and Pt=0.65 MeV/fm3 对称能与中子星的“壳-芯”边界 Parabolic Law fails! Xu/Chen/Li/Ma, PRC79, 035802 (2009) Kazuhiro Oyamatsu, Kei Iida Phys. Rev. C75 (2007) 015801 Parabolic Approximation has been assumed !!! Xu/Chen/Li/Ma, ApJ 697, 1547 (2009)

从原子核到中子星－谈核物质的对称能

从原子核到中子星－谈核物质的对称能

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