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重离子碰撞与核物质状态方程

重离子碰撞与核物质状态方程. 陈列文 ( 上海交通大学物理系 lwchen@sjtu.edu.cn). 2009 威海高能物理暑期论坛暨“ RHIC 物理和 CSR 强子物理”研讨会， 2009 年 8 月 8 日 -14 日，威海，山东. 目录. 非对称核物质的状态方程与 对称能 同位旋相关的重离子碰撞微观输运模型 重离子碰撞：对称核物质的状态方程 重离子碰撞：对称能的低密行为 重离子碰撞：对称能的高密行为 对称能对其他物理量的约束 总结和展望. Main References:

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重离子碰撞与核物质状态方程

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  1. 重离子碰撞与核物质状态方程 陈列文 (上海交通大学物理系 lwchen@sjtu.edu.cn) 2009 威海高能物理暑期论坛暨“RHIC 物理和CSR 强子物理”研讨会，2009年8月8日-14日，威海，山东

  2. 目录 • 非对称核物质的状态方程与对称能 • 同位旋相关的重离子碰撞微观输运模型 • 重离子碰撞：对称核物质的状态方程 • 重离子碰撞：对称能的低密行为 • 重离子碰撞：对称能的高密行为 • 对称能对其他物理量的约束 • 总结和展望 Main References: L.W. Chen, C.M. Ko, B.A. Li, and G.C. Yong, Front. Phys. China 2(3), 327 (2007) B.A. Li, L.W. Chen, and C.M. Ko, Phys. Rep. 464, 113-281 (2008)

  3. Energy, Temperature, Density: Phase Transitions: Liquid-Gas; Chiral Restoration QGP-Hadrons …… Spin: High Spin State and, SD (Super- Deformed), HD (Hyper- Deformed) …… A and Z: SHE (Super-Heavy Elements) …… Isospin: Nuclei far from Beta- Stability Line …… 一、非对称核物质的状态方程与对称能 极端条件下的核物理 HIC’s

  4. 同位旋核物理: 核结构 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

  5. On Earth!!! Transport Theory In Heaven!!! General Relativity EOS for Asymmetric Nuclear Matter Isospin Effects in HIC’s … Neutron Stars … Many-Body Theory Nuclear Force Many-Body Theory Structures of Radioactive Nuclei, SHE … 同位旋核物理: 中能重离子碰撞 HIC’s induced by neutron-rich nuclei (CSR/Lanzhou,FRIB,GSI, RIKEN……) Most uncertain property of an asymmetric nuclear matter Density Dependence of the Nuclear Symmetry Energy Isospin Nuclear Physics What is the isospin dependence of the in-medium nuclear effective interactions???

  6. 同位旋核物理: 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). Isospin physics

  7. 104 GSI RIKEN 103 CSR/HIRFL E (MeV/u) NSCL/MSU 102 GANIL 10 HIRFL 1 200 250 50 150 300 100 A 重离子加速器装置 • HIRFL, CSR/HIRFL (China) • GANIL (France) • GSI (Germany) • NSCL/MSU,FRIB/MSU • RIKEN (Japan) 中能重离子加速器装置 Dubna, LBL, ORNL, TAMU, INFN, KVI,… AGS,RHIC/BNL SPS,LHC/CERN

  8. IMP CIAE Radioactive beam facilities are being built around the world World status of Rare Isotope Accelerators Providing new opportunities for both nuclear physics and astrophysics

  9. 核物质的状态方程

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

  11. The Nuclear Symmetry Energy Symmetric Nuclear Matter Symmetry energy term 核物质的对称能 (Parabolic law) EOS of Asymmetric Nuclear Matter

  12. Nuclear Matter EOS: Many-Body 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 …… • Effective Field Theory Density Functional Theory (DFT) Chiral Perturbation Theory (ChPT) …… • Phenomenological Approaches Relativistic mean-field (RMF) theory • Relativistic Hartree-Fock (RHF) • Non-relativistic Hartree-Fock (Skyrme-Hartree-Fock) Thomas-Fermi (TF) approximations • Phenomenological potential models ……

  13. Nuclear Matter EOS: Many-Body Approaches Saturation Pionts of Symmetric Nuclear Matter from Microscopic Many-Body Approaches: The Coester Line

  14. SIII TM1 Nuclear Matter EOS: Isospin Dependence Van Dalen/Fuchs/Faessler EPJA31, 29 (2007) Z.H. Li, (2007) I. Tanihata Preprint RIKEN-AF-NP-229, July, 1996. N/Z=0,0.2,0.4,0.6,0.8,1 (From top to bottom)

  15. 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

  16. 二、同位旋相关的重离子碰撞微观输运模型 Transport Models Transport Models for HIC’s at intermediate energies: N-body approaches CMD, QMD,IQMD,IDQMD, ImQMD,ImIQMD,AMD,FMD One-body approaches BUU, BNV, LV, IBL RBUU,RVUU,… Broad applications of transport models in astrophyics, plasma physics, electron transport in semiconductor and nanostructures, particle and nuclear physics, nuclear stockpile stewardship

  17. Transport model for HIC’s Isospin-dependent BUU (IBUU) model • Solve the Boltzmann equation using test particle method • 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

  18. Transport model: IBUU04 Isospin- and momentum-dependent potential (MDI) Das/Das Gupta/Gale/Li, PRC67,034611 (2003) Chen/Ko/Li, PRL94,032701(2005) Li/Chen, PRC72, 064611 (2005)

  19. in neutron-rich matter In-medium Nucleon-nucleon cross sections:Effective mass scaling model • Neglecting medium effects on the transition matrix • Medium effects: • effective mass on the incoming current in initial state and level density of the final state is the reduced mass of the colliding pair NN in medium J.W. Negele and K. Yazaki, PRL 47, 71 (1981) V.R. Pandharipande and S.C. Pieper, PRC 45, 791 (1992) M. Kohno et al., PRC 57, 3495 (1998) D. Persram and C. Gale, PRC65, 064611 (2002). • In-medium cross sections are reduced • nn and pp cross sections are splitted • due to the neutron-proton effective mass slitting in neutron-rich matter Li/Chen, PRC72 (2005)064611

  20. 三、重离子碰撞：对称核物质的状态方程 Why Heavy-Ion Collisions? It is very difficult to obtain information on the nuclear matter EOS at higher densities from nuclear properties around normal density which can be extracted from nuclear structure of finite nuclei and nuclear excitation! LW Chen et al., PRC80, 014322 (2009)

  21. Giant Monopole Resonance 对称核物质的状态方程 (1) EOS of symmetric matter around the saturation density ρ0 K0=231±5 MeV PRL82, 691 (1999) Recent results: K0=240±10 MeV G. Colo et al. U. Garg et al. __

  22. 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)

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

  24. 四、重离子碰撞：对称能的低密行为 Promising Probes of the Esym(ρ) in Nuclear Reactions (an incomplete list !)

  25. 对称能探针：同位旋弥散 Isospin Diffusion/Transport ______________________________________ How to measure Isospin Diffusion? PRL84, 1120 (2000) A+A,B+B,A+B X: isospin tracer

  26. int 对称能探针：同位旋弥散 Isospin diffusion in 124Sn+112Sn@E/A=50 MeV and b=6 fm If complete isospin mixing/ equilibrium The theoretical analysis (BUU) did NOT include Momentum Dependence for nuclear potential !

  27. Momentum-independent Momentum-dependent 对称能探针：同位旋弥散 Comparing momentum-dependent IBUU04 clculations with data on isospin transport Chen/Ko/Li PRL94,(2005) 032701 All have the same Esym (ρ)=31.6 (ρ/ρ0)1.05

  28. 对称能探针：同位旋弥散 Symmetry energy, isospin diffusion, in-medium cross section Li/ Chen, PRC72, 064611(2005) Chen/Ko/Li, PRC72,064309 (2005) Isospin Diffusion Data  Kasy=-500±50 MeV L=86±25 MeV

  29. 对称能探针：同位旋标度 Isoscaling in HIC’s Isoscaling observed in many reactions M.B. Tsang et al. PRL86, 5023 (2001)

  30. 对称能探针：同位旋标度 Constraining Symmetry Energy by Isocaling: TAMU Data Shetty et al. PRC75(07);PRC76(07) Consistent with isospin diffusion data!

  31. 0.45gi 0.95 0.4gi 1.05 0.4gi 1 Consistent constraints from the 2analysis of three observables S=12.5(r/ro)2/3+ 17.6(r/ro) 0.4gi 1.05 gi g IBUU04 : S~31.6(r/ro) 0.69g1.05 对称能探针：同位旋弥散和双n/p比率 ImQMD: n/p ratios and two isospin diffusion measurements Tsang/Zhang/Danielewicz/Famiano/Li/Lynch/Steiner, PRL 102, 122701 (2009)

  32. 对称能的亚饱和密度行为 (亚饱和密度：0.2-0.3<ρ/ρ0<1.2) Chen/Ko/Li, PRL 94, 032701 (2005) Tsang et al., PRL 102, 122701 (2009) (ImQMD) (IBUU04) X=-1

  33. 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

  34. 对称能探针：轻粒子产生 Light Cluster Production and Coalescence Model The coalescence model • Depends on constituents’ space-time structure at freeze-out • Neglecting thebinding energy effect (T>>Ebinding), Coalescence probability: Wigner phase-space density in the rest-frame of the cluster. • Rare processhas been assumed (the coalescence process can be treatedperturbatively). • Higher energy collisions and higher energy cluster production! Chen/Ko/Li, PRC68, 014605 (2003); NPA729, 809 (2003)

  35. 对称能探针：轻粒子产生 Isospin symmetric collisions at E/A≈100 MeV Try Coalescence model at intermediate energies! • Deuteron energy spectra reproduced • Low energy tritons slightly underestimated • Inverse slope parameter of 3He underestimated; probably due toneglect of • larger binding effect • stronger Coulomb effect • wave function Chen/Ko/Li, NPA729, 809 (2003) Data are taken from INDRA Collaboration (P. Pawlowski, EPJA9)

  36. 对称能探针：轻粒子产生 Symmetry Energy Effects on t/3He ratio Stiffer symmetry energy gives smaller t/3He ratio

  37. 对称能探针：核子-核子关联函数 Two-Nucleon Correlation Functions How to detect the space-time structure of nucleon emission experimentally? The two-particle correlation function is obtained by convoluting the emission function g(p,x), i.e., the probability of emitting a particle with momentum p from space-time point x=(r,t), with the relative wave function of the two particle, i.e., The two-particle correlation function is a sensitive probe to the space-time structure of particle emission source by final state interaction and quantum statistical effects (φ(q,r)) Correlation After Burner (Crab): including final-state nuclear and Coulomb interactions (S. Pratt, NPA 566, 103 (1994))

  38. 对称能探针：核子-核子关联函数 Space-time structure of nucleon emission Emission times from IBUU Chen/Ko/Li, PRL90, 162701 (2003) • High momentum nucleons emitted earlier than low momentum ones • Earlier emissions for stiffer symmetry energy • Larger separation in neutron and proton emission times for softer symmetry energy

  39. 对称能探针：核子-核子关联函数 Effects ofmomentum-dependenceof nuclear potential Chen/Ko/Li, PRC69, 054606 (2004) MDI Das, Das Gupta, Gale and Li PRC67, (2003) Pairs with P>500 MeV: n-p CF: 11% The isospin effects on two-particle correlation functions are really observed in recent experimental data !!! R. Ghetti et al., PRC69 (2004) 031605 肖志刚等, PLB, (2006)

  40. 五、重离子碰撞：对称能的高密行为 Heavy-Ion Collisions at Higher Energies n/p ratio of the high density region Isospin fractionation! Li/Yong/Zuo, PRC 71, 014608 (2005)

  41. 对称能高密探针:pion比率

  42. 对称能高密探针:pion比率 IBUU04, Xiao/Li/Chen/Yong/Zhang, PRL102, 062502(2009) M. Zhang et al., arXiv:0904.0447 A Quite Soft Esym at supra-saturation densities !!!

  43. 对称能高密探针:Kaon比率 Aichelin/Ko, PRL55, 2661 (1985):Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities Theory: Famiano et al., PRL97, 052701 (2006) Exp.: Lopez et al. FOPI, PRC75, 011901(R) (2007) K0/K+ yield is not so sensitive to the symmetry energy! Lower energy and more neutron-rich system??? Subthreshold K0/K+ yield may be a sensitive probe of the symmetry energy at high densities

  44. 对称能高密探针：挤出n/p比率 In the squeeze-out direction: nucleons emitted from the high density participant region have a better chance to escape without being hindered by the spectators. These nucleons thus carry more direct information about the high density phase of the reaction. Yong/Li/Chen, nucl-th/0703042 PLB650, 344 (2007) The effect can be 40% at higher pT !

  45. 对称能高密探针: n-p差分流 px y Isospin asymmetry of free nucleons Neutron-proton differential flow for n and p symmetry potential is generally repulsive for neutrons and attractive for protons Bao-An Li, PRL 85, 4221 (2000). Yong/Li/Zuo, High energy physics and nuclear physics (2005).

  46. 六、对称能对其他物理量的约束 (1) Symmetry Energy from SHF and RMF Chen/Ko/Li, PRC76, 054316(2007) Chen/Ko/Li, PRC72,064309 (2005) Only 4/21! Only 5/23!

  47. 对称能：中子皮 (2) Neutron-Skin of 208Pb from SHF Chen/Ko/Li, PRC72,064309(2005) Good linear Correlation: S-L

  48. 对称能：中子星的壳芯转变密度 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)

  49. pasta Significantly less than their fiducial values: ρt=0.07-0.08 fm-3 and Pt=0.65 MeV/fm3 对称能：中子星的壳芯转变密度 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), arXiv:0901.2309

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