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对称能与非核子自由度及其它

对称能与非核子自由度及其它. 蒋维洲 东南大学物理系 合作者： Bao-An Li ，陈列文、任中洲 学生：张广华、张东睿、杨荣瑶、向仟飞. Outline. Introduction to quantum many-body approaches and the unsettled Renormalization, vacuum, dark energy? Real puzzle of symmetry energy or mal-definition? Symmetry energy and quarks & hyperons

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对称能与非核子自由度及其它

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  1. 对称能与非核子自由度及其它 蒋维洲 东南大学物理系 合作者：Bao-An Li，陈列文、任中洲 学生：张广华、张东睿、杨荣瑶、向仟飞 May 9, 2013 @ USTC

  2. Outline • Introduction to quantum many-body approaches and the unsettled • Renormalization, vacuum, dark energy? • Real puzzle of symmetry energy or mal-definition? • Symmetry energy and quarks & hyperons • In neutron stars, effect of dark matter? • Concluding remarks May 9, 2013 @ USTC

  3. 从宇宙大爆炸到黑洞形成 10-10--100 s Proton neutron 质子 After 1 Billion years 中子 中子星 (R~10km) 黑洞 May 9, 2013 @ USTC

  4. 核结构——量子多体问题 • 宏观模型、宏观-微观模型 • 准粒子、费米独立气体模型 • Hartree Approximation • Hartree-Fock (反对称化） • Brueckner-Hartree-Fock（since1960’s) • Relativistic models (since 1970’s) Dirac旋量（大分量、小分量），自旋，膺自旋对称性，极化散射 May 9, 2013 @ USTC

  5. Field-theoretic Hamiltonian approach May 9, 2013 @ USTC

  6. May 9, 2013 @ USTC

  7. Hartree-Fock approximation May 9, 2013 @ USTC

  8. Relativistic Hartree-Fock | Relativistic Hartree-Fock-Brueckner May 9, 2013 @ USTC

  9. No quantum effect • Radiation correction requires the quantization of Coulomb field • In strong fields, the renormalization required • Relativistic Hartree Approximation: vacuum polarization of mesons (Chin, AP108, 301 (1977).) No ring energy calculation done in Relativistic Hartree-Fock-Brueckner framework! Two-body correlation is not enough to depict pairing correlation: BCS, Bogoliubov,… May 9, 2013 @ USTC

  10. Jiang & Li,Modern Physics Letters A Vol. 23, No. 40 (2008) 3393 May 9, 2013 @ USTC

  11. 2 纳米管中真空能量的计算 • 真空是无限的，而实际的世界在一定的边界内是有限的。例如，无限的真空能量在平行的不带电的导体板间是有限的，它带来了可观的吸引力。 • 我们的工作在计算同心柱环（多层碳纳米管）的真空能量，给出环层间的吸引。 May 9, 2013 @ USTC

  12. May 9, 2013 @ USTC

  13. Dark Energy The Vacuum Energy? Relevant to Dynamical symmetry breaking Or Explicit symmetry breaking? What Is Vacuum? Are We In Vacuum? F. R. Urban and A. R. Zhitnitsky, Phys. Lett., B688, 9 (2010; Phys. Rev, D 80, 063001 (2009); Nucl. Phys. B835, 135 (2010); also from Prof. Ma Wei-Xing May 9, 2013 @ USTC

  14. “Normal Matter” 4% Dark Energy 73% Dark Matter 23% May 9, 2013 @ USTC

  15. To Recognize the SYMMETRY ENERGY Liquid-drop model for nuclei E= W. D. Myers, W.J. Swiatecki, P. Danielewicz,…… In isospin asymmetric matter: May 9, 2013 @ USTC

  16. Status quo of Equation of state Early stage: Nuclear Potentials by Fitting low energy NN phase shifts and properties of deuteron Most important: Nuclear EoS (1) Saturation properties: Brockmann,Machleidt，PRC42,1965(1990) May 9, 2013 @ USTC

  17. P.Danielewicz, R.Lacey,W.G.Lynch, Science 298(2002)1592 Collective flow data from high energy heavy-ion reactions May 9, 2013 @ USTC

  18. Fuchs, et.al., arXiv:nucl-th/0511070 L.W.Chen,et.al., PRC72, 064309 (05) May 9, 2013 @ USTC

  19. Diverse trends from data 1. Xiao, et.al PRL102, 062502 (2009) 2. Feng&Jin, PLB683 (2010) 140 3. P. Russotto,W. Trauntmann, Q.F. Li et al., PLB697, 471(2011) 31.6(ρ/ρ)γ,with γ=0.9+/-0.4：almost linear May 9, 2013 @ USTC

  20. May 9, 2013 @ USTC

  21. May 9, 2013 @ USTC

  22. 例子: Horowitz,& Piekarewicz, PRL86,5647 Horowitz,& Piekarewicz, PRC64 062802 May 9, 2013 @ USTC

  23. ApJ2010 May 9, 2013 @ USTC

  24. 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) (8) PDR in 68Ni and 132Sn (2010) A. Carbon et al., PRC81, 041301(R)(2010) (10) Opt. Pot. (2010) C. Xu et al., PRC82, 054607 (2010) (9) SHF+N-Skin (2010) L.W. Chen et al., PRC82, 024321 (2010) (11) Nucl. Mass (2010) M. Liu et al., PRC82, 064306 (2010) May 9, 2013 @ USTC Slide from Lie-Wen Chen

  25. Why not I(I+1)? RMF study on finite nuclei suggests E ~T(T+1), Ban, et.al. Phys.Lett.B633:231-236,2006. In nuclear matter, the parabolic approximation suggests E~T*T Why so uncertain at high densities? May 9, 2013 @ USTC

  26. Tensor force Factor to soften greatly the Symmetry Energy: C. Xu and B. A. Li, PRC81, 064612: I. Vidana, A. Polls, and C. Providencia, PRC 84, 062801(R) May 9, 2013 @ USTC

  27. Revisit the tensor force • Mainly from exchange terms. • Pion & rho: the most important ingredients of the chiral perturbative theory. • Rho meson becomes important in the tensor force due to the in-medium mass dropping associated with the partial restoration of the chiral symmetry. • Vacuum effect on the symmetry energy: vacuum condensate • Applications in superheavy nuclei, nuclei near drip lines, high-spin states… May 9, 2013 @ USTC

  28. Non-nucleonic degrees of freedom • Threshold for hyperons reaches at high densities; 2ρ0-4ρ0 • Hadron-Quark transition may occur for nucleon overlaps >2ρ0 • In astrophysical extraction of the symmetry energy, there may be the effect of unknown dark matter. • What is the effect of these components in dense matter? May 9, 2013 @ USTC

  29. EoS with inclusion of hyperons Definition of symmetry energy: at given hyperon fraction. for charge neutral and chemical equilibrated matter May 9, 2013 @ USTC

  30. RMF models: SLC and SCLd Demorest, et al., Nature 467, 1081(2010)：PSR J1614-2230 Jiang，Li，and Chen, PLB653，184 （07）； PRC76, 054314 (07); ApJ756，56（12） RMF model NL3: Lalazissis, et. al. PRC 55, 540(97). May 9, 2013 @ USTC

  31. May 9, 2013 @ USTC

  32. RMF model NL3 May 9, 2013 @ USTC

  33. Symmetry energy with quarks a function of α Y is the quark phase proportion, determined by Gibbs conditions. We just consider the symmetric matterα=0 May 9, 2013 @ USTC

  34. Critical density Calculation detail: Charge chemical potential neglected here! May 9, 2013 @ USTC

  35. May 9, 2013 @ USTC

  36. Symmetry energy of quark flavor May 9, 2013 @ USTC

  37. With Λ hyperons May 9, 2013 @ USTC

  38. 中子星 Tolman-Oppenheimer-Volkoff (TOV)方程 质量~1.4M¤，半径~11km May 9, 2013 @ USTC

  39. 含暗物质及其相互作用的中子星 暗物质与正常物质 只有引力相互作用： May 9, 2013 @ USTC

  40. Symmetry energy extraction with Dark matter Steiner:PRL 108, 081102 (2012) Effect of Dark Matter? May 9, 2013 @ USTC

  41. Free mass of dark matter 10GeV May 9, 2013 @ USTC

  42. Remarks not to summary: • Quantum many-body problems are still problems, some of which are far off unsettled. • Tensor force? three-body force… • Symmetry Energy is a mirror to reflect all these problems. • Vacuum effect on symmetry energy? non-nucleonic degrees of freedom disturb Symmetry Energy. • We should not have to regard Symmetry Energy as a beauty in mind, but a field beyond which we can grasp something, different, new, or even fundamental… • For us, Dark Energy & Dark Matter are still a dream, not a story. May 9, 2013 @ USTC

  43. Acknowledgment Thank you for your attention! • 兰州重离子加速器国家实验室理论物理中心 • National Natural Sciences Foundation of China under grant Nos.10405031, 10235030 , 11275048 • China Jiangsu Provincial Natural Science Foundation under GrantNo.BK2009261 May 9, 2013 @ USTC

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