May 9, USTC Bao-An Li May 9, USTC 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 Outline May 9, USTC s Proton neutron After 1 Billion years (R~10km) May 9, USTC - Hartree Approximation Hartree-Fock ( Brueckner-Hartree-Fock since1960s) Relativistic models (since 1970s) Dirac May 9, USTC Field-theoretic Hamiltonian approach May 9, USTC Hartree-Fock approximation May 9, USTC Relativistic Hartree-Fock | Relativistic Hartree-Fock-Brueckner May 9, USTC 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, USTC Jiang & Li, Modern Physics Letters A Vol. 23, No. 40 (2008) 3393 May 9, USTC 2 May 9, USTC What Is Vacuum? Are We In Vacuum? F. R. Urban and A. R. Zhitnitsky, Phys. Lett., B688, 9 (2010; Phys. Rev, D 80, (2009); Nucl. Phys. B835, 135 (2010); also from Prof. Ma Wei-Xing Dark Energy The Vacuum Energy? Relevant to Dynamical symmetry breaking Or Explicit symmetry breaking? May 9, USTC Dark Matter 23% Dark Energy 73% Normal Matter 4% May 9, USTC E= Liquid-drop model for nuclei To Recognize the SYMMETRY ENERGY W. D. Myers, W.J. Swiatecki, P. Danielewicz, In isospin asymmetric matter: May 9, USTC Status quo of Equation of state Brockmann,Machleidt PRC42,1965(1990) Most important: Nuclear EoS (1) Saturation properties: Early stage: Nuclear Potentials by Fitting low energy NN phase shifts and properties of deuteron May 9, USTC P.Danielewicz, R.Lacey,W.G.Lynch, Science 298(2002)1592 Collective flow data from high energy heavy-ion reactions May 9, USTC L.W.Chen,et.al., PRC72, (05) Fuchs, et.al., arXiv:nucl-th/ May 9, USTC Diverse trends from data 1. Xiao, et.al PRL102, (2009)2. Feng&Jin, PLB683 (2010) P. Russotto,W. Trauntmann, Q.F. Li et al., PLB697, 471(2011) 31.6( /) ,with =0.9+/-0.4 almost linear May 9, USTC : Horowitz,& Piekarewicz, PRL86,5647 Horowitz,& Piekarewicz, PRC May 9, USTC ApJ2010 May 9, USTC Nuclear matter symmetry energy around 0 Current constraints on E sym ( 0 ) 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, (2005); B.A. Li/L.W. Chen, PRC72, (2005) (3) Isoscaling (2007) D. Shetty et al., PRC76, (2007) (5) Iso. Diff. & double n/p (ImQMD, 2009) M.B. Tsang et al., PRL102, (2009); (4) PDR in 130,132 Sn (2007) (LAND/GSI) A. Klimkiewicz et al., PRC76, (R)(2007) (6) IAS+LDM (2009) Danielewicz/J. Lee, NPA818, 36 (2009) (7) DM+N-Skin (2009) M. Centelles et al., PRL102, (2009); M. Warda et al., PRC80, (2009) (9) SHF+N-Skin (2010) L.W. Chen et al., PRC82, (2010) (10) Opt. Pot. (2010) C. Xu et al., PRC82, (2010) (11) Nucl. Mass (2010) M. Liu et al., PRC82, (2010) (8) PDR in 68 Ni and 132 Sn (2010) A. Carbon et al., PRC81, (R)(2010) Slide from Lie-Wen Chen May 9, USTC Why not I(I+1)? RMF study on finite nuclei suggests E ~T(T+1), Ban, et.al. Phys.Lett.B633: ,2006. In nuclear matter, the parabolic approximation suggests E~T*T Why so uncertain at high densities? May 9, USTC Tensor force Factor to soften greatly the Symmetry Energy: C. Xu and B. A. Li, PRC81, : I. Vidana, A. Polls, and C. Providencia, PRC 84, (R) May 9, USTC 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, USTC Non-nucleonic degrees of freedom Threshold for hyperons reaches at high densities; 2 0 -4 0 Hadron-Quark transition may occur for nucleon overlaps > 2 0 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, USTC EoS with inclusion of hyperons Definition of symmetry energy: at given hyperon fraction. for charge neutral and chemical equilibrated matter May 9, USTC RMF models: SLC and SCLd Jiang Li and Chen, PLB653 184 07 PRC76, (07); ApJ756 56 12 Demorest, et al., Nature 467, 1081(2010) PSR J RMF model NL3 : Lalazissis, et. al. PRC 55, 540(97). May 9, USTC RMF model NL3 May 9, USTC Symmetry energy with quarks Y is the quark phase proportion, determined by Gibbs conditions. We just consider the symmetric matter=0 a function of May 9, USTC Critical density Calculation detail: Charge chemical potential neglected here! May 9, USTC Symmetry energy of quark flavor May 9, USTC With hyperons May 9, USTC Tolman-Oppenheimer-Volkoff (TOV) ~1.4M ~11km May 9, USTC May 9, USTC Symmetry energy extraction with Dark matter Steiner:PRL 108, (2012) Effect of Dark Matter? May 9, USTC Free mass of dark matter 10GeV May 9, USTC 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, USTC Acknowledgment National Natural Sciences Foundation of China under grant Nos , , China Jiangsu Provincial Natural Science Foundation under GrantNo.BK Thank you for your attention!