1. Bao-An Li Texas A&M University-Commerce and Xi’an Jiao Tong University Collaborators: F. Fattoyev, M. Gearheart, J. Hooker, W. Lin, W. Newton and Jun Xu, TAMU-Commerce, USA Che Ming Ko, Texas A&M University, USA Plamen G. Krastev, Harvard University, USA Lie-Wen Chen, Shanghai Jiao Tong University, China Wei-Zhou Jiang, Southeast University, China Chang Xu and Zhongzhou Ren, Nanjing University, China Gao-Chan Yong and Wei Zuo, Institute of Modern Physics, China Li Ou, Guangxi Normal University, China De-Hua Wen, South China University of Technology Zhi-Gang Xiao, Tsinghua University, China Ang Li, Xiamen University, China Xiao Han and Gao-Feng Wei, Xi’an Jiao Tong University Nuclear Symmetry Energy and its Astrophysical Impacts

2. Outline: 1.Motivation and introduction: Equation of State (EOS) and symmetry energy of neutron-rich nuclear matter 2. Current understanding and constraints on symmetry energy 3. Several examples illustrating astrophysical impacts of symmetry energy 4. Summary

3. What is the Equation of State of neutron-rich nucleonic matter? 18 12 3 symmetry energy ρ=ρn+ρpρ=ρn+ρp 0 1 density Isospin asymmetry Symmetric matter ρn=ρpρn=ρp Energy per nucleon in symmetric matter Energy per nucleon in asymmetric matter δ Isospin asymmetry ??? The axis of new opportunities ???

4. Examples Symmetry energy (MeV) Density Effective field theory (Kaiser et al.) DBHF RMF BHF Greens function Variational many-body A.E. L. Dieperink et al., Phys. Rev. C68 (2003) 064307 Essentially, all models and interactions available have been used to predict the E sym (ρ)

5. More examples: Skyrme Hartree-Fock and Relativistic Mean-Field predictions 23 RMF models ρ L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. C72, 064309 (2005); C76, 054316 (2007). Density

6. Among interesting questions regarding nuclear symmetry energy: Why is the density dependence of symmetry energy so uncertain especially at high densities? What are the major underlying physics determining the symmetry energy? What is the symmetry free-energy at finite temperature? What is the EOS of low-density clustered matter? How does it depend on the isospin asymmetry of the system? Linearly or quadratically? Can we still define a symmetry energy for clustered matter? What are the effects of n-p pairing on low density EOS? How to constrain the symmetry energy at various densities using terrestrial nuclear experiments and/or astrophysics observations? Current Situation : Many experimental probes predicted Major progress made in constraining the symmetry energy around and below ρ 0 Interesting features found about the EOS of low density n-rich clustered matter Several sensitive astrophysical observables identified/used to constrain Esym High-density behavior of symmetry energy remains contraversial

7. Characterization of symmetry energy near normal density The physical importance of L In npe matter in the simplest model of neutron stars at ϐ -equilibrium In pure neutron matter at saturation density of nuclear matter Many other astrophysical observables, e.g., radii, core-crust transition density, cooling rate, oscillation frequencies and damping rate, etc of neutron stars

8. Thanks to the hard work of many of you Community averages with physically meaningful error bars?

9. Chen, Ko and Li, PRL (2005) Agrawal et al. PRL (2012) Time Line

10. At the mean-field level: C. Xu, B.A. Li and L.W. Chen, PRC 82, 054607 (2010) C. Xu, B.A. Li, L.W. Chen and C.M. Ko, NPA 865, 1 (2011) R. Chen et al., PRC 85, 024305 (2012).

11. Bao-An Li and Xiao Han (2012)

12. Neutron stars as a natural testing ground of grand unification theories of fundamental forces? Nuclear force weak E&M Stable neutron star @ ϐ -equilibrium Requiring simultaneous solutions in both gravity and strong interaction! Grand Unified Solutions of Fundamental Problems in Nature! Connecting Quarks with the Cosmos: Eleven Science Questions for the New Century, Committee on the Physics of the Universe, National Research Council What is the dark matter? What is the nature of the dark energy? How did the universe begin? What is gravity? What are the masses of the neutrinos, and how have they shaped the evolution of the universe? How do cosmic accelerators work and what are they accelerating? Are protons unstable? Are there new states of matter at exceedingly high density and temperature? Are there additional spacetime dimensions? How were the elements from iron to uranium made? Is a new theory of matter and light needed at the highest energies?

13. J.M. Lattimer and M. Prakash, Science Vol. 304 (2004) 536-542.

14. Jun Xu, Lie-Wen Chen, Bao-An Li and Hongru Ma, The Astrophysical Journal 697, 1549 (2009); Jun Xu, Che Ming Ko, Lie-Wen Chen and Bao-An Li, Phys. Rev. C81, 055805 (2010). Core-crust transition density and symmetry energy

15. Size of the pasta phase and symmetry energy W.G. Newton, M. Gearheart and Bao-An Li ThThe Astrophysical Journal (2012) in press. Pasta

16. Dependence of the core and total radii on symmetry energy

17. Upper and lower limits I. ‘Solid pasta’ – μ at crust-core boundary II. ‘Liquid pasta’ – μ at spherical-pasta boundary, Ushomirsky, Cutler, Bildsten MNRAS 319, 2000 Crustal torsional oscillation modes and the quasi-periodical oscillation in the light curves of the soft gamma-ray repeaters Fundamental mode frequency: Shear modulus of the solid crust Fraction of free neutrons Mass and charge of nuclei on the lattice

18. Torsional crust oscillations M. Gearheart, W.G. Newton, J. Hooker and Bao-An Li, Monthly Notices of the Royal Astronomical Society, 418, 2343 (2011).

19. Dependence of the r-mode instability window of rotating neutron stars on symmetry energy De-Hua Wen, W.G. Newton and Bao-An Li, Phys. Rev. C85, 025801 (2012)

20. The proton fraction x at ß -equilibrium in proto-neutron stars is determined by The critical proton fraction for direct URCA process to happen is X p =0.14 for npeμ matter obtained from energy-momentum conservation on the proton Fermi surface Slow cooling: modified URCA: Faster cooling by 4 to 5 orders of magnitude: direct URCA Consequence: long surface thermal emission up to a few million years B.A. Li, Nucl. Phys. A708, 365 (2002). Direct URCA kaon condensation allowed Neutron bubbles formation transition to Λ-matter Isospin separation instability E(ρ,δ)= E(ρ,0)+E sym (ρ)δ 2

21. Bao-An Li, Phys. Rev. Lett. 88 (2002) 192701 Z.G. Xiao et al, Phys. Rev. Lett. 102 (2009) 062502

22. TOV equation: a condition at hydrodynamical equilibrium Gravity Nuclear pressure A challenge: how can neutron stars be stable with a super-soft symmetry energy? If the symmetry energy is too soft, then a mechanical instability will occur when dP/dρ is negative, neutron stars will then all collapse while they do exist in nature For npe matter dP/dρ<0 if E’ sym is big and negative (super-soft) P. Danielewicz, R. Lacey and W.G. Lynch, Science 298, 1592 (2002))

23. A degeneracy: matter content (EOS) and gravity in determining properties of neutron stars Simon DeDeoSimon DeDeo, Dimitrios PsaltisDimitrios PsaltisPhys. Rev. Lett. 90 (2003) 141101 Neutron stars are among the densest objects with the strongest gravity General Relativity (GR) may break down at strong-field limit There is no fundamental reason to choose Einstein’s GR over alternative gravity theories Uncertain range of EOS Gravity Nuclear pressure In GR, Tolman-Oppenheimer-Volkoff (TOV) equation: a condition for hydrodynamical equilibrium Dimitrios Psaltis, Living Reviews in Relativity, 11, 9 (2008) ?? ??????

24. In grand unification theories, conventional gravity has to be modified due to either geometrical effects of extra space-time dimensions at short length, a new boson or the 5 th force String theorists have published TONS of papers on the extra space-time dimensions In terms of the gravitational potential Yukawa potential due to the exchange of a new boson proposed in the super-symmetric extension of the Standard Model of the Grand Unification Theory, or the fifth force N. Arkani-Hamed et al., Phys Lett. B 429, 263–272 (1998); J.C. Long et al., Nature 421, 922 (2003); C.D. Hoyle, Nature 421, 899 (2003) Yasunori Fujii, Nature 234, 5-7 (1971); G.W. Gibbons and B.F. Whiting, Nature 291, 636 - 638 (1981) Do we really know gravity at short distance? Not at all! The neutral spin-1 gauge boson U is a candidate, it is light and weakly interacting, Pierre Fayet, PLB675, 267 (2009), C. Boehm, D. Hooper, J. Silk, M. Casse and J. Paul, PRL, 92, 101301 (2004). A low-field limit of several alternative gravity theories

25. Light Dark Matter Particle 25  Postulate: neutral scalar dark matter particle  with mass 1-10 MeV  Annihilation  e + e -  Annihilation via neutral vector U boson (dark photon)  m(U)~10-100 MeV  Small couplings to SM fermions   Liping Gan University of North Carolina Wilmington

26. 26 Proposals: e+e- colliders, e-A collisions at Jlab, heavy-ion collisions

27. EOS including the Yukawa contribution Supersoft Symmetry Energy Encountering Non-Newtonian Gravity in Neutron Stars De-Hua Wen, Bao-An Li and Lie-Wen Chen, PRL 103, 211102 (2009)

28. Introduction: Tidal Polarizability Static gravitational tidal field due to NS2 Tidal Polarizability Induced quadrupole deformation on NS1 Tidal Love number NS1 NS2 Flanagan, Hinderer, Phys. Rev. D (2008) Hinderer, Astrophys. J. (2008) Binnington, Poisson, Phys. Rev. D (2009) Damour, Nagar, Phys. Rev. D (2009, 2010, 2012) Hinderer et al., Phys. Rev. D (2010) Postnikov et al., Phys. Rev. D (2010) Baiotti et al., Phys. Rev. Lett. (2010) Baiotti et al., Phys. Rev. D (2011) Pannarale et al., Phys. Rev. D (2011) Lackey et al., Phys. Rev. D (2012) Detection RATE: (2-64)/year over a volume-averaged distance of 187 Mpc O’Shaughnessy et al., Astrophys. J. (2010)

29. The Role of the Nuclear Symmetry Energy Fattoyev et al., Phys. Rev. C (2012)

30. Predictions

31. Open questions for discussions 1.Why is the E sym (ρ) still so uncertain especially at supra-saturation densities? what are the underlying physics governing the symmetry energy? role of tensor force, isospin dependence of short-range nucleon-nucleon correlations, spin-isospin dependence of 3-body and many-body forces,…………………….. 2. How to determine the high-density symmetry energy experimentally? In HIC at 1-10 GeV/A range, what are the effects of symmetry energy on Hadron-QGP phase transition, properties of dense matter, production of various mesons, photons and dileptons……………………..? 3. Astrophysical impacts of nuclear symmetry energy Many questions: what are the sensitive observables?

32. Going beyond the mean-field models: Missing: (1)Contribution of tensor-force induced high-momentum tail to the kinetic part of the Esym (1) 2 nd order tensor contribution to the potential part of the Esym General practice in both nuclear physics and astrophysics To understand why various models predict differently and what are the underlying physics governing the Esym

33. Tensor force induced (1) high-momentum tail in single-particle momentum distribution and (2) isospin dependence of NN correlation Theory of Nuclear matter H.A. Bethe Ann. Rev. Nucl. Part. Sci., 21, 93-244 (1971) Fermi Sphere

34. Universal shape of high-momentum tail  due to short-range interaction of two nearby nucleons  scaling of weighted (e,e’) inclusive xsections from light to heavy nuclei: the ratio of weighted xsection should be independent of the scattering variables Tensor force dominance: 270 MeV/c < P < 600 MeV/c 3N correlations, repulsive core and nucleon resonances start playing a role at higher momentum Variational many-body calculations Fourier transform of single-particle wf Jastrow wf including 2b tensor

35. K.S. Egiyan et al (CLAS), PRL96, 082501 (2006) 2n SRC 3n SRC Absolute probability per nucleon in the high momentum tail due to n-p short-range tensor force Four-momentum transfer Energy transfer

36. Kinetic part of the symmetry energy can be negative While the Fermi momentum for PNM is higher than that for SNM at the same density in the mean-field models, if more than 15% nucleons are in the high-momentum tail of SNM due to the tensor force for n-p T=0 channel, the kinetic part of the symmetry energy becomes negative!

37. Confirmation by Microscopic Many-Body Theories 2. High momentum components in the nuclear symmetry energy Arianna CarboneArianna Carbone, Artur Polls, Arnau Rios, arXiv:1111.0797v1, EPL, 97, 22001 (2012)Artur PollsArnau RiosarXiv:1111.0797v1 Self-Consistent Green’s Function Approach with Argonne Av18, CDBonn, Nij1, N3LO interactions 1. Nuclear symmetry energy and the role of the tensor force Isaac VidanaIsaac Vidana, Artur Polls, Constanca Providencia, arXiv:1107.5412v1,Artur PollsConstanca ProvidenciaarXiv:1107.5412v1 PRC84, 062801(R) (2011) Brueckner--Hartree--Fock approach using the Argonne V18 potential plus the Urbana IX three-body force 3. Alessandro Lovato, Omar Benhar et al., extracted from results already published inAlessandro LovatoOmar Benhar Phys. Rev. C83:054003,2011 Using Argonne V’ 6 interaction Fermi gas with tensor correlation Kinetic symmetry E They all included the tensor force and many-body correlations using different techniques

38. Self-Consistent Green’s Function Approach At saturation density, the Fermi gas model prediction is about 13 MeV

39. Tensor force contribution to the potential part of the symmetry energy G.E. Brown and R. Machleidt, Phys. Rev. C50, 1731 (1994). PLB 18, 54 (1965) S.-O. Bacnman, G.E. Brown and J.A. Niskanen, Phys. Rep. 124, 1 (1985).

40. Tensor force contribution to the potential part of the symmetry energy Ang Li and Bao-An Li, arXiv:1107.0496 Found the missing symmetry energy At saturation density, the 2nd order potential contribution due to the tensor force is about 7-14 MeV, it is 9 MeV with Av18 Short-range tensor forces affects the high-density symmetry energy

41. Effects of the tensor force: (1)Reduce the kinetic contribution through the n-p correlation (2)Directly increase the potential contribution at the 2 nd order Current model calculations: (1)Mean-field based and phenomenological models do not consider tensor force effects (2) Most microscopic models do, but the short-range tensor force due to ρ-meson exchange is poorly known Partially responsible for the divergent model predictions

42. Summary The nuclear symmetry energy is still very uncertain especially at high densities due to mainly (1) 3-body force, (2) short-range tensor force and (3) short-range nucleon-nucleon correlation functions Neutron stars are natural testing ground of grand unification theories. High-density symmetry energy, gravity at short distance, possible extra space-time dimensions are all closely related and have to be considered simultaneously. Symmetry energy affects many properties of neutron stars We have learned a lot about the symmetry energy near normal density

43. In grand unification theories, conventional gravity has to be modified due to either geometrical effects of extra space-time dimensions at short length, a new boson or the 5 th force String theorists have published TONS of papers on the extra space-time dimensions In terms of the gravitational potential Yukawa potential due to the exchange of a new boson proposed in the super-symmetric extension of the Standard Model of the Grand Unification Theory, or the fifth force N. Arkani-Hamed et al., Phys Lett. B 429, 263–272 (1998); J.C. Long et al., Nature 421, 922 (2003); C.D. Hoyle, Nature 421, 899 (2003) Yasunori Fujii, Nature 234, 5-7 (1971); G.W. Gibbons and B.F. Whiting, Nature 291, 636 - 638 (1981) Do we really know gravity at short distance? Not at all! The neutral spin-1 gauge boson U is a candidate, it is light and weakly interacting, Pierre Fayet, PLB675, 267 (2009), C. Boehm, D. Hooper, J. Silk, M. Casse and J. Paul, PRL, 92, 101301 (2004).

44. Compact binary inspiral: “chirps” Possible sources of Gravitational Waves: Supernovae / GRBs: “bursts” Elliptically deformed pulsars: “periodic” Examples Orbital decay of the Hulse-Taylor binary neutron star system (Nobel prize in 1993) is the best evidence so far. Non-radial oscillations of neutron stars

45. Pure Neutron Matter Constraints

46. Symmetric Nuclear Matter Constraints Zeta-parameter controls the high-density component of the EOS:

47. Predictions

48. Two useful forums in 2013: A Special Issue on Nuclear Symmetry Energy Euro Physics Journal A (2013) Guest Editors: Bao-An Li, Isaac Vidana and Giuseppe Verde 1-month long program on Symmetry Energy at RIKEN in summer 2013 A proposal to the new GSI+MSU+RIKEN Theory Collaboration Program

49. Looking at the big picture Quantum Transport of electrons in mesoscopic systems and nuclear reactions Density Functional Theory in chemistry, material sciences, geophysics and nuclear physics BigBang

50. 18 12 3 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 may change under different conditions Isospin

51. Equation of State of a finite nucleus at zero temperature and normal density : E(Z,A) Symmetry energy Proton Fermi Sea Neutron Fermi Sea (A simplified version used in some text books)

52. A road map towards determining the nature of neutron-rich nucleonic matter and its EOS FAIR/Germany RIKEN/Japan, FRIB/USA CSR/China KoRIA/Korea Transport of neutrons,protons,pions ?

53. Promising Probes of the E sym (ρ) in Nuclear Reactions (1)Correlations of m ulti-observable are important (2) Detecting neutrons simultaneously with charged particles is critical B.A. Li, L.W. Chen and C.M. Ko, Physics Reports 464, 113 (2008)

54. arXiv:1204.0466arXiv:1204.0466 [pdf]pdf Title: Constraints on the symmetry energy and neutron skins from experiments and theory Authors: M. B. Tsang, J. R. Stone, F. Camera, P. Danielewicz, S. Gandolfi, K. Hebeler, C. J. Horowitz, Jenny Lee, W. G. Lynch, Z. Kohley, R. Lemmon, P. Moller, T. Murakami, S. Riordan, X. Roca-Maza, F. Sammarruca, A. W. Steiner, I. Vidaña, S. J. YennelloM. B. TsangJ. R. StoneF. CameraP. DanielewiczS. GandolfiK. HebelerC. J. HorowitzJenny LeeW. G. LynchZ. KohleyR. LemmonP. Moller T. MurakamiS. RiordanX. Roca-MazaF. SammarrucaA. W. SteinerI. Vidaña S. J. Yennello Latest bound, approximate & model-dependent

55. Iso Diff. (IBUU04, 2005), L.W. Chen et al., PRL94, 32701 (2005) IAS+LDM (2009), Danielewicz and J. Lee, NPA818, 36 (2009) PDR (2007) in 208 Pb Land/GSI, PRC76, 051603 (2007) Constraints extracted from experimental data using various models Iso. Diff & double n/p (ImQMD, 2009), M. B. Tsang et al., PRL92, 122701 (2009). GOP: global optical potentials (Lane potentials) C. Xu, B.A. Li and L.W. Chen, PRC 82, 054606 (2010) PDR (2010) of 68 Ni and 132 Sn, A. Carbone et al., PRC81, 041301 (2010). SHF+N-skin of Sn isotopes, L.W. Chen et al., PRC 82, 024301 (2010) Isoscaling (2007), D.Shetty et al. PRC76, 024606 (2007) DM+N-Skin (2009): M. Centelles et al., PRL102, 122502 (2009) TF+Nucl. Mass (1996), Myers and Swiatecki, NPA601, 141 (1996) E sym (ρ 0 )≈ 31 ± 4 MeV L≈ 60 ± 23 MeV Assuming all model analyses of all data are equally reliable!! Moller, Myers, Sagawa and Yoshida, PRL 108, 052501 (2012)

56. Why is the density dependence of nuclear symmetry energy so uncertain especially at supra-saturation densities? What is the underlying, common physics governing the density dependence of nuclear symmetry energy based on some general principles? What general principles if they exist at all?

57. Relationship between the symmetry energy and the mean-field potentials Lane potential Symmetry energy Isoscarlar effective mass kinetic isoscalar isovector J. Dabrowski, Physics Letters 8, 90 (1964) Using K-matrix theory Both U 0 (ρ,k) and U sym (ρ,k) are density and momentum dependent

58. Reminder of some basics and terminology (a) Symmetry energy of free Fermi gas of neutrons and protons in standard text books (b) 1) For 1-component system at saturation density, P=0, then 2) For 2-components system at arbitrary density

59. C. Xu, B.A. Li, L.W. Chen and C.M. Ko, NPA 865, 1 (2011) R. Chen et al., PRC 85, 024305 (2012). The Lane potential

60. Gogny HF SHF

61. Symmetry potential at saturation density from global nucleon optical potentials Systematics based on world data accumulated since 1969: (1)Single particle energy levels from pick-up and stripping reaction (2)Neutron and proton scattering on the same target at about the same energy (3)Proton scattering on isotopes of the same element (4)(p,n) charge exchange reactions

62. Constraining the symmetry energy near saturation density using global nucleon optical potentials C. Xu, B.A. Li and L.W. Chen, PRC 82, 054606 (2010). Bob Charity on 8/17/2011: Using Dispersive Optical Model 0.32 (N-Z)/A for Z=20,28,N=28 0.26 (N-Z)/A for 208Pb

63. S=1, T=0 Lecture notes of R. Machleidt CNS summer school, Univ. of Tokyo Aug. 18-23, 2005

64. The short and long range tensor force Lecture notes of R. Machleidt CNS summer school, Univ. of Tokyo Aug. 18-23, 2005

65. R Subedi et al. Science 320, 1475 (2008) CERN Courier Jan 27, 2009 Isospin-dependence of Short Range Correlations and Tensor Force Theory explains the pn pair dominance in terms of the tensor force: Schiavilla, Wiringa, Pieper and Carlson, Phys. Rev. Lett. 98, 132501 (2007) Two-nucleon knockout by an electron

66. Repulsive core only Tensor force + Repulsive core How does the tensor force affect the kinetic contribution to the symmetry energy? Chang Xu and Bao-An Li, arXiv:1104.2075arXiv:1104.2075

67. Consequence of At thermal/chemical and/or beta-equilibrium, in both neutron stars and nuclear systems, what is important is the total symmetry energy. Observables at equilibrium can’t tell how big the respective kinetic and potential contributions to the symmetry energy are However, in non-equilibrium dynamical processes, such as, heavy-ion reactions, probing added in afterwards by hand using the Fermi gas model Kinetic Potential Missing symmetry energy? If the kinetic part of the symmetry energy is really very small compared to the Fermi gas model prediction, and the constraints on the potential part from heavy-ion reactions are correct, where is the remaining symmetry energy ?

68. Symmetry (isovector) potential and its major uncertainties Within an interacting Fermi gas model: Structure of the nucleus, M.A. Preston and R.K. Bhaduri (1975) Isospin-dependence of NN correlations and the tensor force Experimental indication: BNL (p,p’pp) and (p,p’pn) and JLab (e,e’pp) and (e,e’pn) experiments, A.Tang et al., PRL 90, 042302 (2003); E. Piasetzky et al., PRL97, 162504 (2006); B.R. Subedi et al. Science 320,1476 (2008)……………… Theories: MANY papers, R. Schiavilla et al., PRL 98, 132501 (2007); M. Alvioli et al., PRL 100, 162503 (2008); L. Frankfurt, M. Sargsian and M. Strikman; T. Neff, H. Feldmeier; W. Dickhoff, Wiringa, …………………….. Spin-isospin dependence of 3-body forces Short-range tensor force due to rho meson exchange NN correlation functions

69. Uncertainty of tensor force at short distance Takaharu Otsuka et al., PRL 95, 232502 (2005); PRL 97, 162501 (2006) Cut-off=0.7 fm Gogny Gogny+tensor

70. Promising Probes of the E sym (ρ) in Nuclear Reactions (1)Correlations of m ulti-observable are important (2) Detecting neutrons simultaneously with charged particles is critical B.A. Li, L.W. Chen and C.M. Ko, Physics Reports 464, 113 (2008)

71. 18 12 3 Simulation as the Third Branch of Science (experiment, theory, simulation) T 1/2 ≈ 119ms

72. *1.44 10 13 G Formation of neutron-star matter in terrestrial nuclear laboratories Li Ou and Bao-An Li, Physical Review C84, 064605 (2011) Highly-magnetized high-density matter is formed in heavy-ion reactions

73. Super-strong magnetic field formation in heavy-ion collisions In sub-Coulomb barrier U+U collisions, the magnetic field B is on the order of 10 14 G J. Rafelski and B. Muller, PRL 36, 517 (1976) In off-central Au+Au collisions at RHIC, D. Kharzeev, L. McLerran and H.Warringa, NPA803:227 (2008)

74. Super-strong magnetic field formation in heavy-ion collisions New opportunities: studying properties neutron star matter in the lab., there are many predictions related to polarized n-rich matter to be tested. New physics related to local parity violation in strong interaction if QGP can be formed in heavy-ion collisions

75. Pion ratio probe of symmetry energy at supra-normal densities GC Coefficients 2

76. Symmetry energy and single nucleon potential used in the IBUU04 transport model ρ C.B. Das, S. Das Gupta, C. Gale and B.A. Li, PRC 67, 034611 (2003). B.A. Li, C.B. Das, S. Das Gupta and C. Gale, PRC 69, 034614; NPA 735, 563 (2004). soft stiff Single nucleon potential within the HF approach using a modified Gogny force: Density ρ/ρ 0 The x parameter is introduced to mimic various predictions on the symmetry energy by different microscopic nuclear many-body theories using different effective interactions. It is the coefficient of the 3-body force term Default: Gogny force Potential energy density

77. Probing the symmetry energy at supra-saturation densitiesSoft Stiff Soft E sym Stiff E sym density Symmetry energy n/p ratio at supra-normal densities Central density π - / π + probe of dense matter n/p ?

78. Appreciable magnetic effects on pion ratio at forward/backward rapidities

79. Circumstantial Evidence for a Super-soft Symmetry Energy at Supra-saturation Densities Z.G. Xiao, B.A. Li, L.W. Chen, G.C. Yong and M. Zhang, Phys. Rev. Lett. 102 (2009) 062502 A super-soft nuclear symmetry energy is favored by the FOPI data!!! W. Reisdorf et al. NPA781 (2007) 459 Data: Calculations: IQMD and IBUU04

80. Upper limits on the strength α and range λ of the Yukawa term M.I. Krivoruchenko et al., PRD 79, 125023 (2009) E.G. Adelberger et al., PRL 98, 131104 (2007) D.J. Kapner et al., PRL 98, 021101 (2007) Serge Reynaud et al., Int. J. Mod. Phys. A20, 2294 (2005) Annu. Rev. Nucl. Part. Sci. 53 (2003) 77 Prog. In Part. and Nucl. Phys., 62 (2009) 102 A motivation of the deep space gravity probe Torsion balance

82. Influences of the Yukawa term on Neutron stars It has NO effect on finite nuclei M.I. Krivoruchenko et al, PRD 79, 125023 (2009)

83. Lower limit to support neutrons stars with a super-soft symmetry energy Upper limits

84. Gravitational Waves = “ Ripples in space-time” What are Gravitational Waves? Amplitude parameterized by (tiny) dimensionless strain h: h(t) = DL/L LxLx L x [1 + h(t)] Traveling GW F + and F x : plus and cross polarization, bounded between -1 and 1 h 0 – amplitude of the gravitational wave signal,  – polarization angle of signal  – inclination angle of source with respect to line of sight,  (t)- phase of pulsar The expected signal has the form (P. Jaranowski, Phys. Rev. D58, 063001 (1998) ) : proper separation between two masses

85. Gravitational waves from elliptically deformed pulsars Equatorial ellipticity of pulsars Mass quadrupole moment Breaking stain of crust EOS B. Abbott et al., PRL 94, 181103 (05) B.J. Own, PRL 95, 211101 (05) Solving linearized Einstein’s field equation of General Relativity, the leading contribution to the GW is the mass quadrupole moment Frequency of the pulsar Distance to the observer Moment of inertia

86. Constraining the strength of gravitational waves P.G. Krastev, Bao-An Li and Aaron Worley, The Astrophysical Journal 676, 1170 (2008) Compare with the latest upper limits from LIGO+GEO observations

87. Liquid pasta Deformation from mountain on crust M. Gearheart, W.G. Newton, J. Hooker and Bao-An Li, Monthly Notices of the Royal Astronomical Society, 418, 2343 (2011). LiquidGas Nuclear constraint

88. There are many interesting questions remain to be answered EOS?

89. Can the symmetry energy become negative at high densities? Yes, it happens when the tensor force due to rho exchange in the T=0 channel dominates At high densities, the energy of pure neutron matter can be lower than symmetric matter leading to negative symmetry energy Example: proton fractions with interactions/models leading to negative symmetry energy Soft Super-Soft M. Kutschera et al., Acta Physica Polonica B37 (2006)

90. + MANY other papers starting from the same 3-body force, Reduced to different 2-body force with α=1/3, 2/3, 1, etc D. Vautherin and D.M.Brink, Phys.Rev.C5, 626 (1972) x 0 controls the mixing of different spin-isospin channels Necessary to fit the saturation properties of nuclear matter α controls the in-medium many-body effects

91. Effects of the 3-body force on the symmetry energy X 0 from -1.56 to 1.92 are used in the over 140 effective interactions in the literature

92. Constraining the Skyrme-HF and RMF 7/23 55/118

94. Camille DucoinCamille Ducoin, Jérôme Margueron, Constança Providência, arXiv:1004.5197Jérôme Margueron Constança ProvidênciaarXiv:1004.5197 Filled: Skyrme Open: RMF BHF Gogny HF With L=40~90 MeV, ρ t =0.07~0.09 fm -3 Core-crust transition density in neutron stars

95. Effects of the symmetry energy on the pasta phase in neutron star crust W.G. Newton et al., 2010 Kazuhiro OyamatsuKazuhiro Oyamatsu, Kei IidaKei Iida Phys. Rev. C75 (2007) 015801 pasta Liquid drop model + Wigner-Seitz approximation including dripped neutrons and the electrons at beta equilibrium

96. W. Reisdorf et al. for the FOPI collaboration, NPA781 (2007) 459 IQMD: Isospin-dependent Quantum Molecular Dynamics C. HartnackC. Hartnack, Rajeev K. Puri, J. Aichelin, J. Konopka,Rajeev K. PuriJ. AichelinJ. Konopka S.A. BassS.A. Bass, H. Stoecker, W. GreinerH. StoeckerW. Greiner Eur. Phys. J. A1 (1998) 151-169 Near-threshold π - /π + ratio as a probe of symmetry energy at supra-saturation densities Indication: Need a symmetry energy softer than the above to make the pion production region more neutron-rich!

97. Using the EOS for symmetric matter consistent with the terrestrial nuclear reaction data up to 5 rho_0, the softest symmetry energy that the TOV is still stable is x=0.93 giving M_max=0.11 solar mass and R=>28 km. For pure nucleonic matter Astrophysical implications

98. The core-crust transition density and the symmetry energy With L=40~90 MeV ρ t =0.7~0.9 fm -3 BHF Filled: SHF Open: RMF Camille DucoinCamille Ducoin, Jérôme Margueron, Constança Providência, arXiv:1004.5197Jérôme Margueron Constança ProvidênciaarXiv:1004.5197 Modified Gogny interaction, Jun Xu et al, PRC 81, 055805 (2010)

99. Effects of the symmetry energy on the pasta phase in neutron star crust W.G. Newton et al., 2010 Kazuhiro OyamatsuKazuhiro Oyamatsu, Kei IidaKei Iida Phys. Rev. C75 (2007) 015801 pasta Liquid drop model + Wigner-Seitz approximation including dripped neutrons and the electrons at beta equilibrium

100. Simulation as the Third Branch of Science (Experiment/observation, theory and simulation) (1) Isospin-dependent Boltzmann transport model, (2) A relativistic transport model, (3) A multi-phase transport model for Relativistic Heavy-Ion Collisions (RHIC)

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

102. 18 12 3 New opportunities for exploring the Equation of State of neutron-rich matter T 1/2 ≈ 119ms

103. (1) including only pion contribution to the tensor force (2) using a hard-core cut-off distance of 0.8 fm

104. Phys. Rev. C80, 065803 (2009)

105. Dirac-Brueckner-Hartree-Fock Calculations

106. A.Tang et al, PRL 90, 042301 (2003) R. Subedi et al. Science 320, 1475 (2008) Isospin-dependence of Short Range NN Correlations and Tensor Force Two-nucleon knockout by a p or e np pp Triggered on nucleon pairs with zero total momentum

107. At saturation density Paris potential I. Bombaci and U. Lombardo PRC 44, 1892 (1991) PRC68, 064307 (2003) Symmetry energy Dominance of the isosinglet (T=0) interaction

109. Recent progress in constraining nuclear symmetry energy near normal density IMP, Lanzhou, Dec. 11, 2012 Impacts of high-density symmetry energy on properties of neutron stars and gravitational waves Bao-An Li Texas A&M University-Commerce Impacts of high-density symmetry energy on neutron stars and gravitational waves Discussions on open questions

110. Lunch conversation with Prof. Dr. Dieter Hilscher on a sunny day in 1993 at HMI in Berlin neutrons protons Ratio of neutrons in the two reaction systems The first PRL paper connecting the symmetry energy with heavy-ion reactions

111. The multifaceted influence of the isospin dependence of strong interaction and symmetry energy in nuclear physics and astrophysics J.M. Lattimer and M. Prakash, Science Vol. 304 (2004) 536-542. A.W. Steiner, M. Prakash, J.M. Lattimer and P.J. Ellis, Phys. Rep. 411, 325 (2005). Isospin physics Isospin physicsn/p isoscaling isoscaling isotransport isotransport isodiffusion isodiffusion t/ 3 He isofractionation isofractionation K + /K 0 isocorrelation isocorrelation π-/π+π-/π+π-/π+π-/π+ in Terrestrial Labs (QCD)(Effective Field Theory)