1. Bao-An Li Texas A&M University-Commerce Collaborators: F. Fattoyev, J. Hooker, W. Newton and Jun Xu, TAMU-Commerce Andrew Steiner, INT, University of Washington Che Ming Ko, Texas A&M University Lie-Wen Chen, Xiao-Hua Li and Bao-Jun Chai, Shanghai Jiao Tong University Chang Xu, Nanjing University Xiao Han and Gao-Feng Wei, Xi’an Jiao Tong University Symmetry Energy and Neutron-Proton Effective Mass Splitting in Neutron-Rich Nucleonic Matter

2. Outline: 1.Why am I here? Connection with the PREX-CREX experiments 2. Why is the symmetry energy is still so uncertain even at saturation density? a) Decomposition of the symmetry energy E sym (ρ 0 ) and its slope L according to the Hugenholtz-Van Hove (HVH) theorem b) An attempt to find out the most uncertain components of L from global neutron-nucleus optical potentials 3. What can we say about the neutron-proton effective mass splitting if both the E sym (ρ 0 ) and L are well determined by PREX-CREX experiments?

3. Constraints from both isospin diffusion and n-skin in 208 Pb ρ ρρ ρ ρ Neutron-skin from nuclear scattering: V.E. Starodubsky and N.M. Hintz, PRC 49, 2118 (1994); B.C. Clark, L.J. Kerr and S. Hama, PRC 67, 054605 (2003) Isospin diffusion data: M.B. Tsang et al., PRL. 92, 062701 (2004); T.X. Liu et al., PRC 76, 034603 (2007) Hartree-Fock calculations A. Steiner and B.A. Li, PRC72, 041601 (05) PREX? J.R. Stone implication Transport model calculations B.A. Li and L.W. Chen, PRC72, 064611 (05) 112 Sn+ 124 Sn

4. Nuclear constraining the radii of neutron stars APR: K 0 =269 MeV. The same incompressibility for symmetric nuclear matter of K 0 =211 MeV for x=0, -1, and -2 Bao-An Li and Andrew W. Steiner, Phys. Lett. B642, 436 (2006) Nuclear limits ●.

5. Astronomers discover the fastest-spinning neutron-star Science 311, 1901 (2006).

6. Chen, Ko and Li, PRL (2005) Agrawal et al. PRL (2012) Time Line W.G. Newton, talk at NN2012 Upper limit Lower limit

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

8. Why is the E sym (ρ) is 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 E sym (ρ 0 ) and L? If possible, how to constrain separately each component of E sym (ρ 0 ) and L?

9. Decomposition of the Esym and L according to the Hugenholtz-Van Hove (HVH) theorem 1) For a 1-component system at saturation density, P=0, then 2) For a 2-components system at arbitrary density

10. C. Xu, B.A. Li, L.W. Chen and C.M. Ko, NPA 865, 1 (2011) The Lane potential Higher order in isospin asymmetry

11. Relationship between the symmetry energy and the mean-field potentials Lane potential Symmetry energy Isoscarlar effective mass kinetic isoscalar isovector Using K-matrix theory, the conclusion is independent of the interaction Both U 0 (ρ,k) and U sym (ρ,k) are density and momentum dependent

12. Gogny HF SHF

13. U sym,1 (ρ,p) in several models R. Chen et al., PRC 85, 024305 (2012).

14. U sym,1 (ρ,p) in several models Gogny

15. U sym,2 (ρ,p) in several models Gogny

16. U sym,2 (ρ,p) in several models

17. Providing a boundary condition on U sym,1 (ρ,p) and U sym,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 Xiao-Hua Li et al., PLB (2103) in press, arXiv:1301.3256arXiv:1301.3256

18. Providing a boundary condition on U sym,1 (ρ,p) and U sym,2 (ρ,p) at saturation density from global neutron-nucleus scattering optical potentials using the latest data base for n+A elastic angular distributions Xiao-Hua Li et al., PLB (2103) in press, arXiv:1301.3256arXiv:1301.3256

19. Constraints on L n from n+A elastic scatterings

20. Applying the constraints from neutron-nucleus scattering

21. Time Line Prediction for CREX CREX 2016±2

22. At the mean-field level:

23. Constraining the n-p effective mass splitting

24. Symmetry energy and single nucleon potential MDI 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

25. U sym,1 (ρ,p) and U sym,2 (ρ,p) in the MDI potential used in IBUU04 transport model

26. 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 ???

27. 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)

28. 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

29. 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

30. 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

31. 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?

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

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

34. 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

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

36. 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))

37. 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) ?? ??????

38. 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

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

40. 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)

41. 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)

42. 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 ?

43. 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

44. 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)

45. 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 Mechanism for enhanced n/p ratio of pre-equilibrium nucleons