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Probing the symmetry energy at high densities

Bao-An Li. & collaborators: De-Hua Wen and Chang Xu, Texas A&M University-Commerce Lie-Wen Chen, Shanghai Jiao-Tung University Zhigang Xiao and Ming Zhang, Tsinghua University, China Gao-Chan Yong, Institute of Modern Physics, China. Probing the symmetry energy at high densities. Outline:

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Probing the symmetry energy at high densities

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  1. Bao-An Li & collaborators: De-Hua Wen and Chang Xu, Texas A&M University-Commerce Lie-Wen Chen, Shanghai Jiao-Tung University Zhigang Xiao and Ming Zhang, Tsinghua University, China Gao-Chan Yong, Institute of Modern Physics, China Probing the symmetry energy at high densities • Outline: • Why is the symmetry energy so uncertain at supra-saturation densities? Can the symmetry energy become super-soft or even negative at high densities? • --- Some observations by a non-expert of many-body theories • Indications of a super-soft symmetry energy at supra-saturation densities from transport model analyses of the FOPI/GSI experimental data on pion production • Can neutron stars be stable with a super-soft or negative symmetry energy at supra-saturation densities? • --- Some observations and attempts by a non-expert of astrophysics

  2. Esym (ρ)predicted by microscopic many-body theories Symmetry energy (MeV) DBHF RMF BHF Effective field theory Greens function Variational Density A.E. L. Dieperink et al., Phys. Rev. C68 (2003) 064307

  3. Why is the symmetry energy so uncertain especially at high densities?Based on the Fermi gas model (Ch. 6) and properties of nuclear matter (Ch. 8) of the textbook: Structure of the nucleus by M.A. Preston and R.K. Bhaduri Kinetic Isovector Isoscalar Correlation function

  4. Correlation function Tensor correlations in the Unitary Correlation Operator Method Thomas Neff, Hans Feldmeier, Nucl. Phys. A713 (2003) 311-371 Nuclear Structure based on Correlated Realistic Nucleon-Nucleon Potentials R. Roth, T. Neff, H. Hergert, H. Feldmeier, Nucl. Phys. A745 (2004) 3-33

  5. Using the Reid93 interaction At saturation density Using Paris potential PRC68, 064307 (2003) I. Bombaci and U. Lombardo PRC 44, 1892 (1991)

  6. The most important contributions of nuclear force Lecture notes of R. Machleidt at 2005 RIKEN summer school

  7. In-medium properties of the short-range tensor force G.E. Brown and Mannque Rho, PLB 237, 3 (1990) G.E. Brown and Mannque Rho, PRL 66, 2720 (1991), Phys Rep. 396, 1 (2004)

  8. Gale-Bertsch-Das Gupta’s parameterization of the K-dependent part of the isoscalar potential Correlation function in Fermi gas Gogny central force

  9. Can the symmetry energy becomes negative at high densities? Yes, when the short-range repulsive tensor force in isosinglet n-p pairs dominates At high densities, the energy of pure neutron matter becomes lower than symmetric matter leading to negative symmetry energy This

  10. In phenomenological models where there is no explicit tensor force, the symmetry energy starts decreasing when the Lane potential becomes negative Gogny-Hartree-Fock L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. C72, 064309 (2005). 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).

  11. Some observations of a non-expert: Why is the symmetry energy so uncertain especially at high densities? • Poor knowledge on • short-range NN correlations • in-medium properties of the short-range tensor force • -------- Can the symmetry energy becomes super-soft or even negative at high densities? • There seems to be NO first principle forbidding it • It happens when the repulsive short-range tensor force due to the ρ-meson • exchange in the n-p singlet channel dominates. • Using a 20% reduction of the ρ-meson mass as required to reproduce the • half-lift of 14C, the symmetry energy becomes negative above about 4ρ0 • The Lane potential Un-Up flips sign when the Esym starts decreasing with density

  12. Momentum and density dependence of the symmetry (isovector) potential Lane potential extracted from n/p-nucleus scatterings and (p,n) charge exchange reactions provides only a constraint at ρ0: P.E. Hodgson, The Nucleon Optical Model, World Scientific, 1994 G.W. Hoffmann and W.R. Coker, PRL, 29, 227 (1972). G.R. Satchler, Isospin Dependence of Optical Model Potentials, in Isospin in Nuclear Physics, D.H. Wilkinson (ed.), (North-Holland, Amsterdam,1969)

  13. Isospin fractionation in heavy-ion reactions low(high)density region is more neutron-rich withstiff(soft)symmetry energy Bao-An Li, Phys. Rev. Lett. 88 (2002) 192701

  14. Pion ratio probe of symmetry energyat supra-normal densities GC Coefficients2

  15. Circumstantial evidence for a super-soft symmetry energy at high densities FOPI/GSI data on pion production Willy Reisdorf et al., NPA781 (2007) 459 Transport model analysis Z. Xiao et al., PRL 102, 062502 (2009) Au+Au 400 MeV/A

  16. Is the super-soft symmetry energy“unpleasant” or “unphysical”? Unpleasant ! E. Chabanat, P. Bonche, P. Haensel, J. Meyer, and R. Schaeffer, NPA627, 710 (1997); NPA635, 231 (1998). Repeated by several others in other papers Unphysical ! Quoted by several people in a number of papers Crazy!

  17. Why ?The only reason stated is that “ if the symmetry energy is too soft neutron stars will then collapse while they do exist in nature” TOV equation P(r+dr) Gravity Nuclear pressure P(r) For npe matter

  18. Do we really know gravity at the Fermi distance? ``It's remarkable that gravity, despite being the first to be discovered, is by far the most poorly understood force," says Nima Arkani-Hamed of Harvard University Roland Pease, Nature411, 986-988 (28 June 2001) Annu. Rev. Nucl. Part. Sci. 2003. 53:77–121

  19. Extra dimension at short length or a new Boson? String theorists have published TONS of papers on the extra dimension Arkani-Hamed, N., Dimopoulos, S. & Dvali, G. Phys Lett. B 429, 263–272 (1998).  J.C. Long et al., Nature421, 922-925 (2003); C.D. Hoyle, Nature421, 899–900 (2003) In terms of the gravitational potential Repulsive 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 Yasunori Fijii, Nature 234, 5-7 (1971); G.W. Gibbons and B.F. Whiting, Nature291, 636 - 638 (1981) The neutral spin-1 gauge boson U is a candidate, it can mediate the interaction among dark matter particles, e.g., Pierre Fayet, PLB675, 267 (2009), C. Boehm, D. Hooper, J. Silk, M. Casse and J. Paul, PRL, 92, 101301 (2004).

  20. Experimental constraints 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)

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

  22. Partially constrained EOS for astrophysical studies Danielewicz, Lacey and Lynch, Science 298, 1592 (2002))

  23. EOS of MDIx1+WILB

  24. Lower limit to support neutrons stars with a super-soft symmetry energy at high densities Upper limit

  25. Some thoughts and observations • The high-density behavior of the nuclear symmetry energy relies on the short-range • correlations and the in-medium properties of the short-range tensor force in the n-p • singlet channel. • The FOPI/GSI pion data indicates a super-soft symmetry energy at high densities • NS can be stable even with a super-soft symmetry energy if one considers the • possibilities of extra-dimensions, new bosons and/or a 5th force as proposed in • string theories and super-symmetric extensions of the Standard Model • It may not be that crazy to think about a super-soft and/or even negative symmetry • energy at supra-saturation densities especially if you are a string theorist!

  26. Themoment of inertia provides a sensitive probe to determine g2/2

  27. Symmetry energy and single nucleon potential used in theIBUU04 transport model The x parameter is introduced to mimic various predictions on the symmetry energy by different microscopic nuclear many-body theories using different effective interactions stiff ρ soft Default: Gogny force Density ρ/ρ0 Single nucleon potential within the HF approach using a modified Gogny force: The momentum dependence of the nucleon potential is a result of the non-locality of nuclear effective interactions and the Pauli exclusion principle 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).

  28. Near-threshold π-/π+ ratio as a probe of symmetry energy at supra-normal densities W. Reisdorf et al. for the FOPI collaboration , NPA781 (2007) 459 IQMD: Isospin-Dependent Molecular Dynamics C. Hartnack, Rajeev K. Puri, J. Aichelin, J. Konopka, S.A. Bass, H. Stoecker, W. Greiner Eur.Phys.J. A1 (1998) 151-169 Need a symmetry energy softer than the above to make the pion production region more neutron-rich! low(high)density region is more neutron-rich with stiff (soft)symmetry energy

  29. Formation of dense, asymmetric nuclear matter Symmetry energy Stiff Central density Soft density π-/ π+ probe of dense matter Soft Esym Stiff Esym n/p ratio at supra-normal densities

  30. Momentum dependence of the isoscalar potential Compared with variational many-body theory

  31. Constraining the radii of NON-ROTATING neutron stars Bao-An Li and Andrew W. Steiner, Phys. Lett. B642, 436 (2006) . ● Nuclear limits APR: K0=269 MeV. The same incompressibility for symmetric nuclear matter of K0=211 MeV for x=0, -1, and -2

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