1. Department of Physics, South China Univ. of Tech. collaborators Bao-An Li 1, Lie-Wen Chen 2 1 Department of Physics and astronomy, Texas A&M University-Commerce 2 Institute of Theoretical Physics, Shanghai Jiao Tong University Super-soft symmetry energy encountering non-Newtonian gravity in neutron stars Please read PRL 103, 211102 (2009) for details De-Hua Wen ( )

2. Outline: I.Symmetry energy and equation of state of nuclear matter constrained by the terrestrial nuclear data ; II. Super-soft symmetry energy encountering non- Newtonian gravity in neutron stars.

3. symmetry energy Energy per nucleon in symmetric matter Energy per nucleon in asymmetric matter δ Isospin asymmetry B. A. Li et al., Phys. Rep. 464, 113 (2008) Symmetry energy I. Symmetry energy and equation of state of nuclear matter constrained by the terrestrial nuclear data

4. Constrain by the flow data of relativistic heavy-ion reactions P. Danielewicz, R. Lacey and W.G. Lynch, Science 298 (2002) 1592 1 2 3 4 Equation of state of the symmetric matter

5. 1. R. B. Wiringa et al., Phys. Rev. C 38, 1010 (1988). 2. M. Kutschera, Phys. Lett. B 340, 1 (1994). 3. B. A. Brown, Phys. Rev. Lett. 85, 5296 (2000). 4. S. Kubis et al, Nucl. Phys. A720, 189 (2003). 5. J. R. Stone et al., Phys. Rev. C 68, 034324 (2003). 6. A. Szmaglinski et al., Acta Phys. Pol. B 37, 277(2006). 7. B. A. Li et al., Phys. Rep. 464, 113 (2008). 8. Z. G. Xiao et al., Phys. Rev. Lett. 102, 062502 (2009). Many models predict that the symmetry energy first increases and then decreases above certain supra-saturation densities. The symmetry energy may even become negative at high densities. According to Xiao et al. (Phys. Rev. Lett. 102, 062502 (2009)), constrained by the recent terrestrial nuclear laboratory data, the nuclear matter could be described by a super softer EOS MDIx1.

7. II. Super-soft symmetry energy encountering non-Newtonian gravity in neutron stars

8. Non-Newtonian Gravity and weakly interacting light boson 1.E. G. Adelberger et al., Annu. Rev. Nucl. Part. Sci. 53, 77(2003). 2.M.I. Krivoruchenko, et al., hep-ph/0902.1825v1 and references there in. The inverse square-law (ISL) of gravity is expected to be violated, especially at less length scales. The deviation from the ISL can be characterized effectively by adding a Yukawa term to the normal gravitational potential In the scalar/vector boson (U-boson ) exchange picture, and Within the mean-field approximation, the extra energy density and the pressure due to the Yukawa term is

9. Hep-ph\0810.4653v3 PRL-2005,94,e240401 Hep-ph\0902.1825 Experiment constraints on the coupling strength with nucleons g 2 /(4 ) and the mass μ (equivalently and ) of hypothetical weakly interacting light bosons.

10. EOS of MDIx1+WILB D.H.Wen, B.A.Li and L.W. Chen, Phys. Rev. Lett., 103(2009)211102

11. M-R relation of neutron star with MDIx1+WILB D.H.Wen, B.A.Li and L.W. Chen, Phys. Rev. Lett., 103(2009)211102

12. Constraints on the coupling strength by the stability and observed global properties of neutron stars

13. Conclusion 1.It is shown that the super-soft nuclear symmetry energy preferred by the FOPI/GSI experimental data can support neutron stars stably if the non-Newtonian gravity is considered; 2.Observations of pulsars constrain the g 2 / 2 in a rough range of 50~150 GeV -2.

14. Thanks

15. Appendix

16. The EOS of nuclear matters with a super-soft symmetry energy (e.g., the original gogny-Hartree-Fock) predicts maximum neutron star masses significantly below 1.4 M sun. The MDIx1 EOS only can support a maximum stellar mass about 0.1M sun, far smaller than the observ- ational pulsar masses. MDIx1: the symmetric part is described by MDI (Momentum-dependent-interaction) and the symmetry energy is described by the orignal Gogny-hartree-Fock model.

17. According to Fujii, the Yukawa term is simply part of the matter system in general relativity. Therefore, only the EOS is modified and the structure equation (TOV equations) remains the same. Fujii, Y., In Large Scale Structures of the Universe, Eds. J. Audouze et al. (1988), International Astronomical Union.

18. The energy density distribution of neutron stars described by the MDIx1 (MDIx0) E sym (ρ) with (without) the Yukawa contribution.

19. D.H.Wen, B.A.Li and L.W. Chen, Phys. Rev. Lett., 103(2009)211102

20. The effect of U-boson on nuclear matter EOS depends on the ratio between the coupling strength and the boson mass squared g 2 / 2, and thus influence the structure of neutron stars. While the coupling between the U-boson ( <1MeV) and the baryons is very weak, U-bosons do not modify observational result of nuclear structure and heavy-ion collisions. M.I. Krivoruchenko, et al., hep-ph/0902.1825v1

21. The value of the isospin asymmetry δ at β equilibrium is determined by the chemical equilibrium and charge neutrality conditions, i.e., δ = 1 2xp with