1. Determining the Nuclear Symmetry Energy of Neutron-Rich Matter and its Impacts on Astrophys ics Outline: Theoretical predictions about density dependence of nuclear symmetry energy How to constrain the symmetry energy with heavy-ion collisions Astrophysical impacts of the partially constrained nuclear symmetry energy Two examples: (1) Mass-radius correlation of rapidly-rotating neutron stars (2) The changing rate of the gravitational constant G due to the expansion of the Universe Summary Collaborators: Wei-Zhou Jiang, Plamen Krastev, Aaron Worley, Texas A&M-Commerce Lie-Wen Chen, Shanghai Jiao-Tung University Che-Ming Ko, Texas A&M University, College Station Andrew Steiner, Michigan State University Gao-Chan Yong, Chinese Academy of Science, Lanzhou Bao-An Li

2. What is the Equation of State in the extended isospin space at zero temperature ? 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 ρ n : neutron density ρ p : proton density Nucleon density ρ=ρ n +ρ p δ Isospin asymmetry ???

3. The E sym (ρ) from model predictions using popular interactions (1) Phenomenological models Density 23 RMF models

4. (2) Microscopic model predictions Symmetry energy (MeV) Density Effective field theory of N. Kaiser and W. Weise Dirac Brueckner Hartree-Fock Relativistic Mean Field Brueckner HF Greens function Variational many-body theory A.E. L. Dieperink, Y. Dewulf, D. Van Neck, M. Waroquier and V. Rodin, Phys. Rev. C68 (2003) 064307

5. Interaction dependence within the Bruckner Hartree-Fock Approach Density With 3-body forces Z.H. Li et al., PRC74, 047304 (2006)

6. 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)

7. A road map towards determining the nature of neutron-rich nucleonic matter FAIR/GSI, RIKEN, RIB CSR Transport neutrons,protons,pions ?

8. The most important input to transport models for reactions involving neutron-rich nuclei The most challenging unknown is the momentum-dependence of the symmetry potential ρρ

9. Momentum and density dependence of the symmetry potential Lane potential extracted from n/p-nucleus scatterings and (p,n) charge exchange reactions provides only a constraint at ρ 0 : P.E. Hodgson, The Nucleon Optical Model, World Scientific, 1994 L. Ray, G.W. Hoffmann and W.R. Coker, Phys. Rep. 212, (1992) 223. G.R. Satchler, Isospin Dependence of Optical Model Potentials, in Isospin in Nuclear Physics, D.H. Wilkinson (ed.), (North-Holland, Amsterdam,1969) momentum Density ρ/ρ 0 δ δ ? ?

10. 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 momentum dependence of the nucleon potential is a result of the non-locality of nuclear effective interactions and the Pauli exclusion principle The x parameter is introduced to mimic various predictions by different microscopic Nuclear many-body theories using different Effective interactions

11. 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 Significant progress has been made recently in constraining the symmetry energy at sub-saturation densities while NOTHING is known at higher densities

12. Neutron-skin in 208 Pb and dE sym /dρ Pressure forces neutrons out against the surface tension from the symmetric core near ρ 0 B.A. Brown PRL85, 5296 (2000)S. Typel and B.A. Brown,PRC 64, 027302 (2001) R n -R p (fm) for 208 Pb B.A. Brown, S. Typel, C. Horowitz, J. Piekarewicz, R.J. Furnstahl, J.R. Stone, A. Dieperink et al. C.J. Horowitz and J. Piekarewicz, PRL 86, 5647 (2001) Neutron-skin 208 Pb

13. Extract the E sym (ρ) at subnormal densities from isospin diffusion/transport Extract the E sym (ρ) at subnormal densities from isospin diffusion/transport for complete isospin mixing X is any isospin-sensitive observable, The degree of isospin transport/diffusion depends on both the symmetry potential and the in-medium neutron-proton scattering cross section. A quantitative measure of isospin transport: For near-equilibrium systems, the mean-field contributes: Isospin transport/diffusion: During heavy-ion reactions, the collisional contribution to D I is expected to be proportional to σ np F. Rami et al. (FOPI/GSI), PRL, 84 (2000) 1120. F. Rami et al. (FOPI/GSI), PRL, 84 (2000) 1120. L. Shi and P. Danielewicz, PRC68, 064604 (2003)

14. M.B. Tsang et al., Phys. Rev. Lett. 92, 062701 (2004); T.X. Liu et al., PRC 76, 034603 (2007) Isospin transport/diffusion experiments at the NSCL/MSU    X 7 = 7 Li/ 7 Be

15. σ σ L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. Lett 94, 32701 (2005); Bao-An Li and Lie-Wen Chen, Phys. Rev. C72, 064611 (2005). Using in-medium NN xsections (reduced wrt the free one) Using free-space NN xsections MSU data range Transport model analysis of the NSCL/MSU data    ρ ρ ρ

16. PRL 99, 162503 (2007)

17. Constraining the dE sym /dρ with data from both isospin diffusion and n-skin in 208 Pb Andrew Steiner and Bao-An Li, PRC 72, 041601 (2005). ρ ρρ ρ ρ Isospin fractionation Neutron-rich cloud Neutron-skin data: V.E. Starodubsky and N.M. Hintz, PRC 49, 2118 (1994); B.C. Clark, L.J. Kerr and S. Hama, PRC 67, 054605 (2003)

18. Comparing with calculations using 23 most popular RMF models widely used in nuclear structure studies and astrophysics L.W. Chen, C.M. Ko and B.A. Li, PRC 76, 054316 (2007)

19. Comparing with Hartree-Fock calculations using 21 most popular Skyrme interactions widely used in nuclear structure studies and astrophysics Current experimental boundaries L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. C72, 064309 (2005). X=0 X=-1 density ρ E sym in the high density region is still not constrained ! Predictions using most of the 21 widely used Skyrme interactions are ruled out ! Only 5 survived !

20. Astrophysical impacts of the partially constrained symmetry energy Nuclear constraints on the moment of inertia of neutron stars Aaron Worley, Plamen Krastev and Bao-An Li, The Astrophysical Journal (2008) in press. Constraining properties of rapidly rotating neutron stars using data from heavy-ion collisions Plamen Krastev, Bao-An Li and Aaron Worley, The Astrophysical Journal, 676, 1170 (2008) Constraining time variation of the gravitational constant G with terrestrial nuclear laboratory data Plamen Krastev and Bao-An Li, Phys. Rev. C76, 055804 (2007). Constraining the radii of neutron stars with terrestrial nuclear laboratory data Bao-An Li and Andrew Steiner, Phys. Lett. B642, 436 (2006). Setting an upper limit on the gravitational waves from isolated, rotating elliptical neutron stars with terrestrial nuclear laboratory data Plamen Krastev, Bao-An Li and Aaron Worley, (2008) in preparation.

21. 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 PSR J0205+6449 in 3C58 was suggested as a candidate Bao-An Li, Phys. Rev. Lett. 88, 192701 (2002).

22. J.M. Lattime and M. Prakash, Phys. Rep. 333, 121 (2000).

23. Constraining the radii of non-rotating 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 ●.

24. J.M. Lattimer and M. Prakash, Science Vol. 304 (2004) 536-542. Mass-radius correlation of non-rotating neutron stars and their EOS EOSs Different EOS predicted by various theories Essentially, none of them was ever tested against reaction data

25. Astronomers discover the fastest-spinning neutron-star Science 311, 1901 (2006). The latest report on the fastest spinning neutron star is XTE J1739-285 spinning at 1122 Hz, P. Kaaret et al., The Astrophysical Journal, V657, Issue 2, L97 (2007)

26. Rapidly rotating neutron stars Plamen Krastev, Bao-An Li and Aaron Worley, The Astrophysical Journal, 676, 1170 (2008) Solving the Einstein equation in general relativity for stationary axi-symmetric spacetime using the RNS code written by Nikolaos Stergioulas and John L. Friedman, Astrophysics J. 444, 306 (1995)

27. Testing the constancy of the “constant” G P. Dirac, Nature 139, 323 (1937) The latest review: J. P. Uzan, Rev. Mod. Phys. 75: 403, 2003 The CODATA is the Committee on Data for Science and Technology, http://www.codata.org/ Suggested that the gravitational force might be weakening with the continuous expansion of the Universe Possibly many detectable astronomical consequences were suggested by Chandrasekhar, Nature 139, 757 (1937); Kothar, Nature 142, 354 (1938) Contrary to most of other physical constants, as the precision of measurements increased, the disparity between measurements of G also increased. This promoted the CODATA in 1998 to raise the uncertainty of G by about a factor of 12 from 0.013% to 0.15%

28. Various Upper Bounds on Terrestrial nuclear lab experiments + observations of old neutron stars: Plamen Krastev and Bao-An Li, PRC 76, 055804 (2007).

29. Different EOSs Direct URCA allowed Only Modified URCA allowed 90% 68% confidence contours of observations PSR J0457-4715

30. A change in G induces a variation in the internal composition of a neutron star, causing dissipation and internal heating. At the stationary temperature: heating (relying on the changing rate of G)=cooling (relying on the symmetry energy) P. Jofre, A. Reisenegger, and R. Fernadez, Phys. Rev. Lett. 97, 131102 (2006) Gravitochemical Heating Method – an outline To obtain from the Gravitochemical heating one needs to know: (1)The surface temperature of a neutron star (2)That the star is certainly older than the time-scale necessary to reach a quasi-stationary state (3)The density dependence of the nuclear symmetry energy PSR J0437- 4715 – the closest millisecond pulsar is a good candidate Surface temperature: By ultraviolet observations O. Kargaltsev et al., AJ 602, 327-335 (2004) Mass: W. Van Straten et al., Nature 412, 158 (2001) Depending on the E sym (ρ)

31. Stationary photon luminosity and surface temperature Diract + Modified URCA Modified URCA only Including hyperon-QGP phase transition Hyperon star

32. Surface temperature vs radius for PSRJ0437-4715

33. Summary and outlook Significant progress has been made in determining the density dependence of symmetry energy at sub-saturation densities using heavy-ion reactions The partially constrained density dependence of symmetry energy has already allowed us to put some constraints on several neutron stras properties and the changing rate of G More challenges: (1) Constraining the symmetry energy at supra-normal densities with high energy radioactive beams (2) probing the momentum and density dependence of the isovector interaction

34. All 23 most popular RMF models give the WRONG momentum dependence of the Lane potential

35. Neutron-proton differential transverse flow: Bao-An Li, PRL 85, 4221 (2000).

36. Squeeze-out of neutrons perpendicular to the reaction plane Neutron-proton differential flow in the reaction plane Ratio of charged pions Azimuthal angle X=-1 X=0

37. Isospin-dependence of nucleon-nucleon cross sections in symmetric matter G.Q. Li and R. Machleidt, Phys. Rev. C48, 11702 and C49, 566 (1994). With other models: 1. Q. Li et al., PRC 62, 014606 (2000) 2. G. Giansiracusa et al., PRC 53, R1478 (1996) 3. H.-J. Schulze et al., PRC 55, 3006 (1997) 4. M. Kohno et al., PRC 57, 3495 (1998) NN cross section in free-space Another input to transport models: nucleon-nucleon cross sections Experimental data

38. Isospin-dependence of nucleon-nucleon cross sections in neutron-rich matter in neutron-rich matter in neutron-rich matter at zero temperature is the reduced effective mass of the colliding nucleon pair NN Applications in symmetric nuclear matter: J.W. Negele and K. Yazaki, PRL 47, 71 (1981) V.R. Pandharipande and S.C. Pieper, PRC 45, 791 (1992) M. Kohno et al., PRC 57, 3495 (1998) D. Persram and C. Gale, PRC65, 064611 (2002). Application in neutron-rich matter: nn and pp xsections are splitted due to the neutron-proton effective mass slitting The effective mass scaling model: according to Dirac-Brueckner-Hatree-Fock calculations F. Sammarruca and P. Krastev, nucl-th/0506081; Phys. Rev. C73, 014001 (2005). Bao-An Li and Lie-Wen Chen, nucl-th/0508024, Phys. Rev. C72, 064611 (2005).

39. Near-threshold pion production with radioactive beams at RIA and GSI However, pion yields are also sensitive to the symmetric part of the EOS yields are more sensitive to the symmetry energy E sym (ρ) since they are mostly produced in the neutron-rich region ρ density stiffsoft

40. Isospin-dependence of nucleon-nucleon cross sections in neutron-rich matter in neutron-rich matter in neutron-rich matter at zero temperature is the reduced effective mass of the colliding nucleon pair NN Applications in symmetric nuclear matter: J.W. Negele and K. Yazaki, PRL 47, 71 (1981) V.R. Pandharipande and S.C. Pieper, PRC 45, 791 (1992) M. Kohno et al., PRC 57, 3495 (1998) D. Persram and C. Gale, PRC65, 064611 (2002). Application in neutron-rich matter: nn and pp xsections are splitted due to the neutron-proton effective mass slitting The effective mass scaling model: according to Dirac-Brueckner-Hatree-Fock calculations F. Sammarruca and P. Krastev, nucl-th/0506081 Phys. Rev. C (2005). Bao-An Li and Lie-Wen Chen, nucl-th/0508024, Phys. Rev. C (2005) in press.

41. NN cross sections in nuclear medium G.Q. Li and R. Machleidt, Phys. Rev. C48, 11702 and C49, 566 (1994). NN cross section in free-space An input to transport models: nucleon-nucleon scattering cross sections Experimental data

42. Formation of dense, asymmetric matter with high energy radioactive beams at CSR/China, RIKEN/Japan, FAIR/Germany, RIA /USA, etc Soft E sym Stiff E sym B.A. Li, G.C. Yong and W. Zuo, PRC 71, 014608 (2005) Soft E sym Stiff E sym density Symmetry energy n/p ratio of matter with density ρ>ρ 0 Central density

43. The n/p ratio of squeezed-out nucleons perpendicular to the reaction plane as a probe of the high density symmetry energy, Yong, Li and Chen, Phys. Lett. B650, 344 (2007). Azimuthal angle n/p Pro.Tar. Squeeze-out of participants n p ø around 90 0 ?

44. Pion ratio probe of symmetry energy GC Coefficients

45. Time evolution of π - /π + ratio in central reactions soft stiff

46. Challenges in Measuring the Radii of Neutron Stars Determine luminosity, temperature and deduce surface area. Assume it is a black body L=4  R 2  T 4, then the radius R can be inferred. –T from X-ray spectrum, such as those from Chandra and X-MM Newton satellites –Need distance to star in parallax and measured flux to get L. –Deduce R from surface area (~30% corrections from curvature of space-time). The radiation radius R ∞ for an observer at infinity is related to the matter radius: z is the gravitational red-shift that can be obtained from the obsorption lines Complications –Spectrum peaks in UV and this is heavily absorbed by interstellar H. –Not a black body: often black body fit to X-ray does not fit visible spectra. –Model neutron star atmospheres (composition uncertain) to correct black body. Current status: available estimates give a wide range “Although accurate masses of several neutron stars are available, a precise measurement of the radius does not exist yet”…… Lattimer and Prakash, Science Vol. 304 (2004) 536 Radii of neutron stars: 10 – 20 Km ???

47. Incompressibility of npe-matter in neutron stars at beta equilibrium: Nuclear contribution K µ nucl Electron contribution K µ β X=0 x-20 1