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Probing the Equation of State of Neutron-Rich Matter with Heavy-Ion Reactions

Probing the Equation of State of Neutron-Rich Matter with Heavy-Ion Reactions. Collaborators: L.W. Chen, C.M. Ko, Texas A&M University. P. Danielewicz and W.G. Lynch, Michigan State University Andrew W. Steiner, Los Alamos National Laboratory

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Probing the Equation of State of Neutron-Rich Matter with Heavy-Ion Reactions

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  1. Probing the Equation of State of Neutron-Rich Matter with Heavy-Ion Reactions Collaborators:L.W. Chen, C.M. Ko, Texas A&M University P. Danielewicz and W.G. Lynch, Michigan State University Andrew W. Steiner, Los Alamos National Laboratory G.C. Yong and W. Zuo, Chinese Academy of Science C.B. Das, C. Gale and S. Das Gupta, McGill University • Equation of State and Symmetry Energy of Neutron-Rich Matter • Current status and major issues • Importance in astrophysics and nuclear physics • A Transport Model for Nuclear Reactions Induced by Radioactive Beams • Some details of the IBUU04 model • Momentum dependence of the isovector nucleon potential in isospin asymmetric matter • 3. Determining the Density Dependence of Nuclear Symmetry Energy • At sub-saturation densities: isospin transport in heavy-ion reactions and neutron-skin in 208Pb • At higher densities: reactions at RIA and GSI using high energy radioactive beams • 4. Summary Bao-An Li Arkansas State University

  2. Equation of State of Neutron-Rich Matter: K. Oyamatsu, I. Tanihata, Y. Sugahara, K. Sumiyoshi and H. Toki, NPA 634 (1998) 3. Isospin asymmetry (TM1) saturation lines N/Z

  3. 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

  4. Esym(ρ)from Hartree-Fock approach using different effective interactions B. Cochet, K. Bennaceur, P. Bonche, T. Duguet and J. Meyer, nucl-th/0309012 J. Stone, J.C. Miller, R. Koncewicz, P.D. Stevenson and M.R. Strayer, PRC 68, 034324 (2003). Bao-An Li, PRL 88, 192701 (2002) (where paramaterizations of Easym and Ebsym are given) New Skyrme interactions Easym HF predictions using 90 effective interactions scatter between Easym and Ebsym Amplication around normal density Ebsym

  5. Themultifaceted influence of symmetry energy in astrophysics and nuclear physicsJ.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. (2005). isodiffusion n/p π-/π+ Isospin physics isotransport isocorrelation isofractionation t/3He K+/K0 Expanding fireball and gamma-ray burst (GRB) from the superdene neutron star (magnetar) SGR 1806-20 on 12/27/2004. RAO/AUI/NSF isoscaling GRB and nucleosynthesis in the expanding fireball after an explosion of a supermassive object depends on the n/p ratio In pre-supernova explosion of massive stars is easier with smaller symmetry energy

  6. 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 Xc=1/9 from energy-momentum conservation on the proton Fermi surface Slow cooling: modified URCA: Critical points of the direct URCA process Consequence: long surface thermal emission up to a few million years APR Akmal et al. Faster cooling by 4 to 5 orders of magnitude: direct URCA PSR J0205+6449 in 3C58 was suggested as a candidate A.W. Steiner, M. Prakash, J.M. Lattimer and P.J. Ellis, Phys. Rep. (2005).

  7. Promising Probes of the Esym(ρ) in Nuclear Reactions (an incomplete list !) Most proposed probes in heavy-ion collisions are based on transport model studies

  8. Hadronic transport equations: Mean-field potential for baryons Baryons: The phase space distribution functions, mean fields and collisions integrals are all isospin dependent Mesons: An example: Simulate solutions of the coupled transport equations using test-particles and Monte Carlo: The evolution of is followed on a 6D lattice (gain) (loss)

  9. Symmetry energy and single nucleon potential used in the IBUU04 transport code for reactions with radioactive beams stiff ρ soft density HF using a modified Gogny force: B.A. Li, C.B. Das, S. Das Gupta and C. Gale, PRC 69, 034614; NPA 735, 563 (2004).

  10. Momentum and density dependence of the symmetry potential δ δ Density ρ/ρ0 momentum Lane potential extracted from n/p-nucleus scatterings and (p,n) charge exchange reactions provides a boundary condition at ρ0: for Ekin < 100 MeV P.E. Hodgson, The Nucleon Optical Model, World Scientific, 1994 G.W. Hoffmann et al., PRL, 29, 227 (1972). Consistent with the Lane potential below 100 MeV

  11. Neutron-proton effective k-mass splitting in neutron-rich matter With the modified Gogny effective interaction B.A. Li, C.B. Das, S. Das Gupta and C. Gale, PRC 69, 034614; NPA 735, 563 (2004).

  12. Nucleon-nucleon crosssections and nuclear stopping power in neutron-rich matter in neutron-rich matter is the reduced mass of the colliding pair NN in medium Effects on the nuclear stopping power and nucleon mean free-path in n-rich 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). • In-medium xsections are reduced • nn and pp xsections are splitted • due to the neutron-proton effective mass slitting in neutron-rich matter

  13. Isospin transport (diffusion) in heavy-ion collisions as a probe of Esym (ρ) at subnormal densities Particle Flux: Isospin Flow: Isospin diffusion coefficient DI depends on the symmetry potential L. Shi and P. Danielewicz, Phys. Rev. C68, 017601 (2003).

  14. Extract the Esym(ρ) from isospin transport A quantitative measure of the isospin non-equilibrium and stopping power In A+B using any isospin tracer X, F. Rami (FOPI), PRL, 84, 1120 (2000). If complete isospin mixing/ equilibrium MSU experiments: R=0.42-0.52 in 124Sn+112Sn at Ebeam/A=50 MeV mid-central collisions. With 112Sn+112Sn and 124Sn+124Sn as references. Use X=7Li/7Be or δ of the projectile residue, etc. M.B. Tsang et al. PRL 92, 062701 (2004) SBKD: momentum-independent Soft Bertsch-Kruse-Das Gupta EOS MDI: Momentum-Dependent Interaction Momentum-independent Momentum-dependent All having the same Esym (ρ)=32 (ρ/ρ0)1.1

  15. Comparing momentum-dependent IBUU04 calculations with data on isospin transport from NSCL/MSU Experiments favors: Esym()=32 (/ρ0 )1.1 for ρ<1.2ρ0 Kasy(ρ0)~-550 MeV L.W. Chen, C.M. Ko and B.A. Li, PRL 94, 32701 (2005). Strength of isospin transport Next step: 1. Reduce the error bars of the data and the calculations 2. Compare with results using other observables 3. Exam effects of in-medium cross sections Isobaric incompressibility of asymmetric nuclear matter

  16. Predictions for reactions with high energy radioactive beams at RIA and FAIR/GSI Examples: • Isospin fractionation • π- yields and π-/π+ ratio Besides many other interesting physics, it allows the determination of nuclear equation of state for neutron-rich matter at high densities where it is most uncertain and most important for several key questions in astrophysics.

  17. Formation of dense, asymmetric nuclear matter at RIA and GSI Soft Esym n/p ratio of the high density region Stiff Esym

  18. Isospin fractionation (distillation): at isospin equilibrium EOS requirement: low(high)density region is more neutron-rich with stiff (soft)symmetry energy Symmetry enengy Isospin asymmetry of free nucleons stiff soft ρ0 density

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

  20. Pion ratio probe of symmetry energy

  21. Time evolution of π-/π+ ratio in central reactions at RIA and GSI From the overlapping n-skins of the colliding nuclei soft stiff

  22. Summary • The EOS of n-rich matter, especially the Esym(ρ) is very important for many interesting questions in both astrophysics and nuclear physics • Transport models are invaluable tools for studying the isospin-dependence of in-medium nuclear effective interactions and properties of n-rich matter • A transport model anaysis of recent isospin transport experiments indicates: Esym()=32 (/ρ0 )1.1 for ρ<1.2ρ0, and Kasy(ρ0)~-550 MeV • High energy radioactive beams at RIA and GSI will allow us to study the EOS of n-rich matter up to 2ρ0. Several sensitive probes of the Esym()are proposed.

  23. Transverse flow as a probe of the nuclear EOS: px y Neutron-proton differential flow as a probe of the symmetry energy: for n and p symmetry potential is generally repulsive for neutrons and attractive for protons

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