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Isovector Equation-of-State in Heavy Ion Collisions and Neutron Stars

Isovector Equation-of-State in Heavy Ion Collisions and Neutron Stars. Collaborators: Theo Gaitanos, LMU Munich -> U. Giessen M. Colonna, M. Di Toro, V. Greco, LNS, Catania V. Baran, R. Ionescu, NIPNE Bucharest C. Fuchs, A, Faessler, U. Tübingen

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Isovector Equation-of-State in Heavy Ion Collisions and Neutron Stars

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  1. Isovector Equation-of-State in Heavy Ion Collisions and Neutron Stars Collaborators: Theo Gaitanos, LMU Munich -> U. Giessen M. Colonna, M. Di Toro, V. Greco, LNS, Catania V. Baran, R. Ionescu, NIPNE Bucharest C. Fuchs, A, Faessler, U. Tübingen T. Mikailova, JINR Dubna, Russia • Outline: • - Motivation: phase diagram of hadronic matter • - the isovector EoS und its uncertainity, Lorentz structure • - transport calculations of heavy ion collisions • - low densities: fragmentation, isospin fractionation • - high densities: flow, particle production • - constraints from neutron star observables Int. School in Nuclear Physics, “Radioactive Beams, Nuclear Dynamics and Astrophysics“, Erice, Sicily, Sept. 16-24, 2006

  2. Quark-hadron coexistence Schematic Phase Diagram of Strongly Interacting Matter SIS Liquid-gas coexistence

  3. Quark-hadron coexistence Schematic Phase Diagram of Strongly Interacting Matter SIS Liquid-gas coexistence 1 neutron stars 0 Z/N

  4. Neutron stars Heavy Ion Collisions (T>0, non-equilibrium! Exotic Nuclei Stable nuclei

  5. Symmetry Energy Expansion around r0 Asy-superstiff Asy-stiff Esym(rB) (MeV) Pressure & compressibility Asy-soft 1 0 2 3 rB/r0 V. Baran, et al.,Phys.Rep.410(2005)335-466

  6. Symmetry energy iso-stiff stiff soft iso-soft The nuclear EoS-Uncertainties the nuclear EoS Esymm[MeV] C. Fuchs, H.H. Wolter, WCI white book, EPJA in press, nucl-th/0511070

  7. Uncertainities in optical potentials Isoscalar Potential Isovector (Lane) Potential

  8. microscopic phenomenological s d w r deJong, Lenske, PRC 58 (98) 890 Density Functional Approach NN Scatt Nuclei

  9. swrd-couplings DD-F NLrd NLr RMF theory with scalar-isovector (d) field

  10. NL(r,rd) DDH(r,rd) Finite nuclei: Effects of dMeson Binding Energies Neutron-Proton Radii  Effects of d meson small in nuclei, except for extreme isospin.  Investigate heavy ion collisions

  11. Relativistic Transport eq. (RBUU) mean field drift “Lorentz Force”→ Vector Fields pure relativistic term Transport Description of Heavy Ion Collisions: BUU

  12. Demonstrative Examples: Observables for Isovector EoS: • Deep Inelastic Collisions • - dissipation in very asymmetric systems • Low Density in HIC: Fragmentation processes • - isospin content of Fragments: Isospin Destillation • Isospin Migration • - Isospin Transport through Neck • - Isoscaling • High Density in HIC: relativistic collisions • - difference of neutron and proton flows • - isospin transparency • - kaon production • Neutron stars: Consistency with NS observables • (see talks by F. Weber, D. Blaschke and T. Klaehn)

  13. Demonstrative Examples: Observables for Isovector EoS: • Deep Inelastic Collisions • - dissipation in very asymmetric systems • Low Density in HIC: Fragmentation processes • - isospin content of Fragments: Isospin Destillation • Isospin Migration • - Isospin Transport through Neck • - Isoscaling • High Density in HIC: relativistic collisions • - difference of neutron and proton flows • - isospin transparency • - kaon production • Neutron stars: Consistency with NS observables • (see talks by F. Weber, D. Blaschke and T. Klaehn)

  14. loss of energy, friction exchange of mass impact parameter b Dissipation Deep Inelastic Collisions with Transport Theory Deflection function Wilczynski - Plot

  15. Dissipative Reaction sensitive to Isovector EoS for very asymmetric systems: 132Sn + 64Ni, 10 A MeV isostiff isosoft Density distribution after 500 fm/c Distribution of deformation of residual nuclei More dissipation with iso-stiff EoS: ->Less repulsive at sub-normal densities

  16. Demonstrative Examples: Observables for Isovector EoS: • Deep Inelastic Collisions • - dissipation in very asymmetric systems • Low Density in HIC: Fragmentation processes • - isospin content of Fragments: Isospin Destillation • Isospin Migration • - Isospin Transport through Neck • - Isoscaling • High Density in HIC: relativistic collisions • - difference of neutron and proton flows • - isospin transparency • - kaon production • Neutron stars: Consistency with NS observables • (see talks by F. Weber, D. Blaschke and T. Klaehn)

  17. Chemical potential: isosoft, isostiff neutrons asy-soft protons bulk neck Isospin migration Isospin fractionation asy-stiff asy-stiff asy-soft V.Baran et al., NPA703(2002)603 NPA730(2004)329 Isospin dynamics at Fermi energies Au+Au, 50 AMeV Central collision, b=2 fm Peripheral collision, b=6 fm

  18. asysoft eos superasystiff eos experimental data (B. Tsang et al. PRL 92 (2004) ) ASYSOFT EOS – FASTER EQUILIBRATION • Asysoft: more efficient for concentration gradients + larger fast neutron emission • Asystiff: more efficient for density gradients + larger n-enrichement of the neck IMFs • Momentum Dependence: faster dynamics and smaller isodiffusion Baran, Colonna, Di Toro, Zielinska-Pfabe, Wolter, nucl-th/05 Isospin Transport through Neck: Rami imbalance ratio:

  19. Effect of momentum dependence onIsospin transport Chen, Ko, B.A.Li, PRL94 (2005)

  20. Demonstrative Examples: Observables for Isovector EoS: • Deep Inelastic Collisions • - dissipation in very asymmetric systems • Low Density in HIC: Fragmentation processes • - isospin content of Fragments: Isospin Destillation • Isospin Migration • - Isospin Transport through Neck • - Isoscaling • High Density in HIC: relativistic collisions • - difference of neutron and proton flows • - isospin transparency • - kaon production • Neutron stars: Consistency with NS observables • (see talks by F. Weber, D. Blaschke and T. Klaehn)

  21. Observables • Some results of Transport Calc. • Symmetric Nuclear Matter • Asymmetric NM V1: Sideward flow V2: Elliptic flow T.Gaitanos, Chr. Fuchs, Nucl. Phys. 744 (2004)

  22. V1: Sideward flow V2: Elliptic flow Results from Flow Analysis (P. Danielewicz, R.Lacey, W. Lynch, Science)

  23. Difference at high pt first stage r+d r n p r+d r Dynamical isovector effects: differential directed and elliptic flow 132Sn + 132Sn @ 1.5 AGeV b=6fm differential directed flow differential elliptic flow r+d r Dynamical boosting of the vector contribution T. Gaitanos, M. Di Toro, et al., PLB562(2003)

  24. Kaon Production: A good way to determine the symmetric EOS (C. Fuchs et al., PRL 86(01)1974) Main production mechanism: NNBYK pNYK • Also useful for Isovector EoS? • charge dependent thresholds • in-medium effective masses • Mean field effects

  25. Density & asymmetry of the K-source aAu≈0.2 Au+Au@1AGeV (HIC) N/ZAu≈1.5 Inf. NM NL→ DDF→NLρ→NLρδ : more neutron escape and more n→p transformation (less asymmetry in the source) Larger isospin effects in NM: - no neutron escape - Δ’s in chemical equilibrium→less n-p “transformation” Strangeness ratio :Infinite Nuclear Matter vs. HIC G. Ferini, et al., NPA762(2005) 147 and nucl-th/0607005

  26. Kaon production as a probe for the isovector EoS T. Gaitanos, G. Ferini, M. Di Toro, M. Colonna, H.H. Wolter, nucl-th/06

  27. Demonstrative Examples: Observables for Isovector EoS: • Deep Inelastic Collisions • - dissipation in very asymmetric systems • Low Density in HIC: Fragmentation processes • - isospin content of Fragments: Isospin Destillation • Isospin Migration • - Isospin Transport through Neck • - Isoscaling • High Density in HIC: relativistic collisions • - difference of neutron and proton flows • - isospin transparency • - kaon production • Neutron stars: Consistency with NS observables • (see talks by F. Weber, D. Blaschke and T. Klaehn)

  28. Heaviest observed neutron star Flow constraint (Danielewicz, et al.) Maximum masses for boundaries of flow constraint Typical neutron stars Consistency of Heavy Ion Resuts with Neutron Star Data T.Klähn, D. Blaschke, S.Typel, E.v.Dalen, A.Faessler, C.Fuchs, T.Gaitanos, H. Grigorian, A.Ho, E.Kolomeitsev, M.Miller, G.Röpke, J.Trümper, D.Voskresensky, F.Weber, H.H.Wolter, Phys.Rev.C, to appear, nucl-th/0602038 Maximum masses and direct URCA cooling limit (see D.Blaschke,T. Klaehn) Lower boundary (LB) leads to too small NS masses! Flow constraint can be sharpened.

  29. Summary and Conclusions: • While the Eos of symmetric NM is fairly well determined, the isovector EoS is still rather uncertain (but important for exotic nuclei, neutron stars and supernovae) • Can be investigated in HIC both at low densities (Fermi energy regime, fragmentation) and high densities (relativistic collisions, flow, particle production) • Data to compare with are still relatively scarce; it appears that the Iso-EoS is rather stiff. • Effects scale with the asymmetry – thus reactions with RB are very important • Additional information can be obtained by cross comparison with neutron star observations

  30. stiff Esym Soft Esym Au+Au central: Pi and K yield ratios vs. beam energy Kaons: ~15% difference between DDF and NLρδ 132Sn+124Sn No sensitive to the K-potential (iso-dep.?) Pions: less sensitivity ~10%, but larger yields

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