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Isovector Equation-of-State

Isovector Equation-of-State in Heavy Ion Collisions (and Neutron Stars). Hermann Wolter Exzellenz(!) – Universität München. Collaborators: Theo Gaitanos, LMU Munich -> U. Giessen M. Di Toro, et al., LNS, Catania C. Fuchs, U. Tübingen S. Typel, GSI

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Isovector Equation-of-State

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  1. Isovector Equation-of-State in Heavy Ion Collisions (and Neutron Stars) Hermann Wolter Exzellenz(!) – Universität München Collaborators: Theo Gaitanos, LMU Munich -> U. Giessen M. Di Toro, et al., LNS, Catania C. Fuchs, U. Tübingen S. Typel, GSI D. Blaschke, et al., Univ. Breslau • Outline: • - Motivation: phase diagram of hadronic matter • - the isovector EoS und its uncertainity, Lorentz structure • - transport calculations of heavy ion collisions • - low vs. high densities: fragmentation vs. flow, particle production • - constraints from neutron star observables • - deconfinement at large assymmetry? Virtual Institute „Dense Hadronic Matter and QCD Phase Transitions“, Workshop III, Rathen, Oct.15-17, 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 Exotic nuclei neutron stars 0 Z/N

  4. 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

  5. The Elusive Symmetry Energy → Asystiff Neutron Stars -formation -mass/radius -cooling -”hybrid structure” ? Esym(r) (MeV) ? ? Asysoft 1 r/r0 2 3 Liquid-Gas P.T. Neutron star crust, merging Nuclear structure Giant Dipole Neutron skin

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

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

  8. Isospin asymmetric (unstable) beams: → From 10 AMeV …. to 10 AGeV HIC probing: - wide range of densities - high momenta - covariant structure • Around normal density: I - Low to Fermi energies • - Deep Inelastic → dissipation, charge equilibration, neck dynamics • Mass/Isospin vs Velocity correlations in fragment production • Fast nucleon emission and Lane Potentials • Isospin Transport • High baryon density: II - Relativistic energies • - n,p flows → light ion flows • Kaon/Pion production • - Deconfinement Precursors?

  9. 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:

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

  11. 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)

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

  13. 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)

  14. Inelastic collisions: Production of particles and resonances Coupled transport equations: • Channels without strangeness • Elastic baryon-baryon collisions: NNNN (in-medium sNN), NDND, DDDD • Inelastic baryon-baryon collisions (hardD-production & absorption): NNND, NNDD • Inelastic baryon-meson collisions (softD-production & absorption) NpD Channels with strangeness (perturbative kaon production) Baryon-Baryon : BBBYK (B=N,D±,0,++, Y=L,S±,0, K=K0,+) Pion-Baryon : pBYK (YKpB not included) Kaon-Baryon : BKBK (elastic, no isospin exchange) No channels with antistrangeness (K-)

  15. 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

  16. soft Esym Stiff Esym Pion and Kaon production in “open” systems (HIC)… Au+Au@1AGeV • Pions: • from entire evolution • compensation • Kaons: • direct early production: high density phase • isovector channel effects

  17. 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

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

  19. stiff Esym Soft Esym Au+Au central: Pi and K yield ratios vs. beam energy Kaons: ~15% difference between DDF and NLρδ 132Sn+124Sn Not sensitive to the K-potential (iso-dep.?) Pions: less sensitivity ~10%, but larger yields

  20. K+production and influence of kaon potentials: Ni+Ni, 1.93 AGeV

  21. 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.

  22. …more exotic phenomena? In a C.M. cell , baryon density temperature quadrupole density resonance density Exotic matter over 10 fm/c ? asymmetry energy density

  23. Testingdeconfinement with RIB’s? Mixed Phase → Hadron-RMF B1/4 =150 MeV (T,rB,rB3) binodal surface NLρ Quark- bag model NLρδ GM3 1 AGeV rtrans onset of the mixed phase → decreases with asymmetry 300 AMeV Signatures? 132Sn+124Sn, semicentral Di Toro, A. Drago, et al. nucl-th/0602052→NPA775(2006)102-126

  24. Transition to deconfined phase at high baryon density Hadron EOS : QHD Quark EOS: MIT-Bag Model H.Mueller NPA618(1997) Symmetric Asymmetric:I=0.4 Mixed Phase liquid-gas P.T. Reduced transition density 1. earlier transition at high isospin density 2. unfavorable model choice? Hadron: rho-meson only, Quark: B1/4=190MeV large Bag-Pressure

  25. 50MeV U+U, 1AGeV, semicentral Lower Boundary of the Binodal Surface vs. NM Asymmetry symmetric vs. Bag-constant choice Proton-fraction Temperature variation Reduction of the crossing density vs. T: delta-meson very efficient!

  26. Isospin content of the Quark Clusters in the Mixed Phase T=50 MeV Quarks Mixed Hadrons Lower boundary Signatures?Neutron migration to the quark clusters (instead of a fast emission) Di Toro,et al., NPA775(2006)102-126

  27. 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). In particular Kaon ratios seem to be a sensitive observable. • 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 • Deconfinement signals at high asymmetry??

  28. stiff Esym Soft Esym “closed” (IHM) vs. “open” system (HIC)… • Consistency between IHM and HIC results (if “fall” of asymmetry in kaon source accounted for)

  29. Phys.Rev. C, to appear Astrophysical Implications of Iso-Vector EOS Neutron Star Structure Constraints on the Equation-of-state - from neutron stars: maximum mass gravitational mass vs. baryonic mass direct URCA process mass-radius relation - from heavy ion collisions: flow constraint kaon producton

  30. Equations of State tested:

  31. Proton fraction and direct URCA Forbidden by Direct URCA constraint Onset of direct URCA Neutron star masses and cooling and iso-vector EOS Tolman-Oppenheimer-Volkov equation to determine mass of neutron star Heaviest observed neutron star Typical neutron stars Klähn, Blaschke, Typel, v.Dalen, Faessler, Fuchs, Gaitanos, Gregorian, Wolter, submitted to Phys. Rev.

  32. Constraints on EoS from stars and HIC Flow-Constraint from HIC: (P.Danielewicz, R. Lacey, W.G. Lynch,Science 298, 1592 (2002))

  33. iso-stiff iso-soft Heavy Ion Collisions and the Isovector Equation-of-State Fragmentation p, K, … Isospin dependence of mean field and threshhold conditions

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