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PROBING THE DENSITY DEPENDENCE OF SYMMETRY ENERGY WITH HIC KITPC Workshop, Beijing, June09, ditoro@lns.infn.it “Recent Progress and New Challenges in Isospin Physics with HIC” Bao-An Li, Lie-Wen Chen, Che Ming Ko Phys. Rep. 464 (2008) 113 “Reaction Dynamics with Exotic Nuclei” V. Baran, M. Colonna, V. Greco, M. Di Toro Phys. Rep. 410 (2005) 335 (Relat. Extension)

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High density (Intermediate energies): Isospin effects on - fragment production in central collisions -“squeeze-out” nucleons and clusters - meson production lack of data, but….SAMURAI at RIKEN CHIMERA+LAND at GSI Cooling Storage Ring at Lanzhou Signals of Deconfinement? Symmetry Energy Effects: 124Sn+112Sn on Isospin Equilibration (132Sn?) 124Sn+124Sn and 112Sn+112Sn on Isospin Distillation 124Sn+64Ni on Neck Fragmentation 58Fe+58Ni on Balance Energy 197Au+197Au on Elliptic Flows …..more RIB data are very welcome!

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Imbalance Ratios: Isospin Equilibration at Fermi Energies E sym (ρ) Sensitivity: asymmetry gradients Isospin Diffusion Asy-soft more effective Value below ρ 0 Interaction time selection → Centrality(?), Kinetic Energy Loss Caution: Disentangle isoscalar and isovector effects! (Overdamped Dipole Oscillation)

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Rami imbalance ratio: ISOSPIN EFFECTS IN REACTIONS Mass(A) ~ Mass(B) ; N/Z(A) = N/Z(B) A dominance mixing B dominance +1 0 Isospin observables: isoscaling vs. Centrality (fixed y) vs. Rapidity (fixed centrality) vs. Transverse momentum (fixed y, centrality)

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b=8fm b=10fm M : 124 Sn + 112 Sn H: 124 Sn + 124 Sn L: 112 Sn + 112 Sn @ 35, 50 Mev/A Smaller R values for: Asy-soft MI interaction Lower beam energy 50 AMeV 35 AMeV I = (N-Z)/A of PLF or TLF B. Tsang et al. PRL 92 (2004) Isospin equilibration: Imbalance ratios SMF simulations J.Rizzo et al. NPA806 (2008) 79 Mom. Independent-asystiff ≈ Mom. Dependent-asysoft: Compensation of isoscalar/isovector effects

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Imbalance ratios: isoscalar vs. isovector effects If: β = I = (N-Z)/A τ symmetry energy t contact dissipation Kinetic energy loss - or PLF(TLF) velocity - as a measure of dissipation (time of contact) R dependent only on the isovector part of the interaction ! Overdamped dipole oscillation

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Fragment Production Stochastic mean field (SMF) calculations b = 4 fmb = 6 fm Sn124 + Sn124, E/A = 50 MeV/A Central collisions Ni + Au, E/A = 45 MeV/A (fluctuations projected on ordinary space) Isospin Distillation + Radial Flow Isospin Migration + Alignement Semi-Central

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Multifragmentation at the Fermi Energies E sym (ρ) Sensitivity: expansion phase, dilute matter Isospin Distillation + Radial Flow Asy-soft more effective Low Density Slope Value: Symmetry Potentials Asy-soft: compensation N-repulsion vs Z-coulomb →Flat N/Z vs kinetic energy

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Isospin Distillation Mechanism: “direction” of the spinodal unstable mode ! y = proton fraction =Z/A Reduced N/Z of bulk Spinodal fragments in n-rich central collisions: Asysoft more effective (Isospin Distillation) PRL86 (2001) 4492

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Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132 E/A = 50 MeV, b=2 fm 1200 events for each reaction Liquid phase: n-depletionGas phase: n-enrichement ISOSPIN DISTILLATION Asy-soft Asy-stiff 112,112112,124124,124 With Asy-stiff in the (112,112) case: - N/Z (gas) below bisectrix - N/Z (gas) < N/Z (liquid) → large proton emission M.Colonna et al., INPC-Tokyo, NPA 805 (2008) Asy-soft Asy-stiff ASY-SOFT MORE EFFECTIVE

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New Observables: N/Z vs fragment energy N = Σ i N i, Z = Σ i Z i 1.64 Double ratio = (N/Z) 2 /(N/Z) 1 3≤ Zi ≤ 10 Asy-stiff Asy-soft neutron repulsion Coulomb p-repulsion Iso-distillation Symmetry p-compensation Proton/neutron repulsion: * n-rich clusters emitted at larger energy in n-rich systems (Δ’>Δ) * flat spectra with Asy-soft Δ’Δ’ Δ Isospin content of IMF in central collisions Isospin Distillation (spinodal mechanism) + Radial Flow + Symmetry Potentials Primary fragment properties M.Colonna et al., PRC 78 (2008) N/Z:

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Neck-fragmentation at the Fermi Energies E sym (ρ) Sensitivity: density gradient around normal density Isospin Migration + Hierarchy Asy-stiff more effective Slope just below ρ 0 IMF Mass, N/Z vs alignement/v transverse : → time sequence of mechanisms: Spinodal → neck instabilities → fast fission→ cluster evaporation

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124 Sn+ 124 Sn 50 AMeV: average asymmetry Asy-stiff: neutron enrichment of neck IMFs Asy-soft Semi-peripheral collisions Isospin migration V.Baran et al., NPA703(2002)603 NPA730(2004)329 gas liquid

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NECK FRAGMENTS: V z -V x CORRELATIONS PLF IMF TLF Large dispersion along transversal direction, v x → time hierarchy ? 124 Sn + 64 Ni 35 AMeV <0 >0 Alignement + centroid at Clear Dynamical Signatures ! Deviations from Viola systematics vs. 4 CHIMERA data E.De Filippo et al. (Chimera Coll.) PRC 71 (2005)

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Beam 1m 1° 30° 176° good angular resolution identification in mass/charge of the detected particles low detection threshold The 4 CHIMERA detector TARGET Forward part 1° 30° 2003 - CHIMERA-ISOSPIN 1192 telescopes p t d 4 He 6 He 3 He Li H.I. E-TOF E-TOF M,E E-E E-E Z,E PSD LCP 176°

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124 Sn + 64 Ni 35 AMeV: CHIMERA data vs. particle multiplicity (centrality) TLF PLF cosθ prox >0.8cosθ prox <0.8 Alignement IMF-PLF/TLF vs PLF-TLF Semicentral (M=7) v// selection of the 3 highest Z fragments: 1: PLF 2: TLF 3: Neck source Neutron enrichement for the largest Viola deviations and the highest degree of alignement : Stiff Symmetry Energy

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Intermediate Energies 1. Relativistic Kinematics but not fully covariant transport equations

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Multifragmentation at High Energies E sym (ρ) Sensitivity: compression phase Isospin Distillation + Radial Flow Asy-stiff more effective High Density Slope Value: Symmetry Potentials Larger N-repulsion with Asy-stiff Problem: large radial flow → few heavier clusters survive, with memory of the high density phase

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ASYSOFT ASYSTIFF KINETIC (FERMI) Low density clustering: spinodal mechanism Asysoft: more symmetric clusters, larger neutron distillation combined to a larger pre-eq neutron emission High density clustering: few-body correlations and p.s. coalescence Asystiff: more symmetric clusters, combined to a larger fast neutron emission The Isospin “Ballet” in Multifragmentation E sym (ρ) ρ ρ0ρ0

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Global fit to experimental charge distributions E.Santini et al., NPA756(2005)468 Fragment Formation in Central Collisions at Relativistic Energies Au+Au, Zr+Zr, Ni+Ni at 400 AMeV Central Stochastic RBUU + Phase Space Coalescence Size dependence: the lightest is the hottest? No but Fast clusterization in the high density phase

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Time-evolution of fragment formation (E. Santini et al., NPA756(2005)468) Au+Au 0.4 AGeV Central Z=3,4 Heavier fragments: “relics” of the high density phase Isospin Content vs. Symmetry Term ? Fast clusterization in the high density phase Stochastic RBUU + Phase Space Coalescence

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Isospin content of Fast Nucleon/Cluster emission, Isospin Flows E sym (ρ) Sensitivity: stiffness, and…. Neutron/Proton Effective Mass Splitting High p_t selections: - source at higher density - squeeze-out - high kinetic energies

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vs. p transverse mid-rapidity |y 0 |<0.3 (squeeze-out) vs. kinetic energy (all rapidities) Particle ratio V.Giordano, ECT * May 09

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Crossing of the symmetry potentials for a matter at ρ≈1.7ρ 0

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Collective flows In-plane Out-of-plane X Z y = rapidity p t = transverse momentum = 1 full out V 2 = 0 spherical = + 1 full in Flow Difference vs.Differential flows + : isospin fractionation -- : missed neutrons, smaller V 1 vs. y V 2 vs p t

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Transverse flow: A probe for mean field behaviour, i.e. for EOS impact parameter b y/y beam Transverse flow flow antiflow Beam energy dependence: balance energy

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Elliptic flow Evolution with impact parameter and energy inversion of pattern: squeeze out J.Lukasic et al. PLB 606 (2005) MeV fm

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Elliptic Flow vs Y/Y 0 m* n >m* p m* n

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Elliptic Flow vs P t Dominance of mass splitting at high pt

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Elliptic proton-neutron flow difference vs p t at mid-rapidity Au+Au 400AMeV Semicentral + relativistic Lorentz force…..(vector charged meson)

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Neutron and Z=1 Elliptic Flows from FOPI-LAND Data at SIS-GSI: Au+Au 400 AMeV W.Trautmann ECT*, May 11 2009

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p t dependence, various centralities and rapidities E sym ~ E sym (fermi) + ρ γ No Mom.Dep. Q. Li

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Elliptic Flow vs Y/Y 0 Increasing relevance of mass splitting m* n >m* p m* n

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Elliptic Flow vs P t

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Cluster Elliptic Flow vs Y/Y 0 Larger flows (collective energy) and less Isospin effects

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Hunting isospin with v 2 : the mass 3 pair A small gradual change in The difference 3 H- 3 He when Raising the beam energy for Au+Au (N/Z = 1.5) W.Reisdorf, ECT* May 09: FOPI 3H-3He V2 Results Au+Au with increasing beam energy Relativistic Lorentz effect?

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differential elliptic flow Q.F. Li and P. Russotto inversion of neutron and hydrogen flows UrQMD vs. FOPI data: Au+Au @ 400 A MeV stiff soft squeeze-out more sensitive than the directed flow Early FOPI data (Y. Leifels) and ASY_EOS Collaboration: 5.5 – 7.5 fm H.Wolter ECT* May 09

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Relativistic Energies Compressed Baryon Matter Quantum Hadrodynamics (QHD) → Relativistic Transport Equation (RMF) Covariant Mean Field Dynamics Phys.Rep.410(2005)335-466 Mean Fields Effective Masses In-medium cross sections Self-Energies, Form factors: “Dressed Hadrons”

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Au+Au 1AGeV central: Phase Space Evolution in a CM cell Testing EoS → CBM K production

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scattering nuclear interaction from meson exchange: main channels (plus correlations) IsoscalarIsovector Attraction & RepulsionSaturation OBE ScalarVectorScalarVector Nuclear interaction by Effective Field Theory as a covariant Density Functional Approach Quantum Hadrodynamics (QHD) → Relativistic Transport Equation (RMF) Relativistic structure also in isospin space ! E sym = kin. + ( vector ) – ( scalar )

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a 4 =E sym fixes (f f ) DBHF DHF f 2.0 2.5 fm2 * No f 1.5 f FREE f 2.5 fm 2 f 5 f FREE Liu Bo et al., PRC65(2002)045201 RMF Symmetry Energy: the δ - mechanism 28÷36 MeV NL NLρ NLρδ Constant Coupling Expectations

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N N-STARS: Present status with observation constraints D.Page, S.Reddy, astro-ph/0608360, Ann.Rev.Nucl.Part.Sci. 56 (2006) 327 Softer EOS→smaller R (larger ρ-central), smaller maximum Mass “The broad range of predicted radii for nucleon EOS will be narrowed in the near future owing to neutron-skin thickness and probably also to heavy-ion experiments” General Relativity AAAAAA

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Proton fraction, y=Z/A, fixed by Esym(ρ) at high baryon density: β-equilibrium Charge neutrality, ρ e =ρ p =yρ Fast cooling: Direct URCA process Fermi momenta matching

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Neutron Star (npeμ) properties Direct URCA threshold Mass/Radius relation NLρ NLρδ NLρ DD-F compact stars & heavy ion data T.Klaehn et al. PRC 74 (2006) 035802 - Transition to quark matter? - Faster Cooling for Heavier NS?

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Self-Energies: kinetic momenta and (Dirac) effective masses Upper sign: n Dirac dispersion relation: single particle energies Chemical Potentials (zero temp.) n-rich: - Neutrons see a more repulsive vector field, increasing with f ρ and isospin density - m*(n)

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RBUU transport equation Collision term: Wigner transform ∩ Dirac + Fields Equation Relativistic Vlasov Equation + Collision Term… Non-relativistic Boltzmann-Nordheim-Vlasov drift mean field “Lorentz Force” → Vector Fields pure relativistic term

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Relativistic Landau Vlasov Propagation Discretization of f(x,p*) Test particles represented by covariant Gaussians in xp-space → Relativistic Equations of motion for x and p* for centroids of Gaussians Test-particle 4-velocity → Relativity: - momentum dependence always included due to the Lorentz term - E*/M* boosting of the vector contributions Collision Term: local Montecarlo Algorithm imposing an average Mean Free Path plus Pauli Blocking → in medium reduced Cross Sections C. Fuchs, H.H. Wolter, Nucl. Phys. A589 (1995) 732

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Isospin Flows at Relativistic Energies E sym (ρ): Sensitivity to the Covariant Structure Enhancement of the Isovector-vector contribution via the Lorentz Force High p_t selections: source at higher density → Symmetry Energy at 3-4ρ 0

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Elliptic flow Difference Difference at high p t first stage approximations 0.3

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Meson Production at Relativistic Energies: - / +, K 0 /K + E sym (ρ): Sensitivity to the Covariant Structure Self-energy rearrangement in the inelastic vertices with different isospin structure → large effects around the thresholds High p_t selections: source at higher density → Symmetry Energy at 3-4ρ 0

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PION PRODUCTION Main mechanism 2. Fast neutron emission: “mean field effect” 1. C.M. energy available: “threshold effect” Vector self energy more repulsive for neutrons and more attractive for protons Some compensation in “open” systems, HIC, but “threshold effect” more effective, in particular at low energies n → p “transformation ” nn n0n0 n-n- p-p- p+p+ n ++ n+n+ p+p+ pp p-p- π(-) enhanced π(+) reduced G.Ferini et al., NPA 762 (2005) 147, NM Box PRL 97 (2006) 202301, HIC No evidence of Chemical Equilibrium!!

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The Threshold Effect: nn →pΔ - vs pp→nΔ ++ pp→nΔ ++ nn →pΔ - Compensation of Isospin Effects Almost same thresholds → the s in (NN) rules the relative yields → very important at low energies increase near threshold

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Pion/Kaon production in “open” system: Au+Au 1AGeV, central Pions: large freeze-out, compensation Kaons: - early production: high density phase - isovector channel effects → but mostly coming from second step collisions… → reduced asymmetry of the source G.Ferini et al.,PRL 97 (2006) 202301

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Au+Au central: Pi and K yield ratios vs. beam energy Pions: less sensitivity ~10%, but larger yields K-potentials: similar effects on K 0, K + Kaons: ~15% difference between DDF and NLρδ Inclusive multiplicities 132Sn+124Sn G.Ferini et al.,PRL 97 (2006) 202301 132Sn+124Sn Soft E sym stiff E sym

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Equilibrium Pion Production : Nuclear Matter Box Results → Chemical Equilibrium Density and temperature like in Au+Au 1AGeV at max.compression (ρ~2ρ0, T~50MeV) vs. asymmetry Larger isospin effects: - no neutron escape - Δ’s in chemical equilibrium, less n-p “transformation” NPA762(2005) 147 ~ 5 (NLρ) to 10 (NLρδ)

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Kaon production in “open” system: Au+Au 1AGeV, central Main Channels K 0 vs K + :opposite contribution of the δ -coupling….but second steps NN BYK --------- N BYK BYK N YK YK

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Au+Au 1AGeV: density and isospin of the Kaon source n,p at High density n/p at High density Drop: Contribution of fast neutron emission and Inelastic channels: n → p transformation Time interval of Kaon production “central” density

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Nuclear Matter Box Results Density and temperature like in Au+Au 1AGeV at max.compression vs. asymmetry Larger isospin effects: - no neutron escape - Δ’s in chemical equilibrium → less n-p “transformation” NPA762(2005) 147

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Kaon ratios: comparison with experiment G. Ferini, et al., NPA 762 (2005) and PRL 97 (2006) Data (Fopi) X. Lopez, et al. (FOPI), PRC 75 (2007) Comparision to FOPI data (Ru+Ru)/(Zr+Zr) equilibrium (box) calculations sensitivity reduced in collisions of finite nuclei single ratios more sensitive enhanced in larger systems larger asymmetries more inclusive data Open system (reaction) calculations

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Gas Liquid Density Temperature 20 200 MeV Plasma of Quarks and Gluons Collisions Heavy Ion 1: nuclei 5? Phases of Nuclear Matter Philippe Chomaz artistic view Isospin ? Mixed Phase In terrestrial Labs.?

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ISOSPIN IN RELATIVISTIC HEAVY ION COLLISIONS: - Earlier Deconfinement at High Baryon Density - Is the Critical Point affected?

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, Exotic matter over 10 fm/c ? In a C.M. cell NPA775(2006)102-126

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EoS of Symmetric/Neutron Matter: Hadron (NLρ) vs MIT-Bag → Crossings Symmetry energies hadron Quark: Fermi only symmetric neutron

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Testing deconfinement with RIB’s? (T, ) binodal surface Hadron-RMF Quark- Bag model (two flavors) trans onset of the mixed phase → decreases with asymmetry Signatures? DiToro,Drago,Gaitanos,Greco,Lavagno, NPA775(2006)102-126 Mixed Phase → NLρ NLρδ GM3 1 AGeV 300 AMeV 132Sn+124Sn, semicentral B 1/4 =150 MeV

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Liu Bo, M.D.T., V.Greco May 09 Mixed Phase: Boundary Shifts at Low Temperature Lower Boundary much affected by the Symmetry Energy

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Liu Bo, M.D.T., V.Greco May 09 m u =m d =5.5MeV Χ=0.0 Χ=1.0 Critical Point for Symmetric Matter? π -production is softening the hadron phase ?

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Lower Χ=0.0 Upper Χ=1.0 Symmetric to Asymmetric (not Exotic) Matter

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lower upper lower NLρδ : more repulsive high density Symmetry Energy In the hadron phase Dependence on the High Density Hadron EoS Long way to reach 20% quark matter, but…

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Isospin Asymmetry in the Quark Phase: large Isospin Distillation near the Lower Border? 20% 0.2 lower upper Signatures? Neutron migration to the quark clusters (instead of a fast emission) → Symmetry Energy in the Quark Phase? χ

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Nuclear Matter Phase Diagram…. Every Complex Problem has a Simple Solution …my journey is around here ….most of the time Wrong (Umberto Eco) Conclusion:

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Points for this week, June 15-19, discussions Status of E sym (ρ); new suggestions? Isoscalar vs. Isovector effects on the Reaction Dynamics E sym (ρ) at high density: N-Stars, Deconfinement…. Microscopic DFT inputs?

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Yoritaka Iwata 1, Naoyuki Itagaki 2, Takaharu Otsuka 1,2,3 1 Department of Physics, University of Tokyo. 2 CNS, University of Tokyo. 3 RIKEN. Competitive.

Yoritaka Iwata 1, Naoyuki Itagaki 2, Takaharu Otsuka 1,2,3 1 Department of Physics, University of Tokyo. 2 CNS, University of Tokyo. 3 RIKEN. Competitive.

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