From the Phys.Dept. Jan.2002Etna Double-Face, Aug.07 ISOSPIN DYNAMICS IN HEAVY ION COLLISIONS From Coulomb Barrier to Deconfinement V.Baran, M.Colonna, M.Di Toro, G.Ferini, Th. Gaitanos, V.Giordano, V. Greco, Liu Bo, F.Matera, M.Pfabe, S. Plumari, C.Rizzo, J.Rizzo, and H.H.Wolter LNS-INFN and Phys.Astron.Dept. Catania, IFIN-HH Bucharest, IHEP Beijing, Univs. of Firenze, Giessen, Munich, Smith College …….and with the contribution of a very lively Etna mountain! KITPC Workshop, Beijing, June09, Oct.12, 2008 From the Etna Melting Pot

Tentative Plan of the Talk(s) 1. “Nuclear Matter” Phase Diagram Symmetry Energy Isospin Equilibration Isospin Distillation Isospin as a Tracer of the Fragment Production Mechanism Heavy Ion Collisions at Intermediate Energies: Isospin Flows 2. Quantum-Hadro-Dynamics: EoS Effective Bosons, Self Energies, N-stars QHD: Fully Covariant Transport Linear Response, Elliptic Isospin Flows, Meson Production 3. Conclusion Looking for the Critical Point at High Baryon and Isospin density

Nuclear Matter Phase Diagram….updated Liquid-Gas Our Tentative “Path” with Heavy Ion Collisions: From Dilute (liquid-gas) to High Baryon and Isospin Density (Landau school)

o o x x N N Z Z kFkF Symmetric → Asymmetric Fermi (T=0) ≈ ε F /3 ~ ρ 2/3 Interaction Two-body ~ ρ, many-body correlations? Symmetry Energy a 4 term (~30MeV) of the Weiszäcker Mass Formula: at saturation E sym (Fermi) ≈ E sym (Interaction) E/A (ρ) = E(ρ) + E sym (ρ)I ² I=(N-Z)/A → search for ~ ρ γ but γ can be density dependent… → momentum dependence? neutron/proton mass splitting

EOS of Symmetric and Neutron Matter Dirac-Brueckner Variational+3-body(non-rel.) RMF(NL3) Density-Dependent couplings Chiral Perturbative Ch.Fuchs, H.H.Wolter, WCI Final Report EPJA 30 (2006) 5-21 “earlier” disagreement symmetric AFDMC V8’+3body Fantoni et al Role of n-body forces (n>3) at ρ>2ρ 0 ?

Iso-Tracer (1): Isospin Transport and Chemical Potentials currents diffusion DiffusionDrift drift Isospin Transport (Equilibration, Distillation………..) → Direct Access to Value and Slope of the Symmetry Energy at ρ ! Asy-soft Asy-stiff E/A (ρ) = E(ρ) + E sym (ρ)I ² I=(N-Z)/A Symmetry energy ρ-slope Isospin chemical potential

124 Sn “asymmetry”  = 0.2 Iso-Tracer (2): Symmetry Potentials and Effective Masses neutron proton Nucleon emission; Flows…. Asy-stiff Asy-soft Lane Potentials Density dependence Momentum dependence (Un-Up)/2I Phys.Rep.410(2005) ρ0ρ0

Near Saturation Properties SYMMETRY PRESSURE SHIFT of SYMMETRIC NUCLEAR MATTER P sym Central density of Heavy Exotic Nuclei ? Compressibility shift Exotic Monopole? Expansion around   28-32MeV SlopeCurvature Stable nuclei: nucl-ex/ :Notre Dame-Osaka exp. GMR in Sn→ ∆K = -550±100 MeV →Very stiff : L ~ +100MeV! L~3a 4 γ →γ ≥1 → n-skin thickness? Saturation density shift Esym ≈ (ρ/ρ 0 ) γ

gainloss STOCHASTIC MEAN FIELD TRANSPORT EQUATION: VLASOV + NN-COLLISIONS and PAULI CORRELATIONS Fluctuations Self-Consistent Mean FieldEquation of State Baran, Colonna, Greco, DiToro Phys.Rep. 410 (2005) 335 (Relat. Extension) Chomaz, Colonna, Randrup Phys.Rep. 389 (2004) 263 (Fermi Energies)

The Boltzmann-Nordheim-Vlasov equation with a non local potential The BNV equation becomes: V 12 (r) form factor: Yukawa…… local

GBD extension Correspondence to Skyrme parameters MSU-RIA05/nucl-th/ , NPA 806 (2008) (Isospin Equilibration) I=0.2 Lane Potential (U n -U p )/2I Momentum Dependence and Effective Masses: Fast Nucleon Emission Skyrme-like parametrization (Yukawa)

Coulomb Barrier Symmetry Energy below Saturation: Fusion → Collective Charge Equilibration

D(t) : bremss. dipole radiation Initial Dipole Pre-equilibrium Dipole Radiation Charge Equilibration Dynamics: Stochastic → Diffusion vs. Collective → Dipole Oscillations of the Di-nuclear System Fusion Dynamics Cooling on the way to Fusion CN: Statistical GDR …tilting lighthouse!

32S + 100Mo (6 AMeV) 32S + 100Mo (9 AMeV) D(t) Dk(t) time(fm/c) Pre-equilibrium dipole emission D.Pierroutsakou et al. PRC71(2005) SPIRALS → Collective Oscillations! DK(t) Bremsstrahlung: Quantitative estimations V.Baran, D.M.Brink, M.Colonna, M.Di Toro, PRL.87(2001) b=0, central TDHF: C.Simenel, Ph.Chomaz, G.de France D(t)

D.Pierroutsakou et al., New Medea Exp. at LNS-Catania, squares 36 Ar + 96 Zr circles 40 Ar + 92 Zr (np)-bremsstrahlung-subtracted spectra at θ γ =90 o vs. Beam Axis 16AMeV Fusion events: same CN selection Difference 36 Ar + 96 Zr 40 Ar + 92 Zr Linearized spectra: divided by the no-GDR CN evaporation component θ γ -study of the extra-yield with MEDEA B.Martin et al., PLB 664 (2008) 47

Dipole Angular Distribution of the Extra-Yield: Anisotropy!! vs Beam Axis a2 = -1 → Pure Dipole oscillation along the Beam Axis → ~ sin 2 θ γ a2 = -0.8 a2 = -0.5 Widening: rotation of the Prompt Dipole Axis vs the Beam Axis ↓ Accurate Angular Distrib. Measure: Dipole Clock! 36Ar+96Zr vs. 40Ar+92Zr: 16AMeV Fusion events: same CN selection B.Martin et al., PLB 664 (2008) 47

The “Monster” 132 Sn Dynamical Dipole: Symmetry Energy 10AMeV, b=4fm Larger Yield (25%) ASYSOFT : Larger Centroid Energy Larger Width PRC 79 (2009) Power Spectrum Prompt Dipole Oscillations Phase Space Correlations Asy soft Asy stiff Present problems: Beam Intensities Low energy facilities

fm/c Density Plots on the Reaction Plane: Rotation of the Oscillation Axis vs the Beam Axis Still emitting,..although damped 132Sn: The Monster Dipole Case b=2fm b=4fm Weighted anisotropies: Total Angular Distribution PRC 79 (2009)

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)

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)

b=8fm b=10fm M : 124 Sn Sn H: 124 Sn Sn L: 112 Sn , 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

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

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

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

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

 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

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:

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

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

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)

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

Non-equilibrium Effects in Fragmentation - IMF hierarchy vs. v ┴ : Isospin Tracer ISOSPIN: Tracer of a “Continuous” Series of Bifurcations → from multi- to neck-fragmentation up to PLF dynamical fission 124Sn+124Sn 50AMeV semicentral low v ┴ → more PLF-correlated → Φ-plane ≈ 0 large N/Z Viola-violation larger masses MULTI-MODALITY Fragmentation …….just in one shot Histogram: no Viola-violation selection Time Hierarchy: Early Formation via fast Spinodal Mechanism for Light Fragments → Large v transv → Low alignement → Low N/Z Chimera data: see E.De Filippo, P.Russotto INPC-Tokyo, NPA 805 (2008)

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

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

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

 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

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

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

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

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

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

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

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

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

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

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

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

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

Elliptic Flow vs Y/Y 0 Increasing relevance of mass splitting m* n >m* p m* n <m* p Large rapidities not much affected

Elliptic Flow vs P t

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

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?

differential elliptic flow Q.F. Li and P. Russotto inversion of neutron and hydrogen flows UrQMD vs. FOPI data: 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

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!

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

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

 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 )

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

N N-STARS: Present status with observation constraints D.Page, S.Reddy, astro-ph/ , 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

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

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) Transition to quark matter? - Faster Cooling for Heavier NS?

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)<m*(p) asymmetry parameter

DIRAC OPTICAL POTENTIAL Dispersion relation Schrödinger mass upper signs: neutron Asymmetric Matter RMF Phys.Rep.410(2005) , MSU-RIA05 nucl-th/ AIP Conf. 791(2005)70-82 ~50 MeV Dirac mass

BEYOND RMF: k-dependence of the Self-Energies Schroedinger mass Asymmetric Matter DBHF High momentum saturation of the optical potential High momentum increase of the Dirac Mass Phys.Rep.410(2005) , MSU-RIA05 nucl-th/ AIP Conf. 791(2005)70-82 Problem still open……..sensitive observables

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

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

Local Mean Free Path Montecarlo Collision Procedure - i,j collision candidates if - Collisional time: - Collision Probability - Random choice of x in (0,1) → if accepted Then check Pauli Blocking A.Bonasera et al. Phys.Rep. 243 (1994)

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

Au+Au 800 A MeV elliptic flows, semicentral Rapidity selections v2(n) |y°| < 0.5 v2(n), v2(p) vs. p_t v2(p) All rapidities v2(n) v2(p) Low p_t spectator contributions

Elliptic flow Difference Difference at high p t first stage approximations   0.3<Y/Y proj < Sn+132Sn, 1.5AGeV, b=6fm: NL-  NL-(  +  High p t neutrons are emitted “earlier” Dynamical boosting of the vector contribution V.Greco et al., PLB562(2003)215 Equilibrium (ρ,δ) dynamically broken: Importance of the covariant structure

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

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 n0n0 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) , HIC No evidence of Chemical Equilibrium!!

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

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) Sn+124Sn Soft E sym stiff E sym

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)

asysoft asystiff  -/  + increase around threshold for large asymmetries: FOPI data vs. transport models vs. IBUU (B.A.Li) vs. IQMD W.Reisdorf et al. NPA781 (2007) 459 ……not fully covariant approaches The Threshold Puzzle

Au+Au 400 A MeV, semicentral: Pion production: Threshold effect π-/π+ ratios vs. p_t, all rapidities π-/π+ ratios vs. beam energy, inclusive Sharp increase at low energy Too large values: - Semicentral (less  - abs.)? - Exp.filters? Very soft Symmetry Term!! Z.Xiao et al PRL 102 (2009)

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)

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   BY   BYK  N  YK   YK

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

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

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 finite nucleus calculations sensitivity reduced in collisions of finite nuclei single ratios more sensitive enhanced in larger systems larger asymmetries more inclusive data H.Wolter, ECT* May 09

Gas Liquid Density   Temperature 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.?

“Exotic Matter” in collisions of n-rich systems at few AGeV Gibbs Conditions and Symmetry Repulsion at high density 132Sn and 238U “paths” Signals from a Mixed Phase? Isospin in Partonic Effective Lagrangians ISOSPIN IN RELATIVISTIC HEAVY ION COLLISIONS: - Earlier Deconfinement at High Baryon Density - Is the Critical Point affected?

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

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) Mixed Phase → NLρ NLρδ GM3 1 AGeV 300 AMeV 132Sn+124Sn, semicentral B 1/4 =150 MeV

Lower Boundary of the Binodal Surface vs. NM Asymmetry vs. Bag-constant choice Proton-fraction symmetric NPA775(2006) α = 1-2 Z/A

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

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

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?

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

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…

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

NJL Effective Lagrangian (two flavors): non perturbative ground state with q-qbar condensation M.Buballa, Phys.Rep. 407 (2005) Gap Equation → 1 → 0 → 1/2 Large μ Large T 0 or Chiral restoration

M.Buballa, Phys.Rep. 407 (2005) Parameters: Λ p, G, m vs. M π, f π, (estimation) ρ B =0T=0 m u,d =5.5MeV m u,d =0.0 NJL Phase Diagram

S.Plumari, Thesis 2009 Standard Parameters ● Coexistence ◊ Spinodal

Isospin Extension of the NJL Effective Lagrangian (two flavors) Mass (Gap) – Equation with two condensates α : flavor mixing parameter → α = ½, NJL, Mu=Md α → 0, small mixing, favored → physical η mass α → 1, large mixing M.Buballa, Phys.Rep. 407 (2005) Quark Dynamics at High Baryon Density

Neutron-rich matter at high baryon density: |Фd| decreases more rapidly due to the larger ρ d → (Ф u – Ф d ) < 0 α in the range 0.15 to 0.25……

Very n-rich matter: I=(N-Z)/A=0.4 Masses in the Chiral Phase α =0.2 α =1 Solutions of the Iso-Gap Equation S.Plumari, Thesis 2009 Iso-NJL m = 6MeV Λ = 590MeV G 0 Λ 2 =2.435 → M vac =400MeV =(-241.5MeV) 3 m π =140.2MeV f π =92.6MeV

Symmetry Energy in the Chiral Phase: something is missing ….only kinetic contribution

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

Back-up Slides

Isospin Equilibration: Dynamical Dipole in Fusion Reactions E sym (ρ) Sensitivity Value (<ρ 0 ) Restoring Force → Centroid, Yield Neutron Emission Reaction Mechanism NN cross sections Damping Anisotropy

Linear Response Dirac Eq. in Wigner formalism Fermi-Dirac distribution System of eq.s 4 Expansion at I° order Collective modes perturbation “zero sound” (V S >V F ) Asymmetric NM  p  n ≠ ρ p /ρ n Longitudinal Wave

Two kinds of collective modes Two kinds of collective modes: I)Isoscalar : in phase  p  n ) II)Isovector : out of phase  p  n  K E sym Pomeranchuck stability condition = Density of states at k F Landau Fermi liquid response

Relativistic Dispersion Relation in SNM Isovector Lindhard function K E sym Isoscalar smaller M* larger f  same monopole if larger K NM larger f  larger f  same a 4 but reduced dipole frequency

NLρδ NLρ Liquid-gas Phase Transition In Asymmetric Matter: Isospin Distillation Instability region (T=0) “Dilute” response not much affected by the δ-meson but effects at high densities….