1. Symmetry energy from Giant Resonances to Neutron Stars ditoro@lns.infn.itditoro@lns.infn.it, NNINT Catania,18.06.2015 Massimo Di Toro LNS-INFN, Catania, Italy

2. o o x x N N Z Z kFkF Symmetric → Asymmetric Kinetic: Fermi (T=0) → ε F /3 ~ ρ 2/3 Potential → 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)β ² β=(N-Z)/A → search for ~ ρ γ but γ can be density dependent… → momentum dependence? neutron/proton mass splitting Two contributions :

3. Asysoft Asystiff Slope: Neutron Skin – Giant Monopole Pigmy Dipole – Isospin transport (density gradients) Value: Dynamical Dipole – Symmetry repulsion in ternary events Isospin Diffusion (N/Z gradients) - Isospin Distillation (liquid-gas) Value and effective masses: Nucleon emission – Collective Flows Pion/Kaon production – Transition to Quark Matter Below Saturation High Density SENSITIVE OBSERVABLES 20 70 100

4. Near Saturation Properties: Giant Monopole Compressibility shift Stable nuclei: GMR vs neutron excess Notre Dame-Osaka-Groeningen exps. PRL99(2007)162503, GMR in 112-124Sn → ΔK = -550±100 MeV PLB718(2012)447, GMR in 106-116Cd → ΔK = -555±75 MeV →rather stiff : L ~ +70-100MeV Cd Isotopes Esym(2/3ρ 0 ) = a 4 - L/9 + K sym /162 Giant Dipole Resonance: Restoring force → Symmetry energy below saturation Different (L vs. K sym ) interplay Skew corr.s Piekarewicz-Centelles PRC 79 (2009)

5. Probing the Nuclear Equation of State with Heavy Ion Collisions Theory Guidelines - Landau two-component Fermi liquids - Energy density functionals - Transport : Boltzmann-Langevin-Vlasov Relativistic Mean Field - Gibbs conditions for Phase Transitions Experiment Guidelines (a theorist view) - Multidetectors (fragments, light ions, photons?) - Mass-charge telescopes (low thresholds?) - Neutron detectors - Good coverage of mid-rapidity - High P T selections Event Generators

6. gainloss STOCHASTIC MEAN FIELD TRANSPORT EQUATION: VLASOV + NN-COLLISIONS and PAULI CORRELATIONS Fluctuations Self-Consistent Mean FieldEquation of State Baran, Colonna, Greco, Di Toro Phys.Rep. 410 (2005) 335 (Relat. Extension) + Montecarlo collision term: A.Bonasera et al. Phys.Rep. 243 (1994) SMF approach : fluctuations projected onto ordinary space → density fluctuations δρ Fragments → Density cuts + velocity correlations

7.  Isovector dipole moment (L = 1) X neutrons – protons X c core neutrons-protons Y excess neutrons - core Neutron center of mass Proton center of mass The Isovector Dipole Response (DR) in neutron-rich nuclei Analysis of collective motion with transport theory (Vlasov) → Giant DR → Pygmy DR Giant Dipole Mode Pigmy Dipole Mode

8. Stability of ground state properties: SMALL OSCILLATIONS AROUND EQUILIBRIUM VALUE OF NEUTRON AND PROTON MEAN-SQUARE RADII

9. Pygmy-like initial conditions (Y) X Y Fourier transform of D Strength of the Dipole Response X c -- soft -- stiff -- superstiff Baran et al. 132Sn Neutron skin and core are coupled The low energy centroid is not sensitive to the asy-stiffness

10. THE DIPOLE STRENGTH FUNCTION Baran et al. PRC88 (2013) 044610 PDR GDR Total PDR strength vs. neutron skin 132Sn 140Sn 208Pb 124Sn

11. MID-RAPIDITY FRAGMENTATION MULTIFRAGMENTATION NECK-FRAGMENTATION SYMMETRY ENERGY EFFECTS ON NUCLEAR MATTER INSTABILITIES

12. Fragment Production Stochastic mean field (SMF) calculations (fluctuations projected on ordinary space) Central collisions Multifragmentation Ni + Au, E/A = 45 MeV/A Isospin Distillation + Radial Flow

13. X<0 Y>0 X = 1+F s, Y= 1+F a In Symmetric NM   chemical UNIQUE INSTABILITY: isoscalar-like Instability Region: just from!! Isospin Asymmetric Nuclear Matter: Coupling of pure isoscalar and isovector modes Instability parameters: X ↔ Isoscalar-like mode Y ↔ Isovector-like mode Corresponding Landau Parameters In dilute asymmetric matter Isoscalar (mechanical) instability with isospin rearrangement in the mixed phase: ISOSPIN DISTILLATION I=(N-Z)/A y: proton fraction

14. 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: Isospin Distillation (“Asysoft” more effective) PRL86 (2001) 4492 symmetric

15.  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 M.Colonna et al., INPC-Tokyo, NPA 805 (2008) Asy-soft Asy-stiff ASY-SOFT MORE EFFECTIVE Problems: -Decays on the way to the detectors - No neutron measurements

16. b = 4 fmb = 6 fm Sn124 + Sn124, E/A = 50 MeV/A Isospin Migration + Alignement Semi-Central : Neck Fragmentation

17. Asy-stiff: neutron enrichment of neck IMFs Asy-soft Isospin migration Isospin Drift (density gradients) 124 Sn+ 124 Sn 50 AMeV: average asymmetry Even for isospin symmetric systems (58Ni+58Ni) PLB625(2005)33 V.Baran et al. NPA 730 (2004)

18. 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

19. RELATIVISTIC COLLISIONS

20.  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 )

21. Liu Bo et al., PRC65(2002)045201 RMF Symmetry Energy: the δ - mechanism 28÷36 MeV NL NLρ NLρδ Balance of large isospin fields *

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

23. 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

24. Meson Production at Relativistic Energies:  - /  +, K 0 /K + 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

25. 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 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) 202301, HIC No evidence of Chemical Equilibrium!!

26. Central Au+Au: comparing calculations & experiments Ferini, PRL97(2006) disagreement in magnitude, particularly at low energies, Threshold effect too strong Others have the opposite problem W.Reisdorf et al. NPA781 (2007) 459 Exp.: Rapidity and p T selection important Theory: Width of the ∆ resonances π - potentials No exp. Filters Only Coulomb for pions Threshold effect reduced with a smaller Δ-width

27. New RBUU calculation with same covariant interactions (different Δ widths) → Confirmation of a strong Threshold-Effect T.SONG, C.M.KO, PRC 91 (2015) 014901 Total number of pions Reduction of production cross section is needed A~ 1.2 is fine Pion optical potential?

28. Zhigang Xiao et al. PRL 102, 062502 (2009) Circumstantial Evidence for a very soft E sym at high ρ ? → ISOVECTOR INSTABILITIES?

29. 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… G.Ferini,H.H.Wolter et al., PRL 97 (2006) 202301

30. TRANSITION TO QUARK-GLUON-PLASMA AT HIGH BARYON AND ISOSPIN DENSITY In memory of Liu Bo (IHEP-Beijing), suddenly disappeared at the end of February 2015

31. T B. Friman et al. QCD-Phases 2010 Relevance of hadronic degrees of freedom at high chemical potentials: Two-EOS Approach?

32. Exotic Isospin Asymmetric matter over 10 fm/c ? ρ≈3ρ 0, Z/A≈.35, T≈50-60 MeV In a C.M. cell Asymmetric Nuclear Matter at High Isospin and Baryon Density: A transition to QGP? DiToro, Drago, Gaitanos, Greco, Lavagno, NPA 775 (2006)

33. EoS of Symmetric/Neutron Matter: Hadron (NLρ) vs MIT-Bag → Crossings Symmetry energies hadron Quark: Fermi only symmetric neutron MIT-Bag Energy density: ε(free gas) + B M.DiToro, B.Liu et al., PRC83 (2011)

34. (T,      ) : binodal surface, mixed phase Hadron-RMF Quark- MIT Bag NJL PNJL (two flavors) Mixed Phase → Asymmetric Matter → Gibbs conditions for two conserved charges

35. B 1/4 =160 MeV B 1/4 =190 MeV Decreasing the Bag-constant → Squeezing of the mixed phase at intermediate T,ρ: the hadron pressure cannot match the quark pressure →appearance of a Critical-End-Point Artifact of the Bag Model? Isospin effect Earlier density onset of the mixed phase at low temperatures Larger shift for more repulsive hadron symmetry energy HADRON-MIT Bag P(Q)=P(free gas)-B B.Liu, M.DiToro et al., EPJA 47(2011)

36. Isospin Asymmetry in the Quark Phase: large Isospin Distillation near the Lower Border? 20% 0.2 lowerupper Signatures? Neutron migration to the quark clusters (instead of a fast emission) χ Isospin Densities in the Two Phases Au+Au 1AGeV, high density stage (initial N/Z=1.5) Hadronic 20% q-phase N/Z 1.25 3.0 NLρ 1.2 5.7 NLρδ

37. HADRON-PNJL Phase Transition symmetric asymmetric - Critical-End-Point - Large isospin effects at high densities and finite temperatures (NICA-FAIR regions) Isospin Distillation in the mixed phase even at rather high temperatures G.Y.Shao, M.Di Toro, B. Liu,V.Greco, et al., NICA White Paper, and PRD 84 (2011) 034028 No Vector Fields

38. Hadron-Quark transition in the T-μ B plane Two-EoS approach symmetric asymmetric Critical-End-Point: T=166 MeV, μ B =600 MeV …not far from μ q /T c ≈ 1

39. Vector-isovector ρ-field + Vector-isoscalar ω-field r ρ = G ρ /G r ω = G ω /G r ω = 0.2 Larger repulsion in the quark sector: mixed phase at higher baryon density (chemical potential) Critical-End-Point not affected Shao, Colonna, DiToro, B.Liu, Matera PRD 85 (2012) Hybrid N-Stars: Shao, Colonna, DiToro, X.Y.Liu, B.Liu PRD 87 (2013)

40. Isoscalar vector term in the NJL Lagrangian H-Q transition vs. isoscalar-vector coupling R V = G V /G Mixed phase Maximum density in the Nstar core - Transition shifted to higher densities - No Hybrid stars for R V larger than 0.5 Shao, Colonna, DiToro, X.Y.Liu, B.Liu PRD 87 (2013) Only a mixed phase can be reached inside a Nstar

41. Suggestions for the Mixed Phase Signatures: Quark degrees of freedom: - Reduced v 2 at high p t (EoS softening) - Onset of the n q –scaling of the flows Isospin asymmetric matter → Isospin Trapping: - Reduction of n-rich cluster emission Isospin Distillation: d-rich quark phase→ - At high p T : Enhanced π - / π + ratio Anomalous production of Isospin-rich hadrons - u-d mass splitting (m u >m d ) Experiments Best region T≈ 50-100 MeV, μ B ≈ 1200-1800 MeV → ρ ≈ 3-6 ρ 0 → HIC (fixed target) 3-10 A GeV, →NICA (Dubna), FAIR (GSI) R3B Exp. unstable beams at 2 AGeV Theory - Hadrons (Isovector Interaction, vector terms) in Effective QCD Lagrangians Only one EoS (Effective Lagrangian) → Spinodal Dynamics, Fireball Expansion

42. PEOPLE M.Colonna, V.Greco G.Ferini,V.Giordano, J.Rizzo, C.Rizzo LNS Catania V.Baran, Univ. Bucharest H.H. Wolter, LMU Munich Liu Bo, IHEP Beijing (deceased) M.Zielinska-Pfabe, Smith College USA T.I.Mikhailova, JINR Dubna T.Gaitanos, Giessen Univ., now at Thessaloniki Univ. G.Y.Shao, Peking Univ. now at Xian Univ.

43. ….. and the friendly, romantic Etna Vulcano

44. BACK-UP SLIDES

45. L-dependence: Crust-core transition region Structure of the Crust Nuclear structure Correlation between n-skin and L Properties of n-rich nuclei depend on low-density Esym (because of surface effects !) Nuclei- neutron star connection ! J: symmetry energy value at saturation Rn-Rp → PREX data 48Ca, CREX? Hartree-Fock calculations of n-skin (with effective interactions) Further connection: Esym at high baryon density X PREX

46. High density (Intermediate energies): Isospin effects on -- “squeeze-out” nucleons and clusters -- meson production -- transition to quark matter lack of data, but…SAMURAI at RIKEN CSR-LANZHOU CHIMERA+LAND at GSI CBM at FAIR NICA-JINR at DUBNA Asy-stiff Asy-soft     E sym    MeV) The Elusive Symmetry Energy 12 Subsaturation density (low to Fermi energies): - Isospin Equilibration: Dynamical Dipole Imbalance Ratios - Mid-rapidity Fragmentation: Isospin Distillation Neck fragments RIBs at Fermi Energies→ FRIB, EURISOL FAZIA Detector Heavy Ion Collisions ↓ Away from saturation

47. Heavy Ion Collision: Initial – Final State Correlation Transport is needed to consistently probe the nuclear EoS far from normal conditions thermal + expansion INPUTS ? EoS FREEZE-OUT DETECTORS Source: C.Fuchs H.H.Wolter DYNAMICS IN PHASE SPACE

48. Sn ISOTOPES THE NEUTRON AND PROTON MEAN SQUARE RADII NEUTRON SKIN THICKNESS

49. INTERMEDIATE ENERGIES: Effects of Symmetry Energy and Nucleon Mass splitting on Collective Flows

50. 124 Sn “asymmetry”  = 0.2 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)335-466 ρ0ρ0

51. asy-stiff asy-soft Light isobar 3 H/ 3 He yields Mass splitting: N/Z of Fast Nucleon Emission At high p T, observables very sensitive At high p T, observables very sensitive to the mass splitting and not to the asy-stiffness 197 Au+ 197 Au 400 AMeV central, y(0)  0.3 m* n >m* p m* n <m* p V.Giordano et al., PRC 81(2010) asy-stiff asy-soft n/p ratio yields Rapidity: y ≡ arth v parallel Lorentz sum of velocities → simple sum of the rapidities

52. 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 V 1 vs. y V 2 vs p t

53. m* n <m* p : larger neutron squeeze out at mid-rapidity - Larger neutron repulsion for asy-stiff Mass splitting impact on Elliptic Flow m*n < m*p m*n > m*p 197 Au+ 197 Au, 400 AMeV, b=5 fm, y (0)  0.3 v 2 vs p T Increasing relevance of isospin effects for m* n <m* p v 2 vs scaled rapidity Asy stiff Asy soft m*n > m*p m*n < m*p y (0)  0.3 n p

54. 2. Compensation of Isospin Effects in s th due to simple nucleon-pion isospin structure for Σ(Δ) The Threshold Effect: nn→pΔ - vs pp→nΔ ++ 1. If you have one inelastic collision how do you conserve the energy? At threshold this is really fundamental! For elastic collision the issue is not there! What is conserved is not the effective E*,p* momentum-energy but the canonical one.

55. 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

56. Isovector Landau Parameter Landau linear response → matter unstable vs. neutron-proton oscillations, neutron-proton separation? ≈ 1.33 at ρ 0 Good GDR Mode! Iso-Instabilities

57. 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 Relevance of in-medium Δ-properties: Nπ channel about 3 times the NΔ channel → too large Δ width?

58. Relativistic collisions: symmetry energy sensitive observables Isospin flows from high density regions: Elliptic Flow differences vs p t Meson Production - pi(-)/pi(+) yield ratios vs p t - pi(-)/pi(+) flows - pi(-)/pi(+) around the threshold: Pion Potentials and Δ-resonance effects - K(0)/K+ yield ratios vs p t - pi(-)/pi(+), K(0)/K+ Excitation Functions up to 2 AGeV → ASYEOS Exp. at GSI