Constraints on the Symmetry Energy from Heavy Ion Collisions

1. Constraints on the Symmetry Energy from Heavy Ion Collisions Hermann Wolter Ludwig-Maximilians-Universität München 44th Karpacz Winter School of Theoretical Physics, and 1st ESF CompStar Workshop, „The Complex Physics of Compact Stars“, Ladek Zdroj, Poland, 25.-29.2.08

2. Outline: • the symmetry energy and its role for neutron stars • knowledge of the symmetry energy • Investigation in heavy ion collisions • below saturation density: Fermi energies, diffusion, fragmentation • high densities: relativistic energies; flow, particle production • summary • Punchline: • we identify several observables in heavy ion collisions which are sensitive to the symmetry energy • however, the situation is not yet at a stage (experimentally and theoretically) to fix the symmetry energy Collaborators: M. Di Toro, M. Colonna, LNS, Catania Theo Gaitanos, U. Giessen C. Fuchs, U. Tübingen; S. Typel, GANIL Vaia Prassa, G. Lalazissis, U. Thessaloniki

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

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

5. High density: Neutron stars Asy-superstiff Asy-stiff Esym(rB) (MeV) heavy ion collisions in the Fermi energy regime Asy-soft 1 0 2 3 rB/r0 Around normal density: Structure, neutron skins Symmetry Energy: Bethe-Weizsäcker Massenformel

6. Vij phenomenological microscopic (fitted to nucl. matter)(based on realistic NN interactions non-relativistic Skyrme-typeBrueckner-HF (BHF) (Schrödinger) Relativistic Walecka-type Dirac-Brueckner HF (DB) (Quantumhadrodyn.) Relativistic: Hadronic Lagrangian y, nucleon, resonances s,w, p,.... mesons Density functional theory Theoretical Description of Nuclear Matter Non-relativistic: Hamiltonian H = S Ti + S Vij,; V nucleon-nucleon interaction

7. Decomposition of DB self energy Density (and momentum) dependent coupling coeff. s d r w Dirac-Brueckner (DB) Density dep. RMF (alternative: non-linear model (NL) meson self interactions)

8. 28÷36 MeV RMF Symmetry Energy: No dfr1.5 frFREE fd =2.5 fm2 fr 5frFREE NLρδ NLρ NL PRC65(2002)045201

9. stiff empirical iso-EOS‘s cross at about soft iso-stiff iso-soft The Nuclear Symmetry Energy in different Models The symmetry energy as the difference between symmetric and neutron matter: microscopic iso-EOS`s soft at low densities but stiff at high densities C. Fuchs, H.H. Wolter, EPJA 30(2006)5,(WCI book)

10. data Uncertainities in optical potentials Isoscalar Potential Isovector (Lane) Potential

11. Incident energy of Heavy Ion Collision: GSI SIS LNS, GANIL, MSU Low energy (Fermi regime): Fragmentation, liquid-gas phase transition, Deep inelastic High energy (relativistic): Compression, particle production, temperature. Modificaion of hadron properties

12. Fluctuations from higher order corr.; stochastic treatment 3 4 loss term gain term 1 2 Simulation with Test Particles: 1 1 1 Relativistic BUU eq. effective mass Kinetic momentum Field tensor Transport description of heavy ion collisions: For Wigner transform of the one-body density: f(r,p;t) 2-body hard collisions Vlasov eq.; mean field

13. 124Sn + 124Sn 112Sn + 112Sn Central Collisions at Fermi energies: Investigation of ratio of emitted pre-equilibrium neutrons over protons soft stiff Data: Famiano et al. PRL 06 Calc.: Danielewicz, et al. 07 SMF simulations, V.Baran 07

14. asy-stiff asy-soft isospin diffusion/transport Isospin current due to density and isospin gradients: drift coefficients diffusion coeffients Differences in tranport coefficients simply connected to symmetry energy Opposite effects on drift and diffusion for asy-stiff/soft Density range in peripheral collisions Peripheral collision at Fermi energies: Schematic picture of reaction phases and possible observables ternary events: asymmetry of IMF Velocity corr. binary events: asymmetry of PLF/TLF transport ratios pre-equilibrium emission: Gas asymmetry Proton/neutron ratios Double ratios

15. Imbalance (or Rami, transport) ratio: (i = proj/targ. rapidity) (also for other isospin sens.quantities) Isospin Transport through Neck: Limiting values: R=0 complete equilibration R=+-1, complete trasnparency Discussed extensively in the literature, and experimental data (MSU) e.g. L.W.Chen, C.M.Ko, B.A.Li, PRL 94, 032701 (2005) V. Baran, M. Colonna, e al., PRC 72 (2005)  Momentum dependence important

16. exp. MSU Asymmetry of IMF in symm. Sn+Sn collisions Isospin Transport through Neck:

17. Stiff-soft, 124 Stiff-soft, 112 Stiff-soft, 112 Stiff-soft, 124 Asymmetry of IMF in symm. Sn+Sn collisions • Asymmetry of IMF in peripheral collision rather sensitive to symmetry energy, esp. for • MD interactions • when considered as ratio relative to asymmetry of residue • Effects of the order of 30%,  sensitive variable! MI MD bIMF

18. v1: Sideward flow v2: Elliptic flow Flow and elliptic flow described in a model which allows to vary the stiffness (incompressibility K), and has a momentum dependence Results from Flow Analysis (P. Danielewicz, R. Lynch,R.Lacey, Science) Deduced limits for the EOS (pressure vs. density) for symmetric nm (left). The neutron EOS (i.e. the symmetry energy) is still uncertain, thus two areas are given for two different assumptions.

19. differential elliptic flow r+d r n p r+d r r+d r • Difference at high pt first stage Dynamical boosting of the vector contribution Asymmetric matter: Differential directed and elliptic flow 132Sn + 132Sn @ 1.5 AGeV b=6fm differential directed flow Proton-neutron differential flow T. Gaitanos, M. Di Toro, et al., PLB562(2003) and analogously for elliptic flow

20. Finite nucleus simulation: Pion production: Au+Au, semicentral Equilibrium production (box results) ~ 5 (NLρ) to 10 (NLρδ)

21. Transverse Pion Flows - W.Reisdorf et al. NPA781 (2007) 459 Antiflow: Decoupling of the Pion/Nucleon flows - + + Simulations: V.Prassa Sept.07 - + - + • OK general trend. but: • smaller flow for both • - and + • not much dependent • on Iso-EoS

22. Kaon Production: A good way to determine the symmetric EOS (C. Fuchs, A.Faessler, 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

23. Inelastic cross section K-potential (isospin independent) K-potential (isospin dependent) Effect of Medium-Effects on Pion (left) and Kaon (right) Ratios

24. Equations of State tested: 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 Klähn, Blaschke, Typel, Faessler, Fuchs, Gaitanos,Gregorian, Trümper, Weber, Wolter, Phys. Rev. C74 (2006) 035802

25. 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 (now retracted) Typical neutron stars

26. Constraints of different EOS‘s on neutron star and heavy ion observables Gravitational vs. Baryon Mass Direct Urca Cooling limit Mass-Radius Relations Heavy Ion Collision obsevables Maximum mass

27. Summary: • 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