The Density Dependence of the Symmetry Energy from Heavy Ion Collisions Hermann Wolter Ludwig-Maximilians-Universität München (LMU) collaborators: Massimo Di Toro, Maria Colonna, V. Greco, Lab. Naz. del Sud, Catania Theodoros Gaitanos, Univ. of Giessen Vaia Prassa, Georgios Lalazissis, Univ. Thessaloniki Malgorzata Zielinska-Pfabe, Smith Coll., Mass., USA 50th Winter Meeting in Nuclear Physics, Bormio, Jan. 23-27, 2012

Points to discuss Density (and momentum) dependence of the nuclear Symmetry Energy (SE); uncertainties, importance, astrophysics II. Situation from many-body theory III. Study of Symmetry Energy in heavy ion collisions, choice of asymmetry and density regime. transport theory IV. Discuss specific examples: < r0, isospin transport, Fermi energies > r0 momentum distributions („flow“), meson production

Equation-of-State and Symmetry Energy BW mass formula density-asymmetry dep. of nucl.matt. neutron matter EOS Symmetry energy: Diff. between neutron and symm matter, rather unknown, e.g. Skyrme-like param.,B.A.Li asy-stiff asy-soft rB/r0 stiff soft saturation point Fairly well fixed! Soft! EOS of symmetric nuclear matter density r asymmetry d Esympot(r) often parametrized as useful around r=r0. Expansion around r0 :

SE The Nuclear Symmetry Energy in different „realistic“ models stiff soft Rel, Brueckner Nonrel. Brueckner Variational Rel. Mean field Chiral perturb. The EOS of symmetric and pure neutron matter in different many-body approaches C. Fuchs, H.H. Wolter, EPJA 30(2006)5,(WCI book) The symmetry energy as the difference between symmetric and neutron matter: SE asy-soft at r0 (asystiff very similar) Different proton/neutron effective masses Isovector (Lane) potential: momentum dependence SE ist also momentum dependen t  effective mass asy-stiff asy-soft Why is symmetry energy so uncertain?? ->In-medium r mass, and short range tensor correlations (B.A. Li, PRC81 (2010)); -> effective mass scaling (Dong, Kuo, Machleidt, arxiv 1101.1910)

Importance of Nuclear Symmetry Energy supernovae,neutron stars) heavy ion collisions in the Fermi energy regime Isospin Transport properties, (Multi-)fragmentation (diffusion, fractionation, migration) Esym (rB) (MeV) rB/r0 1 2 3 Asy-stiff Asy-soft ASYEOS Collaboration p, n rel. Heavy ion collisions Nuclear structure (neutron skin thickness, Pygmy DR, IAS) Slope of Symm Energy

Astrophysics: Supernovae and neutron stars A normal NS (n,p,e) or exotic NS? r0 PSR J1614-2730 typical neutron stars heaviest neutron star Onset of direct URCA: Yp>.11 Supernova evolution: range of densities and temperatures and asymmetries:

Determination of nuclear SE in heavy ion collisions  Transport theory Z/N, asymmetry degree of freedom 1 neutron stars Supernovae IIa exotic Deconfinement for asymmetric matter earlier? Determination of nuclear SE in heavy ion collisions  Transport theory equation of motion in semiclass. approx: BUU equation isospin dependent, pp,nn,pn In-medium! 1 2 3 4 isoscalar and isovector (~10%) EOS 2-body collisions loss term gain term Approximation to a much more complicated non-equilibrium quantum transport equation (Kadanoff-Baym) by neglecting finite width of particles Coupled transport eqs. for neutrons and protons Isovector effects are small relative to isoscalar quantities Relativistic transport equations: Walecka-type (RMF) models Inelastic collisions (particle production; mesons p,K)

Reaction Mechanisms in Heavy Ion Collisions Coulomb barrier to Fermi energies Relativistic energies peripheral central Isospin migration Isospin fractionation, multifragm deep-inelastic pre-equil. dipole pre-equil. light particles N/Z of PLF residue = isospin diffusion Production of particles, p,K Flow: directed and elliptic N/Z ratio of IMF‘s N/Z of neck fragment and velocity correlations

Central collisions at Fermi energies: Ratios of emitted pre-equilibrium particles Early emitted neutrons and protons reflect difference in potentials in expanded source, esp. ratio Y(n)/Y(p). more emission for asy-soft, since symm potential higher protons vs. neutrons 124Sn + 124Sn 112Sn + 112Sn asy-soft asy-stiff 124Sn + 124Sn 112Sn + 112Sn „Double Ratios“ softer symmetry energy closer to data SMF simulations, M.Pfabe IWM09 Data: Famiano, et al., PRL 06 asy-soft asy-stiff qualitatively as seen in ImQMD, but quantitatively weaker dependence on SymEn Y. Zhang, et al., arXiv (2011)

Check momentum dependence of SE: 136,124Xe+124,112Sn, E = 32,…,150 AMeV data R. Bougault (Ganil, prelim, IWM11) son: asysoft, mn*>mp* stn: asystiff, „ sop: asysoft, mn*<mp* stp: asystiff, „ Comparison of yield ratios 136Xe+124Sn, central Prelim. data 136+124, 32 AMeV, INDRA favors a asy-stiff with mn*<mp* mn*<mp* soft n/p ratio stiff mn*>mp* E=65 AMeV E=100 AMeV E=32 AMeV Etrans/A [MeV] t/3He ratio Etrans/A [MeV] 1.5 E=32 AMeV The single t/3He ratios seem to be a promissing observable, double ratios under study

Centelles, et al., PRL 102 (2009): Catania results, limits approx. N/Z of IMF, double ratio Catania results, limits approx.

r+d r+d r r Heavy Ion Collisions at Relativistic Energies: “Flow“ Fourier analysis of momentum tensor : „flow“ Global momentum space v2: elliptic flow v1: sideward flow 132Sn + 132Sn @ 1.5 AGeV b=6fm r+d, stiff dynamical boosting of vector contribution T. Gaitanos, M. Di Toro, et al., PLB562(2003) r n p differential elliptic flow Proton-neutron differential flow Elliptic flow more sensitive, since particles emitted perpendicular r+d r r+d r ASYEOS Experiment See talk by W. Trautmann

Particle production as probe of symmetry energy Difference in neutron and proton potentials p, n „direct effects“: difference in proton and neutron (or light cluster) emission and momentum distribution „secondary effects“: production of particles, isospin partners p-,+, K0,+ NN ND Np LK D in-medium self-energies and width p potential , NLK in-medium in-elastic s , K and L potential (in-medium mass) 1. Mean field effect: Usym more repulsive for neutrons, and more for asystiff  pre-equilibrium emission of neutron, reduction of asymmetry of residue 2. Threshold effect, in medium effective masses:  m*N,, m*D, contribution of symmetry energy; m*K, models for K-potentials G.Ferini et al.,PRL 97 (2006) 202301

Pion ratios in comparison to FOPI data (W. Reisdorf et al Pion ratios in comparison to FOPI data (W.Reisdorf et al. NPA781 (2007) 459) MDI, x=0, mod. soft Xiao,.. B.A.Li, PRL 102 (09) MDI, x=1, very soft NLd, stiff Ferini, Gaitanos,.. NPA 762 (05) NL, soft, no Esym g=2, stiff Feng,… PLB 683 (10) SIII, very soft FOPI, exp Contradictory results of different calculations; Reason: Treatment of D dynamics? Kaons better probe? , V. Prassa, et al., NPA 832 (2010)

Dynamics of particle production (D,p,K) in heavy ion collisions Au+Au@1AGeV stiff Esym soft Esym Central density D and K: production in high density phase Pions: low and high density phase Sensitivity to asy-stiffness NLrd NLr NL p and D multiplicity Dependence of ratios on asy-stiffness n/p D0,-/D+,++  p-/p+, K0/K+  n/p ratio governs particle ratios K0,+ multiplicity  time [fm/c] G.Ferini et al.,PRL 97 (2006) 202301

Present constraints on the symmetry energy p+/p- ratio, Feng, et al. (ImIQMD) Moving towards a better determination of the symmetry energy Large uncertainties at higher density Conflicting theore-tical conclusions for pion observables. Work in exp. and theory necessary! Au+Au, 400AMeV, FOPI Fermi Energy HIC, MSU p+/p- ratio B.A. Li, et al.

Summary and Outlook Thank you While the EOS of symmetric NM is now fairly well determined, the density (and momentum) dependence of the Symmetry Energy is still rather uncertain, but important for exotic nuclei, neutron stars and supernovae. Constraints come from neutron star observables and from HIC both at sub-saturation (Fermi energy regime) and supra-saturation densities (relativistic collisions). At subsaturation densities the constraints become increasingly stringent (g~1), but constraints are largely lacking at supra-saturation densities. Observables for the suprasaturation symmetry energy N/Z of pre-equilibrium light clusters, difference flows, (first hints -> ASYEOS) part. production rations p-/p+ , K0/K+ (FOPI,HADES) More work to do in exp. (more data) and theory (consistency of transport codes, p,D dynamics) Nuclear symmetry energy: an interesting field that connects areas of nuclear structure, reactions and astrophysics Thank you

Neutron star masses and cooling and the symmetry energy Proton fraction and direct URCA Onset of direct URCA Forbidden by Direct URCA constraint Tolman-Oppenheimer-Volkov equation to determine mass of neutron star PSR-J1614_2230 Typical neutron stars Klähn, Blaschke, Typel, Faessler, Fuchs, Gaitanos,Gregorian, Trümper, Weber, Wolter, Phys. Rev. C74 (2006) 035802

stiff stiff stiff soft soft soft Careful study of consistency between nuclear structure and astrophysics: Than, Khoa, Van Gai, PRC80 (2009); Loan, Tan, Khoa, Margeron, PRC83 (2011) Two classes of eff. NN interactions: M3Y-Pn, Gogny-D1S, asy-soft very good fit to nuclear struct CDM3Yn, SLy5, asy-stiff, fit to nuclei struct not so good Mass-Radius relationship for NS, compared to evaluations by Özel. et al (left) and Steiner et al. (right) Symmetry energy Flow constraints from HIC (Danielewicz, et al.,) stiff stiff stiff soft soft soft EOS‘s that fit better nuclear structure have difficulties with high density behaviour of SE and with neutron star observables

around normal density: Structure Expansion of SE around r0: Symmetry pressure strong linear correlation between neutron skin thickness and SE slope L~p0 (or also a4) strong correlation between Dipole strength of Pygmy resonance and SE slope L  possibility to determine slope of SE, but also neutron skin thickness PDR neutron skin of Pb as ~ slope L (MeV)

Transport approaches Transport theory describes the non-equilibrium aspects of the temporal evolution of a collision. The central quantitiy is the phase space density (coordinate and momentum distribution). Demonstrate two aspects: Evolution in coordinate space:  movies curtesy T. Gaitanos, T.Chossy 2. Evolution in momentum space non-equilibrium, non-sphericity of local momentum distributions time (fm/c) density (fm-3)  Transport theory!!!

I.8 Importance of Symmetry energy: neutron stars dependence of maximum neutron star mass on symmetry energy. However, other constraints, e.g. coling due to URCA process Klähn, Blaschke, Typel, Faessler, Fuchs, Gaitanos,Gregorian, Trümper, Weber, Wolter, Phys. Rev. C74 (2006) 035802 Onset of direct URCA Typical neutron stars Heaviest observed neutron star Forbidden by Direct URCA constraint

Neutron Stars: a Laboratory for the High-Density Equation-of-State A normal NS (n,p,e) or exotic NS? PSR J1614-2730 typical neutron stars Onset of direct URCA (fast cooling) core crust Composition of NS matter Klähn, Blaschke, Typel, Faessler, Fuchs, Gaitanos,Gregorian, Trümper, Weber, Wolter, Phys. Rev. C74 (2006) 035802

The Nuclear Symmetry Energy in different „realistic“ models stiff soft Rel, Brueckner Nonrel. Brueckner Variational Rel. Mean field Chiral perturb. The EOS of symmetric and pure neutron matter in different many-body approaches C. Fuchs, H.H. Wolter, EPJA 30(2006)5,(WCI book) The symmetry energy as the difference between symmetric and neutron matter: asy-stiff asy-soft Esym(r) BHF Skyrme RMF many more in: B.A. Li et al., Phys. Rep. 464 (2008)

Momentum Dependence of the Symmetry Energy asy-soft at r0 (asystiff very similar) Different proton/neutron effective masses -> crossing around Fermi momentum! data m*n < m*p m*n > m*p Isovector (Lane) potential: momentum dependence Why is symmetry energy so uncertain?? ->In-medium r mass, and short range tensor correlations (B.A. Li, PRC81 (2010)); -> effective mass scaling (Dong, Kuo, Machleidt, arxiv 1101.1910)

Astrophysical Connection Ranges of density, temperature, asymmetry in SN event Liebendörfer, et al., NIX XI, 2010 Composition of the matter collapse post-bounce density: log10n [g/cm3] entropy: log10s[kB/baryon] not uniform, but light and heavy clusters (nuclei embedded in the medium) [g/cm3] Hillebrandt, et al., Scient. Americ. 2006 Symmetry energy plays an essential role in astrophysics

Check momentum dependence of SE in detail: 136,124Xe+124,112Sn, E = 32,…,150 AMeV data R. Bougault (Ganil, prelim, IWM11) Xe+Sn, 136+124 neutron-rich 124+112 neutron poor E=32 AMeV, central Protons, neutron-rich neutron-poor asy-soft at r0 (asystiff very similar) Protons, neutron-rich data neutron-poor Mass3 data: neutron-rich t 3He neutron-poor t 3He Mass3 calc: neutron-rich t 3He Effect of asystifffnes as large as m*- effect

Comparison of SE determinations at lower energy From isospin diffusion and p/n emission ratios isospin diffusion, Ri(b), peripheral N/Z of IMF, central pre-equ p/n double ratio, central N/Z of evap. LCP from PLF, peripheral asy-stiff asy-soft Note: for Catania results: Limits approximate! B. Tsang, et al., PRL 102, 122701 (2009) Current state: Generally consistent with each other , but still uncertainties. More work necessary, also on consistency of codes

Differential elliptic flow Au+Au, 400 AMeV t-3He pair similar but weaker Au+Au, 600 AMeV asystiff asysoft m*n>m*p Inversion of elliptic flows because of inversion of n,p-potentials with effective mass m*n<m*p V.Giordano, M.Colonna et al., arXiv 1001.4961, PRC81(2010) W. Reisdorf, Experimental indication of splitting of ell- flow with effective mass Elliptic flow more sensitive, since determined by particles that are emitted perp to the beam direction

ASY-EOS: Hunting the high density symmetry energy with v2 Russotto, et al., PLB 697, 471 (2011) FP2 g=0.98(35) inversion of neutron and hydrogen flows Indication of an asy-stiff symmetry energy at suprasaturation density SIS experiment S394 First beamtime May 2011

r+d r Heavy Ion Collisions at Relativistic Energies: “Flow“ p n r+d r Fourier analysis of momentum tensor : „flow“ Global momentum space v2: elliptic flow v1: sideward flow 132Sn + 132Sn @ 1.5 AGeV b=6fm p n r+d r for 124Sn “asymmetry” I = 0.2 neutron proton Asy-stiff Asy-soft Proton/neutron potentials Proton-neutron differential flow r+d r dynamical boosting of vector contribution T. Gaitanos, M. Di Toro, et al., PLB562(2003) and analogously for elliptic flow

In-medium Klein-Gordon eq. for Kaon propagation: Two models for medium effects tested: One-Boson Exchange (Schaffner-Bielich et al.) Chiral perturbation (Kaplan, Nelson et al.) ChPT OBE Splitting for K0,+ In-medium K energy (k=0) Isospin-dependence DPG08_kaon 5

Kaon potential models sfree seff Two models for medium effects tested: 1.Chiral perturbation (Kaplan, Nelson, et al.) (ChPT) 2.One-boson-exch. (Schaffner-Bielich, et al.,) (OBE) density and isospin dependent and two models for NN sin-med sfree K+ multiplicity/Apart seff In-Medium K energy (k=0) w/o pot ChPT OBE Splitting for K0,+ and NLr and NLrd K0/K+ ratios depend. on  sin-med (no) iso-EOS K potential isosp. dep of K potential V.Prassa, et al.,NPA832(2010)88