Observables for the High-Density Symmetry Energy from Heavy Ion Collisions

1. Observables for the High-Density Symmetry Energy from Heavy Ion Collisions Hermann Wolter Ludwig-Maximilians-Universität München (LMU) HIM-Meeting, Pohang, Korea, APRIL 13, 2012

2. Observables for the High-Density Symmetry Energy from Heavy Ion Collisions Munich at Eastern 2012 Hermann Wolter Ludwig-Maximilians-Universität München (LMU) HIM-Meeting, Pohang, Korea, APRIL 13, 2012

3. Observables for the High-Density Symmetry Energy from Heavy Ion Collisions HIM-Meeting, Pohang, Korea, APRIL 13, 2012

4. Points to discuss • Motivation: • The nuclear Symmetry Energy: density (and momentum) dependence, uncertainties from many-body theory, • importance, astrophysics II. Study of Symmetry Energy in heavy ion collisions, choice of asymmetry and density regime. non-equilibrium: transport theory • Discussion of observables in the regime possible obervables correlation and consistency between observables sparse data: projects like KORIA important 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

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

6. asy-soft at r0 stiff SE ist also momentum dependent  effective mass soft asy-stiff Different proton/neutron effective masses Isovector (Lane) potential: momentum dependence asy-soft The Nuclear Symmetry Energy in different „realistic“ models 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) SE 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)

7. supernovae,neutron stars) heavy ion collisions in the Fermi energy regime p, n Isospin Transport properties, (Multi-)fragmentation (diffusion, fractionation, migration) Asy-stiff Esym(rB)(MeV) rel. Heavy ion collisions Asy-soft 0 1 rB/r0 2 3 Nuclear structure (neutron skin thickness, Pygmy DR, IAS) Slope of Symm Energy Importance of Nuclear Symmetry Energy ASYEOS Collaboration

8. supernovae,neutron stars) heavy ion collisions in the Fermi energy regime p, n Isospin Transport properties, (Multi-)fragmentation (diffusion, fractionation, migration) Asy-stiff Esym(rB)(MeV) rel. Heavy ion collisions Asy-soft 0 1 rB/r0 2 3 Nuclear structure (neutron skin thickness, Pygmy DR, IAS) Slope of Symm Energy Importance of Nuclear Symmetry Energy ASYEOS Collaboration

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

10. 1 exotic 3 4 Deconfinement for asymmetric matter earlier? Supernovae IIa neutron stars isospin dependent, pp,nn,pn In-medium! 1 2 Z/N, asymmetry degree of freedom 1 1 EOS 1 isoscalar and isovector (~10%) 2-body collisions gain term loss term Determination of nuclear SE in heavy ion collisions  Transport theory equation of motion in semiclass. approx: BUU equation • 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)

11. Investigation of the Symmetry Energy in Different Density Ranges neutron skin of Pb as ~ slope L (MeV) • r<<r0: expanding fireball in Fermi-energy heavy ion collisions. • cluster correlations at low density and temperature •  talk by C. Horowitz and my talk on monday • r<r0:Isospin transportin Fermi energy central • and peripheral collisions, (multi-)fragmentation, •  see talks by Betty Tsang • r~r0: structure and low energy excitations of (asymmetric) • nuclei: skin thickness, Pygmy resonances, IAS, • talk by Betty • r>r0:Intermediate energy heavy ioncollisions: • light cluster emission, • flow and particle production, •  more here • r>>r0: Ultrarelativistic HI collisions, • dependence of mixed and deconfinement phase on asymmetry? •  not here, e..g. DiToro, et al.,

12. n p K N t N D p Asy-stiff Asy-soft N N p Inel.collisions Particle product. NN->ND->NLK Np Flow, In-plane, transverse Squeeze-out, elliptic Pre-equilibr emiss. (first chance, high momenta) disintegration Y n neutron Yield and spectra of light part. e.g.asy-stiff n preferential n/p residual source more symm. n/p p en proton Differential p/n flow (or t/3He) flow diff # p,n (asymmetry of system) diff. force on n,p nn -> D- p np- pp -> D++ n p-/p+ pp+ (asystiff) Pion production Sketch of reaction mechanism at intermediate energies and observables Reaction mechanism can be tested with several observables: Consistency required!

13. Ratios of emitted pre-equilibrium particles 124Sn + 124Sn 112Sn + 112Sn asy-soft asy-stiff asy-soft asy-stiff „Double Ratios“ Data: Famiano, et al., PRL 06 SMF simulations, M.Pfabe IWM09 Early emitted neutrons and protons reflect difference in potentials in expanded source, esp. ratio Y(n)/Y(p). more neutron emission for asy-soft, since symm potential higher protons vs. neutrons 124Sn + 124Sn 112Sn + 112Sn softer symmetry energy closer to data qualitatively as seen in ImQMD, but quantitatively weaker B.Tsang, et al., PRL102, 122701 (09)

14. asy-soft at r0 (asystiff very similar) n-rich: 136Xe+124Sn n-poor, 124Xe+112Sn calc. using diff asy-stiffness and m*. protons protons data Etransv/A [MeV] Etransv/A [MeV] triton 3He triton 3He Look at ratios: p/n, t/3He, etc Etransv/A [MeV] Etransv/A [MeV] Check density and momentum dependence of symmetry energy in detail: 136,124Xe+124,112Sn, E = 32,…,150 AMeV data R. Bougault (Ganil, IWM11) prelim. calc. M. Pfabe

15. t/3He ratio t/3He ratio 1.5 Etrans/A [MeV] Check momentum dependence of SE: 136,124Xe+124,112Sn, E = 32,…,150 AMeV son: asysoft, mn*>mp* stn: asystiff, „ sop: asysoft, mn*<mp* stp: asystiff, „ Yield ratios 136Xe+124Sn, central Asy-EOS – eff mass dominates mn*<mp* soft n/p ratio stiff mn*>mp* E=65 AMeV E=100 AMeV E=32 AMeV Etrans/A [MeV] E=100 AMeV E=32 AMeV

16. t/3He ratio t/3He ratio 1.5 Prelim. data 136+124, 32 AMeV, INDRA favors a asy-stiff with mn*>mp* Etrans/A [MeV] 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 Asy-EOS – eff mass dominates mn*<mp* soft n/p ratio stiff mn*>mp* E=65 AMeV E=100 AMeV E=32 AMeV Etrans/A [MeV] E=32 AMeV The single t/3He ratios seem to be a promissing observable, double ratios under study

17. Global momentum space 132Sn + 132Sn @ 1.5 AGeV b=6fm r+d, stiff r n p differential elliptic flow Proton-neutron differential flow v1: sideward flow v2: elliptic flow Elliptic flow more sensitive, since particles emitted perpendicular r+d r+d r r T. Gaitanos, M. Di Toro, et al., PLB562(2003) “Flow“, Momentum distribution of emitted particles Fourier analysis of momentum tensor : „flow“

18. Au+Au @ 400 AMeV, FOPI-LAND (Russotto, et al., PLB 697, 471 (11)) neutron proton hydrogen directed flow (v1) not very sensitive, but elliptic flow (v2), originates in compressed zone determines a rather stiff symmetry energy (g~1) g=0.5 g=1.5 Each band: soft vs. stiff eos of symmetric matter, (Cozma, arXiv 1102.2728)  robust probe new ASYEOS experiment at GSI May 2011, being analyzed First measurement of isospin flow

19. Particle production as probe of symmetry energy B.A.Li et al., PRL102 NN ND p, n LK NLK Np in-medium in-elastic s , K and L potential (in-medium mass) D in-medium self-energies and width p potential , • Two limits: • isobar model • (yield determined by CG-Coeff of D->Np • 2. chemical equilibrium • -> p-/p+ hould be a good probe! box calculation Ferini et al., Difference in neutron and proton potentials • „direct effects“: difference in proton and neutron (or light cluster) emission and momentum distribution • „secondary effects“: production of particles, isospin partners p-,+, K0,+

20. Particle production as probe of symmetry energy Two effects: 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: Canonical momenta have to be conserved. To convert to kinetic momenta, the self energies enter In inelastic collisions, like nn->pD-, the selfenergies may change. Simple assumtion about self energies of D.. Yield of pions depends on Detailed analysis gives Competing effects! Not clear, whether taken into account in all works. Assumptions may also be too simple. G.Ferini et al.,PRL 97 (2006) 202301

21. soft Esym stiff Esym NLrd NLr NL Dynamics of particle production (D,p,K) in heavy ion collisions Au+Au@1AGeV Central density D and K: production in high density phase Pions: low and high density phase Sensitivity to asy-stiffness p and D multiplicity Dependence of ratioson 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

22. 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;

23. Other pion observables, or kaons or kaon ratios: Kaons were a decisive observable to determine the symmetric EOS. Au+Au perhaps other pion observables: flow

24. 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 S(r) [MeV] r/r0 Fermi Energy HIC, MSU p+/p- ratio B.A. Li, et al.

25. Summary and Outlook: • 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. • Different probes for the Symmetry Energy in heavy ion collisions with transport theory at different energy (density) ranges • Explore the sensitivity of observables to the ingredients (asy-EOS, momentum dependence of SymEn, medium, esp. isospin dependence of cross sections. • Consistent description of many observables mandatory, also from structure and astrophysics • High density region particularly open. Experimental constraints very important. Thank you!