and the nuclear equation of state Flow observables and the nuclear equation of state W. Trautmann GSI Helmholtzzentrum, Darmstadt, Germany 52nd International Winter Meeting on Nuclear Physics Bormio, January 27- 31, 2014

FOPI data: directed and elliptic flow and IQMD for Au+Au at 1.5 AGeV SM favored by directed and elliptic flows FOPI data: directed and elliptic flow and IQMD for Au+Au at 1.5 AGeV protons, deuterons, tritons 0.4 – 1.5 AGeV W. Reisdorf et al., NPA 876 (2012) see also, Danielewicz et al., Science 298 (2002)

dN/d(Φ-ΦR) = N0/2π · (1+2Σvncosn(Φ-ΦR)) v2 second azim. Fourier coeff. collective flow (elliptic flow, squeeze-out)) (directed flow) dN/d(Φ-ΦR) = N0/2π · (1+2Σvncosn(Φ-ΦR))

the symmetry energy =1.5 =0.5 γ L (MeV) EA(ρ,δ) = EA(ρ,0) + Esym(ρ) ∙ δ2 + O(δ4) parameterization in transport theory: UrQMD, Q.F. Li et al. asymmetry parameter δ = (ρn–ρp)/ρ =1.5 =0.5 linear supersoft ρ/ρ0 Fuchs and Wolter, EPJA 30 (2006) nuclear many-body theory Brueckner-Hartree-Fock (BHF) approach using the realistic Argonne V18 nucleon-nucleon potential plus a phenomenological three-body force of Urbana type. Esym = Esympot+Esymkin L = 3ρo·dEsym/dρ at ρ=ρ0 = 22 MeV·(ρ/ρ0)γ+12 MeV·(ρ/ρ0)2/3 γ L (MeV) 0.5 57 1.0 90 1.5 123

with explicit momentum dependence in the isovector part the symmetry energy EA(ρ,δ) = EA(ρ,0) + Esym(ρ) ∙ δ2 + O(δ4) parameterization in transport theory: MDI, Chen et al. asymmetry parameter δ = (ρn–ρp)/ρ Fuchs and Wolter, EPJA 30 (2006) nuclear many-body theory Brueckner-Hartree-Fock (BHF) approach using the realistic Argonne V18 nucleon-nucleon potential plus a phenomenological three-body force of Urbana type. force developed by Das, Das Gupta, Gale, and Bao-An Li, Phys. Rev. C 67 (2003) 034611 with explicit momentum dependence in the isovector part 5

"A way forward in the study of the symmetry energy ..." Horowitz et al., arXiv:1401.5839 maximum sensitivity of structure data near 2/3 ρ0 Zhang and Chen (arXiv:1302.5327) use isotope binding energy difference and neutron skin thickness of Sn isotopes; B.A. Brown (arXiv:1308.3664) uses Skyrme, properties of doubly-magic nuclei (binding energies, rms charge radii, and single-particle energies) and Δrnp=0.20 fm for 208Pb.

high density: elliptic flow squeeze-out)) high density: elliptic flow differential: neutrons vs. protons t vs. 3He, 7Li vs 7Be, ... UrQMD: significant sensitivity predicted; neutron vs. proton elliptic flows inverted reanalysis of FOPI-LAND data Au+Au @ 400 MeV per nucleon: γpot = 0.9 ± 0.4 from n-H ratios L = 83 ± 26 MeV Russotto, Wu, Zoric, Chartier, Leifels, Lemmon, Li, Łukasik, Pagano, Pawłowski, Trautmann, PLB 697 (2011) 471 Trautmann and Wolter, IJMPE 21, 1230003 (2012) Cozma et al., PRC 88, 044912 (2013) Russotto et al., EPJA special volume, submitted (directed flow) v2 second azim. Fourier coeff.

high density: elliptic flow UrQMD: Q. Li et al., arXiv_1305.4730 differential: neutrons vs. protons t vs. 3He, 7Li vs 7Be, ... UrQMD: significant sensitivity predicted; neutron vs. proton elliptic flows inverted reanalysis of FOPI-LAND data Au+Au @ 400 MeV per nucleon: γpot = 0.9 ± 0.4 from n-H ratios L = 83 ± 26 MeV Russotto, Wu, Zoric, Chartier, Leifels, Lemmon, Li, Łukasik, Pagano, Pawłowski, Trautmann, PLB 697 (2011) 471 Trautmann and Wolter, IJMPE 21, 1230003 (2012) Cozma et al., PRC 88, 044912 (2013) Russotto et al., EPJA special volume, submitted 0.25 < b0 < 0.45 ard oft data: Reisdorf et al., NPA (2012) graphics by Y. Leifels

FOPI/LAND experiment acceptance in pt vs. rapidity SB LAND 2 LAND 1 SB: shadow bar for background measurement Forward Wall for centrality and reaction-plane orientation SB Large Area Neutron Detector main yield here LAND 2 LAND 1 5 m neutron squeeze-out: Y. Leifels et al., PRL 71, 963 (1993)

results from FOPI/LAND Experiment =1.5 linear =0.5 =1.5 =0.5 neutron/hydrogen FP1: γ = 1.01 ± 0.21 FP2: γ = 0.98 ± 0.35 neutron/proton FP1: γ = 0.99 ± 0.28 FP2: γ = 0.85 ± 0.47 adopted: γ = 0.9 ± 0.4

Qingfeng Li et al., Phys. Rev. C 83, 044617 (2011) parameterizations in UrQMD Medium modifications (FU1, …) and momentum dependence (FP1, …) of nucleon-nucleon elastic Xsections v2 40% larger with FP2 small effect on ratios =ρ/ρ0 Qingfeng Li et al., Phys. Rev. C 83, 044617 (2011)

analysis with Tübingen QMD*) M.D. Cozma, PLB 700, 139 (2011) difference of neutron and proton squeeze-outs Au + Au @ 400 A MeV steps towards model invariance: tested in UrQMD: FP1 vs. FP2, i.e. momentum dep. of NNECS tested in T-QMD: soft vs. hard compressibility K density dependence of NNECS asymmetry dependence of NNECS width L of nucleon wave packet can this be done more systematically? iso-soft iso-stiff effective mass scaling model for the in-medium NN cross-sections and explicit momentum dependence of the symmetry energy part. Requires experimental data for the elliptic flow of both charged and neutral particles of high quality, of an accuracy of 1% or better. bands show uncertainty due to isoscalar field “soft to hard” *) V.S. Uma Maheswari, C. Fuchs, Amand Faessler, L. Sehn, D.S. Kosov, Z. Wang, NPA 628 (1998) 12

more systematic parameter test with Tübingen QMD*) M.D. Cozma et al., PRC 88, 044912 (2013) elliptic flow ratio and difference Au + Au @ 400 A MeV conclusion: super-soft not compatible with FOPI-LAND data steps towards model invariance: tested in UrQMD: FP1 vs. FP2, i.e. momentum dep. of NNECS tested in T-QMD: soft vs. hard 190<K<280 MeV density dependence of NNECS asymmetry dependence of NNECS wave packet 2.5<L<7.0 fm2 optical potential momentum dep. of isovector potential effective mass scaling model for the in-medium NN cross-sections and explicit momentum dependence of the symmetry energy part. Requires experimental data for the elliptic flow of both charged and neutral particles of high quality, of an accuracy of 1% or better. superstiff supersoft *) V.S. Uma Maheswari, C. Fuchs, Amand Faessler, L. Sehn, D.S. Kosov, Z. Wang, NPA 628 (1998) 13

more systematic parameter test with Tübingen QMD*) elliptic flow difference steps towards model invariance: tested in UrQMD: FP1 vs. FP2, i.e. momentum dep. of NNECS tested in T-QMD: soft vs. hard 190<K<280 MeV density dependence of NNECS asymmetry dependence of NNECS wave packet 2.5<L<7.0 fm2 optical potential momentum dep. of isovector potential effective mass scaling model for the in-medium NN cross-sections and explicit momentum dependence of the symmetry energy part. Requires experimental data for the elliptic flow of both charged and neutral particles of high quality, of an accuracy of 1% or better. superstiff supersoft *) V.S. Uma Maheswari, C. Fuchs, Amand Faessler, L. Sehn, D.S. Kosov, Z. Wang, NPA 628 (1998) 14

more systematic parameter test with Tübingen QMD*) elliptic flow ratio steps towards model invariance: tested in UrQMD: FP1 vs. FP2, i.e. momentum dep. of NNECS tested in T-QMD: soft vs. hard 190<K<280 MeV density dependence of NNECS asymmetry dependence of NNECS wave packet 2.5<L<7.0 fm2 optical potential momentum dep of isovector potential effective mass scaling model for the in-medium NN cross-sections and explicit momentum dependence of the symmetry energy part. Requires experimental data for the elliptic flow of both charged and neutral particles of high quality, of an accuracy of 1% or better. superstiff supersoft *) V.S. Uma Maheswari, C. Fuchs, Amand Faessler, L. Sehn, D.S. Kosov, Z. Wang, NPA 628 (1998) 15

parameter tests with Tübingen QMD and UrQMD M.D. Cozma et al., PRC 88, 044912 (2013) elliptic-flow ratio and difference Cozma et al. Russotto et al. averaged result: x = -1.0±1.0 L = 106±46 MeV conclusion: super-soft not compatible with FOPI-LAND data effective mass scaling model for the in-medium NN cross-sections and explicit momentum dependence of the symmetry energy part. Requires experimental data for the elliptic flow of both charged and neutral particles of high quality, of an accuracy of 1% or better. for comparison with IBUU04 see Qingfeng Li et al., arXiv:1306.4783[nucl-th] 16

Asy-Eos experiment S394 in May 2011

Asy-Eos experiment S394 in May 2011 CHIMERA, ALADIN Tof-wall, μ-ball, for impact parameter orientation and modulus studied reactions: 197Au + 197Au @ 400 A MeV 96Ru + 96Ru @ 400 A MeV 96Zr + 96Zr @ 400 A MeV

19

CHIMERA LAND beam Kraków hodoscope ALADiN ToF-Wall CHIMERA

CHIMERA LAND beam KraTTA (see NIMA) ALADiN ToF-Wall neutron flow at mid-rapidity

a first preliminary result CHIMERA LAND a first preliminary result Russotto (INPC 2013) γ = 0.9 ± 0.6 0.35 < y < 0.55 b < 7.5 fm beam neutron flow at mid-rapidity

latest news from Catania: 1991 data, Russotto et al., PLB 697, 471 2011 data, Russotto et al., 2014, preliminary γ = 0.84 ± 0.11 L= 79 ± 8 MeV γ = 1.01±0.21 preliminary result from S394: obviously less fluctuations and smaller errors, previous result confirmed within uncertainties

summary and outlook high-densities probed in reactions at SIS energies; γpot = 0.9 ± 0.4 from FOPI/LAND elliptic flow (2011); super-soft and super-stiff ruled out; studies of model invariance under way: L = 80 – 110 MeV; analysis of ASY-EOS experiment in progress! kaon and pion ratios interesting probes but results presently inconclusive: new activity at RIKEN (Samurai) and MSU; HADES kaon data for Ar+KCl and Au+Au potentially useful; new model studies for kaon ratios? future: PREX and CREX in 2015 heavier neutron stars and smaller radii? tidal polarizability of neutron stars via gravitational waves?? FAIR operating in 2019!

present outlook on FAIR

present outlook on FAIR NeuLAND

K+/K0 double ratio 2014: Horowitz et al., arXiv:1401.5839 96Zr+96Zr cite Ferini et al. PRL 97 (2006) 96Zr+96Zr 96Ru+96Ru X. Lopez et al. PRC (2007) static calc. for infinite nucl. matter Au+Au 1AGeV different assumptions on symmetry energy FOPI data HIC HIC scenario: - fast neutron emission (mean field) NN=>NΔ threshold effects nn=>pΔ- (no chemical equilibrium) see, e.g., di Toro et al., J.Phys.G (2010) pion ratios presently inconclusive

high density: isotopic particle (double) ratios FOPI data K+/K0 ratio π-/ π+ ratio Reisdorf et al., NPA 781 (2007) PRC (2007) static calc. for infinite nucl. matter Au+Au HIC 40Ca+40Ca the HIC scenario exhibits two important dynamical effects: fast neutron emission (mean field effect) and transformation of neutron into proton in inelastic channels (no-chemical equilibrium HIC scenario: - fast neutron emission (mean field) NN=>NΔ threshold effects nn=>pΔ- (no chemical equilibrium) see, e.g., di Toro et al., J.Phys.G (2010) Ferini et al. (RMF) stiffer for ratio up Xiao et al. (IBUU) softer “ Feng & Jin (ImIQMD) stiffer “ Xie et al. (ImIBL) softer “ consequence: extremely stiff (soft) solutions

Danielewicz et al., Science 298 (2002) symmetric matter KAOS data K+ ratios Au+Au vs. C+C normalized to <Apart> ... ... favor soft EoS 1 A GeV Au+Au pressure contours density contours flow data rule out repulsive and super-soft EoS Danielewicz et al., Science 298 (2002) Sturm et al., Fuchs et al., PRL 86 (2001)

γ = 0.84 ± 0.11 L= 79 ± 8 MeV

2013: Li and Han, arXiv:1304.3368 analyses of terrestrial experiments average: S0 = 31.5 MeV astrophysical observations astrophysical observations analyses of terrestrial experiments average: L = 58.9 MeV