International Workshop on Nuclear Dynamics and Thermodynamics Probing nuclear symmetry energy with nucleon collective flow W. Trautmann GSI Helmholtzzentrum, Darmstadt, Germany Cozma et al. Russotto et al. International Workshop on Nuclear Dynamics and Thermodynamics Texas A&M University, College Station, Texas August 19-22, 2013 1

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 3

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 Russotto, Wu, Zoric, Chartier, Leifels, Lemmon, Li, Łukasik, Pagano, Pawłowski, Trautmann, PLB 697 (2011) 471 Trautmann and Wolter, IJMPE 21 (2012) Russotto et al., EPJA special volume, submitted (directed flow) v2 second azim. Fourier coeff.

UrQMD: Qingfeng Li et al. high density: elliptic flow UrQMD: Qingfeng Li et al. 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 Russotto, Wu, Zoric, Chartier, Leifels, Lemmon, Li, Łukasik, Pagano, Pawłowski, Trautmann, PLB 697 (2011) 471 Trautmann and Wolter, IJMPE 21 (2012) 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 conclusion: super-soft not compatible with FOPI-LAND data iso-soft iso-stiff 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? 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) 9

more systematic parameter test with Tübingen QMD*) M.D. Cozma et al., arXiv:1305.5417 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) 10

parameter test with Tübingen QMD*) M.D. Cozma et al., arXiv:1305.5417 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) 11

parameter tests with Tübingen QMD and UrQMD M.D. Cozma et al., arXiv:1305.5417 elliptic-flow ratio and difference Au + Au @ 400 A MeV averaged result: x = -1.0±1.0 L = 106±46 MeV Cozma et al. Russotto et al. 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] 12

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

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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

summary and outlook high-densities probed in reactions at SIS energies; γpot = 0.9 ± 0.4 from FOPI/LAND elliptic flow (2011); super-soft ruled out; studies of model invariance under way; 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 NeuLAND

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