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The symmetry energy at high density: experimental probes

The symmetry energy at high density: experimental probes. W. Trautmann GSI Helmholtzzentrum, Darmstadt, Germany. Symposium on applied nuclear physics and innovative technologies Kraków, June 5, 2013. binding energy of nuclei.

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The symmetry energy at high density: experimental probes

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  1. The symmetry energy at high density:experimental probes W. Trautmann GSI Helmholtzzentrum, Darmstadt, Germany Symposium on applied nuclear physics and innovative technologies Kraków, June 5, 2013

  2. binding energy of nuclei B(A,Z) = aV·A - aS·A2/3 - aC·Z2/A1/3 - asym·(A-2Z)2/A + aP·δ/A1/2 asym = 23.2 MeV Tsang et al., PRC (2012) following Brown, PRL (2000) nuclear matter E/A(ρ,δ) = E/A(ρ,δ=0) + Esym(ρ)·δ2 + O(δ4) with asymmetry parameter δ = (ρn–ρp)/ρ

  3. isospin diffusion remember T. Twaróg, yesterday figure from Lattimer and Prakash, Phys. Rep. (2007) Tsang et al., PRL 102, 122701 (2009): 0.4≤γ≤1.0 (112,124Sn+112,124Sn, 50 AMeV) 45 MeV ≤L≤ 100 MeV from isospin diffusion and neutron-proton double ratios interpreted with ImQMD calculations by Y. Zhang et al. recently M.B. Tsang, PRC 86 (2012): L = 70 ± 15 MeV previously: Esym(ρ) ≈ 31.6·(ρ/ρ0)0.69 with IBUU04, Li and Chen, PRC72(2005)

  4. =1.5 =0.5 the symmetry energy 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 linear supersoft ρ/ρ0 Fuchs and Wolter, EPJA 30 (2006) nuclear many-body theory 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

  5. slide from talk of X. Viñas, ECT*, Trento, June 2011

  6. slide from talk of X. Viñas, ECT*, Trento, June 2011 Tsang et al., PRC (2012)

  7. high density: needs higher energy observables: collective flows and meson production central density number of baryons and average density in high –density phase Xu et al., arXiv:1305.0091

  8. (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, review in IJMPE 21 (2012) (directed flow) v2 second azim. Fourier coeff.

  9. high density:elliptic flow asy-stiff =1.5 UrQMD 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, review in IJMPE 21 (2012) asy-soft =0.5

  10. high density:elliptic flow asy-stiff =1.5 UrQMD 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, review in IJMPE 21 (2012) asy-soft =0.5 v2 ratios

  11. =1.5 =0.5 the symmetry energy EA(ρ,δ) = EA(ρ,0) + Esym(ρ) ∙ δ2 + O(δ4) param. in transport: UrQMD, Q.F. Li et al. asymmetry parameter δ = (ρn–ρp)/ρ FOPI/LAND ρ/ρ0 Fuchs and Wolter, EPJA 30 (2006) Esym = Esympot+Esymkin L = 3ρo·dEsym/dρ at ρ=ρ0 L ≈ 80 MeV = 22 MeV·(ρ/ρ0)γ+12 MeV·(ρ/ρ0)2/3 γ L (MeV) 0.5 57 1.0 90 1.5 123

  12. GSI Helmholtzzentrum für Schwerionenforschung

  13. main yield here FOPI/LAND experiment acceptance in pt vs. rapidity SB: shadow bar for background measurement Forward Wall for centrality and reaction-plane orientation >700 elements SB Large Area Neutron Detector LAND 2 LAND 1 5 m neutron squeeze-out: Y. Leifels et al., PRL 71, 963 (1993)

  14. azimuthal angular distributions relative to the reaction plane for neutrons, background subtracted near target rapidity mostly directed flow at mid-rapidity strong squeeze-out near projectile rapidity mostly directed flow fitted with: f(Δφ)=a0*(1.0+2v1*cos(Δφ)+2v2*cos(2Δφ)) Δφ = φparticle – φreaction plane and compared to UrQMD model predictions Q. Li et al., J. Phys. G 31(2005); 32 (2006) 0 Δφ 2π

  15. AsyEos experiment S394 in May 2011 studied reactions: 197Au + 197Au @ 400 A MeV 96Ru + 96Ru @ 400 A MeV 96Zr + 96Zr @ 400 A MeV KRATTA ALADIN ToF wall four rings of μ-ball four double rings of CHIMERA μ-ball, CHIMERA, ALADIN Tof-wall for impact parameter orientation and modulus

  16. CHIMERA LAND beam Kraków hodoscope experiment in May 2011 ALADiN ToF-Wall

  17. CHIMERA LAND Kraków hodoscope beam experiment in May 2011 coverage βtγ vs. y flow at mid-rapidity

  18. high density: isotopic particle (double) ratios FOPI data π-/ π+ ratio K+/K0 ratio Reisdorf et al., NPA 781 (2007) PRC (2007) Au+Au static calc. for infinite nucl. matter HIC 40Ca+40Ca • 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

  19. The Asy-Eos Collaboration authors of proposal 2009

  20. summary and outlook • L ≈ 60 MeV (γ ≈ 0.6) from nuclear structure and reactions probing densities of ≈ 2/3 ρ0; big expectations on PREXII, CREX (2015) • increasingly more precise data from neutron-star observations, typically L ≈ 40 MeV; e.g. Steiner, Lattimer and Brown, ApJ (2010) • high-densities probed in reactions at SIS energies; • γpot = 0.9 ± 0.4 from FOPI/LAND elliptic flow; • super-soft ruled out; study 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 • interesting new results from effective field theory (ρ≤ρ0) • future: tidal polarizability of neutron stars via gravitational waves

  21. parameter test with Tübingen QMD*) M.D. Cozma et al., arXiv:1305.5417 difference of neutron and proton squeeze-outs Au + Au @ 400 A MeV conclusion: super-soft not compatible with FOPI-LAND data first 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 dep. of NNECS asymmetry dep. of NNECS width L of nucleon wave packet momentum dependence of isovector potential superstiff supersoft *) V.S. Uma Maheswari, C. Fuchs, Amand Faessler, L. Sehn, D.S. Kosov, Z. Wang, NPA 628 (1998)

  22. parameter test with Tübingen QMD*) M.D. Cozma et al., arXiv:1305.5417 difference of neutron and proton squeeze-outs Au + Au @ 400 A MeV conclusion: super-soft not compatible with FOPI-LAND data superstiff supersoft *) V.S. Uma Maheswari, C. Fuchs, Amand Faessler, L. Sehn, D.S. Kosov, Z. Wang, NPA 628 (1998)

  23. high density: inconsistent results from pion ratios analysis of π-/π+ ratios in Au+Au at 400 A MeV FOPI data, Reisdorf et al., NPA (2007) π ratios + IBUU04: x=1 super soft π ratios + IBUU04: x=1 super soft π ratios + ImIQMD: SLy6 with =2 very stiff Xiao et al., PRL 102 (2009) Feng and Jin, PLB 683 (2010)

  24. the symmetry energy EA(ρ,δ) = EA(ρ,0) + Esym(ρ) ∙ δ2 + O(δ4) parameterization in transport theory: Bao-An Li et al. asymmetry parameter δ = (ρn–ρp)/ρ Fuchs and Wolter, EPJA 30 (2006) 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

  25. the symmetry energy: present status (2012) near and below saturation density 21 refs 10 refs from Bao-An Li, Lie-Wen Chen, Farrukh J. Fattoyev, William G. Newton and Chang Xu, arXiv:1212.0284v1 Lecture at the International Summer School for Advanced Studies, July 2012, Predeal, Romania

  26. δr neutron matter in the laboratory neutron skins e.g., 132Sn, 208Pb ρ neutron density ρn proton density ρp skin δR = <rn2>1/2 - <rp2>1/2 r balance of asymmetry pressure inside and neutron-matter EoS at reduced density in skin

  27. the nuclear equation of state from nuclear many-body theory why so uncertain at high density? related to uncertainty of three-body and tensor forces at high density balance determines skin thickness Esym Fuchs and Wolter, EPJA 30 (2006) normal nuclear density

  28. PREX I neutron radius of 208Pb from parity-violating electron scattering Hall A Jefferson Lab polarized e- 1.06 GeV ≈ 60 μA 208Pb target twin HRS θlab ~ 5o nearly only elastic events “a landmark for isospin physics” (Roca-Maza et al.) for first results see S. Abrahamyan et al., PRL 108 (2012) the Z0 couples mainly to the neutron: weak charge of the proton: 1-4sinθW with sinθW=0.23

  29. Coulomb excitation of the pygmy dipole resonance projectile Coulomb excitation high-Z target Neutron detector LAND heavy fragment neutron(s) Dipole magnet Aladin ~20 m excitation energy reconstructed from four-momenta of all outgoing projectile-like particles and γ rays Crystal Ball with target beam A. Klimkiewicz et al., PRC 76 (2007) (slide from talk at CHIMERA-GSI workshop) 8/15/2014 W. Trautmann, GSI Darmstadt, Istanbul 2008 30

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