W. Trautmann GSI Helmholtzzentrum, Darmstadt, Germany Symposium on applied nuclear physics and innovative technologies Kraków, June 5, 2013

binding energy of nuclei Tsang et al., PRC (2012) following Brown, PRL (2000) B(A,Z) = a V ·A - a S ·A 2/3 - a C ·Z 2 /A 1/3 - a sym ·(A-2Z) 2 /A + a P ·δ/A 1/2 nuclear matter E/A(ρ,δ) = E/A(ρ,δ=0) + E sym (ρ)·δ 2 + O(δ 4 ) a sym = 23.2 MeV with asymmetry parameter δ = (ρ n –ρ p )/ρ

isospin diffusion figure from Lattimer and Prakash, Phys. Rep. (2007) Tsang et al., PRL 102, (2009): 0.4≤ γ ≤1.0 ( 112,124 Sn+ 112,124 Sn, 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: E sym (ρ) ≈ 31.6·(ρ/ρ 0 ) 0.69 with IBUU04, Li and Chen, PRC72(2005) remember T. Twaróg, yesterday

 =1.5  =0.5 parameterization in transport theory: UrQMD, Q.F. Li et al. Fuchs and Wolter, EPJA 30 (2006) nuclear many-body theory the symmetry energy E sym = E sym pot +E sym kin L = 3ρ o ·dE sym /dρ at ρ=ρ 0 ρ/ρ0ρ/ρ0 asymmetry parameter δ = (ρ n –ρ p )/ρ E A (ρ,δ) = E A (ρ,0) + E sym (ρ) ∙ δ 2 + O(δ 4 ) γ L (MeV) = 22 MeV·(ρ/ρ 0 ) γ +12 MeV·(ρ/ρ 0 ) 2/3 linear supersoft

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

Tsang et al., PRC (2012)

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:

differential: neutrons vs. protons t vs. 3 He, 7 Li vs 7 Be,... UrQMD: significant sensitivity predicted; neutron vs. proton elliptic flows inverted reanalysis of FOPI-LAND data 400 MeV per nucleon: γ pot = 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) high density:elliptic flow (elliptic flow squeeze-out)) (directed flow) v 2 second azim. Fourier coeff.

differential: neutrons vs. protons t vs. 3 He, 7 Li vs 7 Be,... UrQMD: significant sensitivity predicted; neutron vs. proton elliptic flows inverted reanalysis of FOPI-LAND data 400 MeV per nucleon: γ pot = 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) high density:elliptic flow asy-stiff asy-soft UrQMD  =1.5  =0.5

differential: neutrons vs. protons t vs. 3 He, 7 Li vs 7 Be,... UrQMD: significant sensitivity predicted; neutron vs. proton elliptic flows inverted reanalysis of FOPI-LAND data 400 MeV per nucleon: γ pot = 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) high density:elliptic flow asy-stiff asy-soft UrQMD v 2 ratios  =1.5  =0.5

 =1.5  =0.5 param. in transport: UrQMD, Q.F. Li et al. the symmetry energy ρ/ρ0ρ/ρ0 FOPI/LAND γ L (MeV) E sym = E sym pot +E sym kin L = 3ρ o ·dE sym /dρ at ρ=ρ 0 L ≈ 80 MeV = 22 MeV·(ρ/ρ 0 ) γ +12 MeV·(ρ/ρ 0 ) 2/3 Fuchs and Wolter, EPJA 30 (2006) asymmetry parameter δ = (ρ n –ρ p )/ρ E A (ρ,δ) = E A (ρ,0) + E sym (ρ) ∙ δ 2 + O(δ 4 )

GSI Helmholtzzentrum für Schwerionenforschung

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

azimuthal angular distributions near target rapidity mostly directed flow at mid-rapidity strong squeeze-out near projectile rapidity mostly directed flow fitted with: f(Δφ)=a 0 *(1.0+2v 1 *cos(Δφ)+2v 2 *cos(2Δφ)) Δφ = φ particle – φ reaction plane and compared to UrQMD model predictions Q. Li et al., J. Phys. G 31(2005); 32 (2006) relative to the reaction plane for neutrons, background subtracted 0 Δφ 2 π

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

experiment in May 2011 ALADiN ToF-Wall Kraków hodoscope beam LANDCHIMERA

experiment in May 2011 beam LANDCHIMERA Kraków hodoscope coverage β t γ vs. y flow at mid-rapidity

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) high density: isotopic particle (double) ratios static calc. for infinite nucl. matter FOPI data HIC 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 Au+Au PRC (2007) Reisdorf et al., NPA 781 (2007) K + /K 0 ratio π - / π + ratio 40 Ca+ 40 Ca

authors of proposal 2009

summary and outlook L ≈ 60 MeV ( γ ≈ 0.6) from nuclear structure and reactions probing densities of ≈ 2/3 ρ 0 ; 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; γ pot = 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≤ρ 0 ) future: tidal polarizability of neutron stars via gravitational waves

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

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

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 Xiao et al., PRL 102 (2009) Feng and Jin, PLB 683 (2010) high density: inconsistent results from pion ratios π ratios + IBUU04: x=1 super soft π ratios + ImIQMD: SLy6 with  =2 very stiff

Fuchs and Wolter, EPJA 30 (2006) the symmetry energy asymmetry parameter δ = (ρ n –ρ p )/ρ E A (ρ,δ) = E A (ρ,0) + E sym (ρ) ∙ δ 2 + O(δ 4 ) parameterization in transport theory: Bao-An Li et al. force developed by Das, Das Gupta, Gale, and Bao-An Li, Phys. Rev. C 67 (2003) with explicit momentum dependence in the isovector part

from Bao-An Li, Lie-Wen Chen, Farrukh J. Fattoyev, William G. Newton and Chang Xu, arXiv: v1 Lecture at the International Summer School for Advanced Studies, July 2012, Predeal, Romania 21 refs10 refs the symmetry energy: present status (2012) near and below saturation density

neutron matter in the laboratory neutron skins e.g., 132 Sn, 208 Pb balance of asymmetry pressure inside and neutron-matter EoS at reduced density in skin δrδr r ρ neutron density ρ n proton density ρ p skin δR = 1/2 - 1/2

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

PREX I the Z 0 couples mainly to the neutron: weak charge of the proton: 1-4sinθ W with sinθ W =0.23 neutron radius of 208 Pb from parity-violating electron scattering Hall A Jefferson Lab polarized e GeV ≈ 60 μA 208 Pb target twin HRS θ lab ~ 5 o nearly only elastic events “a landmark for isospin physics” (Roca-Maza et al.) for first results see S. Abrahamyan et al., PRL 108 (2012)

7/7/2016W. Trautmann, GSI Darmstadt, Istanbul Coulomb excitation of the pygmy dipole resonance neutron(s) heavy fragment beam Crystal Ball with target Dipole magnet Aladin Neutron detector LAND ~20 m high-Z target projectile Coulomb excitation excitation energy reconstructed from four-momenta of all outgoing projectile- like particles and γ rays A. Klimkiewicz et al., PRC 76 (2007) (slide from talk at CHIMERA-GSI workshop)