The Nuclear Equation-of-State and the Symmetry Energy

Transcription

1 The Nuclear Equation-of-State and the Symmetry Energy Connections between astrophysics and heavy ion colisions Hermann Wolter, University of Munich, Germany Science Day, Research Area G, DFG Excellence Cluster Origin and Structure of the Universe Garching, July 9, 015

2 Equation-of-State and Symmetry Energy densityasymmetry dep. of nucl.matt. Many-Body calculations: Rel, Brueckner Variational Rel. Mean field Chiral perturb. 4 E( ρb, δ ) / A = Enm( ρb ) + Esym( ρb ) δ + O( δ ) +... Symmetry energy Why is symmetry energy so uncertain?? Short range isovector tensor correlations; 3-body forces E sym (MeV) δ = ρ ρ n n asystiff asysoft ρ + ρ p p C. Fuchs, H.H. Wolter, EPJA 30(006)5 Heavy ion collisions to investigate EoS in the laboratory non-equilibrium, transport theory

3 Importance of the Nuclear Symmetry Energy in Nuclear and Astro-Physics 4 E( ρ, δ ) / A = E( ρ ) + Esym ( ρ ) δ + O( δ ) +... Heavy ion collisions in the Fermi energy regime; multifragmentation δ = ρ n ρ ρ p traditional NS or other? E sym (ρ Β ) (MeV) 0 Light cluster correlations at very low density, E sym >0 Asy-stiff Asy-soft 1 ρ Β /ρ 3 0 supernovae Nuclear structure (neutron skin thickness, Pygmy DR, IAS) Slope of Symm Energy supernova simulations covers large range of thermodyn. conditions

4 Large range of thermodynamic conditions in astrophysical applications core collapse supernovae mass-radius relation of neutron stars determined uniquely for gives EoS 1/1000<ρ/ρ 0 <-3 T=0-50 MeV 0.1<x p <0.5 solar mass NS analysis by S. Guillot, R. Rutledge, APJ 77, 7G (013) R NS =9.1±1.4km (assume pure H atmospheres and identical radii for all NS) analysis by A. Steiner, J. Latitmer, E. Brown, APJ Lett, 765, L5 (013) R NS = km (Bayesian analysis of qlmxb s)

5 Recent reviews of the Nuclear Symmetry Energy Vol. 50 J. Phys. G: Nucl. Part. Phys. 41 (014)

6 Clustering of very dilute nuclear matter x=proton fraction decrease energy by inhomogeneity fractionation into clusters at higher density and neutron gas x=0 neutron matter x=0.5 symm matter very low density: p,n composition as fct of density Mott density: clusters melt, homogeneous p,n matter; Increasing density: clusters arise: deuteron first, but then α dominates here heavier nuclei (embedded into a gas) become important here Can this be cecked in heavy ion collisions? yes!

7 Investigation of warm, low density matter in heavy ion collisions Semi-central heavy ion collisions, ( 64 Zn+ 9 Mo, 197 Au at 35MeV/A) and time-resolved measurement of light fragments from decay of fireball S. Kowalski, J. Natowitz, et al.,prc (007) J. Natowitz, G. Röpke,, HHW, PRL 104, 0501 (010) extracted symmetry energy in comp. with quantumstat. calculation of clusters in medium trajectory of evolution of expanding source time, cooling conditions of neutrinosphere: densities 1/1000 to 1/10 ρ ο temperature T=1-5 MeV asymmetry Y e =

8 Results relevant for neutrino opacity in ν-sphere in CC SNe workshop in ECT*, Trento ν sphere ν-opacities important for ν-driven wind and r-process nucleosynthesis direct interface with heavy ion physics, Supernova Femtonova (heavy ion collision)

9 Chemical Equilibrium Constants for light clusters in different clusterization models alpha deuteron comparison of equilibrium constants (rather than particle fractions), more robust 3He triton theories with medium modifications of light clusters work very well: QS (Quantumtat. Green fct. Röpke et al.), grdf (gen. Rel. Dens. Funct., Typel etal,) many traditional SN EoS not so well M.Hempel, et al., PRC 91 (015)

10 S. Typel (GSI), M. Oertel (LUTH Paris), T. Klähn (Wroclaw)

11 Correlation of parameters of Symmetry Energy and with experiment e.g. expansion of Symmetry energy around saturation E sym ( ρ ) S( ρ ) = S 0 + L 3 ρ ρ0 ρ 0 K + 18 correlations derived from different observables may determine S 0,L sym ρ ρ 0 + ρ0 ρ 3 ρ0 SE fitted to nuclear masses cross below saturation density, (average density of a finite nucleus) induces a correlation between value and slope at ρ 0, eg. in lin. approx. 1 S( ρ 3 ρ0 ) = S 0 9 L correlations between model parameters and between model parameters and observables in two models (SLy5, DDRMF, G. Colo, Nusym15) J.Lattimer, A. Steiner, EPJA 50, 40 (014) Note: correlations are model dependent!

12 p, n ± π,k +, 0 - Directed flow not very sensitive to SE (involves many different densities) - Elliptic flow in this energy region probe of high density The Symmetry Energy at High Density Fourier analysis azimuthal distribution ( Θ ; y, p ) = N ( 1 + v cosθ + v cos Θ...) 400 AMeV, FOPI-LAND neutron proton hydrog en γ=1.5 γ=0.5 (Russotto, et al., PLB 697, 471 (11)) N t v 1 : directed flow E sym ( ρ ) = 1 3 ε F ρ ρ 0 v : Elliptic flow / 3 not very precise (yet) but indicates rather stiff SE, γ~1 γ ρ ρ + C 0 preliminary result from new experiment ASY-EOS (Russotto,NuSYM 015, Krakow)

13 Constraints on EOS of symmetric nuclear matter -pressure-density diagram -analysisin a particular model, shaded area constraint in this model -densitiesin therange from 4.5 ρ 0 -eliminatessome extreme model (P.Danielewicz, et al., Science 98(0)159) Limits on the EOS in β-equilibrium ratio of K+ production in heavy (Au+Au, compression) relative to light system (C+C,small compression) favors soft EOS C. Fuchs, PPNP56(06) constraints on EoS of symmetric nuclear matter from HIC, neutron stars, and microscopic calculations seem to converge to soft EoS A. Steiner, J. Lattimer, E.F.Brown, arxiv

14 Constraints on the Symmetry Energy n/p flow at MeV/A symmetry energy rather stiff mass fits clusterization at very low density HICollis isobaric analog states π /π+ ratio, still a difficulty!

15 SUMMARY: Equation-of-State (EoS) of nuclear matter of interest in itself and important imput for astrophysics (CC-SN, nucleosythesis, NS structure) Investigation of EoS in the laboratory in Heavy Ion Collisions (interpretation in complex transport models) EoS of symmetric nuclear matter (ρ n =ρ p ) fairly well determined, but symmetry energy area of very active investigations experimentally (new facilities) and theoretically: constraints around ρ 0 rather stringent cluster effects at very low densities, corresponding cond. of ν-sphere few experiments for high density, biggest uncertainty

16 Thanks to my collaborators: Heavy ion collisions: Maria Colonna, Massimo Di Toro, Enzo Greco, Joseph Rizzo (Lab. Naz. del Sud, INFN, Catania), Malgorzata Zielinska-Pfabe (Smith Coll. Mass, USA) Theo Gaitanos (Univ. Thesaloniki), et al., Clustering in dilute Matter, SN and NS EoS: Stefan Typel (Navi, GSI) Gerd Röpke (Univ. of Rostock) David Blaschke, Thomas Klähn (Univ. of Wroclaw) Discussions with Experiment: Wolfgang Trautmann (GSI) Betty Tsang, W, Lynch (MSU) Abdou Chbihi (GANIL), and many other and to you for your attention

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18 Example: Ratios of emitted pre-equilibrium particles in central collisions n,p,t, 3 He,α Early emitted Light Clusters reflect difference in potentials in expanded source, e.g. ratio Y(n)/Y(p). Y(n)/Y(p) 136 Xe+ 14 Sn, 150 MeV Y(t)/Y( 3 He) 14 Sn+ 14 Sn, 150 MeV asysoft m n *<m p * asystiff m n *>m p * Asy-EOS dominates for slow particles; asysoft has larger repulsion at lower densities son: asysoft, m n *>m p * stn: asystiff, m n *>m p * sop: asysoft, m n *<m p * stp: asystiff, m n *<m p * Effective mass dominates for fast particles; smaller eff. mass favors emission H.H. Wolter, et al., EPJ Web of Conf. &&, (014) Effect also exists for light clusters (easier to measure) but somewhat reduced Y. Zhang, M.B.Tsang,et al., PLB 73, 186 (014) similar findings for Sn+Sn collisions (MSU) role of clusters?

19 Composition of dilute matter x proton fraction decrease energy by inhomogeneity fractionation into clusters at higher density and neutron gas x=0 neutron matter x=0.5 symm matter p x P clust p F ρ Pauli-correlations weakens cluster: medium effects dep. on ρ, T, P clust, e.g. change of binding energy x clusterization increases with ρ,t, P cm

20 Particle Fractions very low density: p,n Increasing density: clusters arise: deuteron first, but then α dominates S.Typel, G. Röpke, et al., PRC 81 (010) Mott density: clusters melt, homogeneous p,n matter; here heavier nuclei (embedded into a gas) become important here composition as fct of Temp. heavy cluster fraction Symmetry Energy comparison to data from heavy ion collisions finite at T=0 due to PT

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23 Chemical Equilibrium Constants for light clusters in different clusterization models alpha deuteron 3He triton M.Hempel, et al., PRC 91 (015)

24 A. Steiner, et al., ApJ 765, L5 (013)

25 Status of determination of symmetry energy around saturation density: E sym ( ρ ) S( ρ ) = S L vs. S L ρ ρ K ρ0 18 sym ρ ρ 0 ρ0 + S vs. ρ nuclear mass fits isobaric analog states dipole excitations heavy ion collisions clustering at very low densities A consistent picture emerges!

26 Transport equations Boltzmann-Ühling-Uhlenbeck (BUU) f t + p m ( r ) f U( r ) ( p ) f ( r, p ; t ) = dv dv dv v 3 ( Ω ) ( π ) δ ( p + p [ f f ( 1 f )(1 f ) f f ( 1 f )(1 f ' ) ] 1 ' ' 1 ' 1 ' 1 σ ' 1 p 1 ' p ' ) Can be derived: Classically from the Liouville theorem Semiclassically from THDF From non-equilibrium theory (Kadanoff-Baym) collision term included mean field and in-medium cross sections consistent, e.g. from BHF collision term added (and fluctuations) T T T T Spectral fcts, off-shell transport, quasi-particle approx. ( x, p ) ( p * Γ ( x, p ) m * ) + Γ ( A x, p ) Γ x, p ) = m * Im Σ + p * Im ( s QPA + µ µ Σ δ ( p * m * ) Θ( p * 0 ) Transport theory is on a well defined footing, in principle

27 6. Flow observables Flow Observables y x Measurement of momenta of emitted particles: i.e. momentum tensor. Possible to measure for all particles: p,n, d,..,α, fragments, mesons (π, π,k,η),.. z Rapidity distribution (stopping) dn/dy before Transverse flow (compression) <p x > Flow modern approach: after y/y beam y/y beam rapidity : N ( Θ ; y, p t, b ) = N 0 ( 1 + v 1 ( y, p t ) cos Θ + v ( y, pt ) cos Θ +... y = 1 1+ β z ln 1 β z v 1 : Sideward flow v : Elliptic flow impact parameter selection: Observable that is strongly crrelated to impact parameter, like mutiplicity, transvers energy, etc. charged particle multipli city charged part. multipl. pmul1 pmul5 impact parameter b