Equation of state of asymmetricic nuclear matter at supra- saturation densities CBM collaboration meeting April 15, 2010, Darmstadt, Germany Laboratory for nuclear physics Division of Experimental Physics Ruđer Bošković Institute, Zagreb, Croatia Laboratory for nuclear physics Division of Experimental Physics Ruđer Bošković Institute, Zagreb, Croatia Zoran Basrak 1950 – 2010

 Introduction  Symmetry energy  Low densities  High density  Ongoing projrcts  Summary and outlook Outline

*D.H. Youngblood et al., PRL 82 (1999) 691 From the nuclear monopole resonance* K ∞ of symmetric nuclear matter E ( ,T ) = E (  T=0) + E’ ( ,T ) K ∞ = 231 ± 5 MeV Nuclear EOS Side flow v 1 Eliptic flow v 2 P. Danielewicz et al., Science 298 (2002) 1592 C. Fuchs et al., PRL 86 (2001) 1974 Data from KAOS N = Z

E( ,  ) = E( ,0) +  2  E sym (  ) + O(  4 )  = (  n -  p ) /  = (N-Z)/A B (N,Z) = a V A - a S A 2/3 – a C Z (Z - 1)/A 1/3 - a sym (N – Z ) 2 / A + Δ (A) Bethe – Weizsäcker mass formula Nuclear EOS – Asymmetric term many more in: B.A. Li et al., PhRep. 464 (2008) 113 E sym (  ) ≈ E(  ) neutr. matter - E(  ) sym. nucl. matter Various notations: E sym (  ) = S(  ),  = x = I a sym = 23.7 MeV BHF Skyrme RMF L.W. Chen et al., PR C80 (2009)

Symmetry energy The asymmetry term contributes a greater uncertainty than does the symmetric matter EOS. (Bao-An Li) C. Fuchs and H.H. Wolter, EuPhJ A30 (2006) 5 Z. Xiao et al., PRL 102 (2009)

Where E sym shows up Nuclear structure Nuclear reactions GDR & PYGNY RESONANCE Supernova collapse  p /  n ≤ 0.1 – 0.2  c ≤ (2-15)  0

Neutron star E sym dependent Observables  Cooling rates of proto-neutron star  Cooling rates for X-ray bursters  NS masses, radii and moments of inertia J.M. Lattimer and M. Prakash, Science 304 (2004) 536

N-star observations PULSAR BINARY OBJECTS Direct or modified Urca process R & M coupled observables “SQM” vs. “normal” matter EOS ? J.M. Lattimer and M. Prakash, Science 304 (2004) 536

By HIC in the Fermi energy regime P N before after Intermediate & relativistic energy HIC Isospin sensitive observables - n/p differential flow - meson production, π + /π -,K 0 /K + - etc. Lack of data, but … - ASY-EOS GSI - RIKEN Constraining E sym Finite symmetry energy at zero energy due to clustering effects p, n Intermediate & relativistic energy HIC Isospin sensitive observables - n/p differential flow - meson production, π + /π -,K 0 /K + - etc. Nuclear structure data

M.B. Tsang et al., PRL 92 (2004) E sym /A = 12.5 (  /  0 )   = 2 BUU transport model calculation without momentum dependence E sym as f( ρ ) from MSU data L.W. Chen et al., PRL 94 (2005) B.A. Li & L.W. Chen, PRC 72 (2005) E sym /A = 31.6 (  /  0 )   = 1.05 E sym /A = 31.6 (  /  0 )   = 0.69

(Courtesy of W.G. Lynch) Sub-saturation densities E sym (  ) = 12.5·u 2/3 + C·u γ M.B. Tsang et al., PRL 102 (2009) Expansion around ρ 0 E sym (ρ) = S 0 + L·ξ/3 + K sym ·ξ 2 /18 + …, ξ = (ρ - ρ 0 )/ρ 0 Symmetry slope L & curvature K sym L = 3·[∂E sym /∂ρ] ρ=ρ 0 /ρ 0 = 3·P sym /ρ 0 u = ρ/ρ 0 P. Danielewicz and Lee, NPA 818 (2009) A. Klimkiewicz et al., PRC 76 (2007) Two parameterizations HIC fited by transport codes IBUU04, ImQMD Isobaric analog states & Pygny dipole resonance

Supra-saturation densities The only available data (FOPI and FOPI–LAND) result in a contradictory predictions for E sym : (Courtesy of M.B. Tsang) Z.Q. Feng, G.M. Jin, PL B683 (2010) 140

Constraining E sym (  >  0 ) Two experimental proposals: - GSI: n-p differential flow - Nishina / RIKEN: pion production

SIS18 ASY-EOS experiment S394 Spoakpersons of ASY-EOS experiment R. Lemmon and P. Russotto (approved by GSI-PAC) Zagreb, Croatia Caen, Orsay, France Darmstadt, Frankfurt, Germany Ioannina, Greece Catania, Milano, Napoli, Italy Katowice, Krakow, Warsaw, Poland Bucharest, Romania Santiago de Compostela, Spain Lund, Malmo, Sweden Daresbury, Liverpool, United Kingdom Kolkata, India NSCL-MSU, Rochester, USA

Main observable: n/p differential flow SIS18 ASY-EOS experiment S A MeV (increased statistics) 96 Zr A MeV 96 Ru A MeV (increased isospin sensitivity) } IPJ phoswich MSU miniball.5 m Lund-SdC Califa GSI LAND LNS Chimera

Towards FAIR 132 Sn, 106 Sn beams

RIKEN experiment Main partners: MSU & RIKEN Main requirements: - pion detector with large solid angle - centrality filter Solution: - SAMURAI superconducting dipole - TPC detector – should be operational in and many more (neutron wall, light charged particles, IMFs, …) B.A. Li, PRC 67 (2003) SAMURAI A/Z = 3 E kin = 250A MeV Bρ = 7.3 Tm AT-TPC

 differences in available - beams, - energies, and - intensities  different observables chosen  complementary parts in a global effort to constrain symmetry energy NSF-PIRE project

European Science Foundation Research Networking Programmes Constraining the Symmetry EnergyCoSymE European Science Foundation Research Networking Programmes Constraining the Symmetry EnergyCoSymE Z. Basrak, M. Colonna and W. Trautmann

What for ? - new intensive RIB facilities - train up a new generation of scientists to take over leadership

CBM & E sym (  >>  0 )

Nuclear matter physics at SIS100  Nuclear equation-of-state: What are the properties and the degrees-of-freedom of nuclear matter at neutron star core densities?  Hadrons in dense matter: What are the in-medium properties of hadrons? Is chiral symmetry restored at very high baryon densities?  Strange matter: Does strange matter exist in the form of heavy multi-strange objects?  Heavy flavor physics: How ist charm produced at low beam energies, and how does it propagate in cold nuclear matter? s s s u u d ? Λ Λ

Who ? European Science Foundation at present 30 member states

Who ? 1Croatia 2France 3Germany 4Italy 5Poland 6Romania 7Spain 8Sweden 9United Kingdom European Science Foundation at present 30 member states

Road map ? More info:

E sym related activities  FOPI days in Split, May 2005  LAND Collaboration Meeting, 2006  Chimera-GSI Workshop, Dec  FOPI Collaboration Meeting, Apr  Asy-EOS Workshop, Catania, June 2008  R 3 B Collaboration Meeting, GSI, Apr  ESF Exploratory Workshop, Zagreb, Oct  Letter of Intent, spring 2008  Proposal for GSI PAC, spring, 2009  Submitted ESF RNP CoSymE, Oct  Asy-EOS 2 Workshop, Noto/Sicily, May 2010

Equation of state of asymmetricic nuclear matter at supra- saturation densities CBM collaboration meeting April 15, 2010, Darmstadt, Germany Laboratory for nuclear physics Division of Experimental Physics Ruđer Bošković Institute, Zagreb, Croatia Laboratory for nuclear physics Division of Experimental Physics Ruđer Bošković Institute, Zagreb, Croatia Zoran Basrak 1950 – 2010 Thank you for your attention