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Constraining the symmetry energy of the EoS in relativistic heavy - ion reactions

Constraining the symmetry energy of the EoS in relativistic heavy - ion reactions. A. Krasznahorkay, ATOMKI, Debrecen. Introduction. The neutron-skin thickness. neutrons protons. Krasznahorkay et al ., PRL, 82 (1999) 3216 . Krasznahorkay et al ., NP 731, 224 (2004).

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Constraining the symmetry energy of the EoS in relativistic heavy - ion reactions

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  1. Constraining the symmetry energy of the EoS in relativistic heavy-ion reactions A. Krasznahorkay, ATOMKI, Debrecen

  2. Introduction The neutron-skinthickness neutrons protons

  3. Krasznahorkay et al., PRL, 82 (1999) 3216. Krasznahorkay et al., NP 731, 224 (2004)

  4. Constraining the symmetry energy Furnstahl, Nucl. Phys. A706 (2002) 85

  5. The symmetry energy in nuclear matter Bethe – Weizsäcker mass formula B (N,Z) = aVA- aSA2/3 – aCZ (Z - 1)/A1/3-asym (N – Z )2 / A+ Δ(A) asym = 23.7 MeV

  6. Symmetry energy • The density dependence of symmetry energy is largely unconstrained. • What is “stiff” or “soft” (curvature) is density dependent Z. Xiao et al., PRL102 (2009) 062502 The asymmetry term contributes a greater uncertainty than does the symmetric matter EOS.

  7. Recent workshops and conferences • Asy-EOS-2010, "International Workshop on Nuclear Symmetry Energy at Medium Energies", May 21 to May 24, 2010, in the town Noto (SR), Italy. • International symposium on Nuclear Symmetry Energy, July 26 to July 28, 2010 at RIKEN, Wako, Japan. • Probing the Equation of State of Neutron-Rich Matter with Heavy-Ion Reactions • Properties of Asymmetric nuclear matter within Extended BHF Approach • Determining the Nuclear Symmetry Energy of Neutron-Rich Matter and its Impacts on Astrophysics • The Nuclear Symmetry Energy and Neutron Star Crusts

  8. Supernova collapse Where Esym shows up Nuclear structure PygmyDipoleResonance Nuclear reactions

  9. Neutron star Esymdependent • Stability against gravitational collapse • Radial density profile • Internal structure, composition and evolution • Cooling mechanism J.M. Lattimer and M. Prakash, Science 304 (2004) 536

  10. BINARY OBJECTS N-star observations • Cooling rates of proto-neutron star • Cooling ratesfor X-ray bursters • NS masses, radii and moments of inertia R & M coupled observables PULSAR “SQM” vs. “normal” matter EOS ? J.M. Lattimer and M. Prakash, Science 304 (2004) 536 Quark Stars still theoretical, but evidence continues to accumulate to support them Quark Stars would offer unique opportunities to study exotic matter

  11. p, n Constraining Esym Nuclear structure data Intermediate & relativistic energy HIC Isospin sensitive observables - n/p differential flow - meson production, π+/π-,K0 /K+ - etc. Lack of data, but … - ASY-EOS experiment @ GSI - SAMURAI @ RIKEN Intermediate & relativistic energy HIC Isospin sensitive observables - n/p differential flow - meson production, π+/π-,K0 /K+ - etc. By HIC in the Fermi energy regime

  12. SIS18 EOS- neutron-skin experiment S408 Spoakperson: A. Krasznahorkay (approved by GSI-PAC) R3B , EXL, ALADIN, … collaborations Institute of Nuclear Research (ATOMKI), Debrecen, Hungary GSI, Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany IFIC (CSIC-Univ. Valencia), Valencia, Spain Kernfysisch Versneller Instituut, Groningen, The Netherlands Daresbury, Liverpool, United Kingdom

  13. Sum rule for the SDR strength Neutron-skinthickness Bohr, MottelssonNuclearStructure (1969) Vol. 2 A. Krasznahorkay et al., Phys. Rev. Lett. 82 (1999) 3216.

  14. Problems with the SDR method • Quenching of the SDR is not known • Normalization of the strength is not solved • Spin-Dipole Res.S[r(i)x(i)]t−(i) • IAS St−(i) • The QFC background is not precisely defined

  15. The previous sum rule is valid also for the GDR if it excited in (p,n) reaction !!! • (actually the analog of the GDR is excited) • We are proposing the excitation of the well known GDR in (p,n) reaction

  16. Advantages of the proposedGDR method • Very little quenching, and it is precisely known for the whole nuclear chart • Normalisation can be more precise • GDR Sr(i)t −(i) => DL =1 • IAS St −(i) => DL =0 • In coincidence with γ-decay no QFC background is expected

  17. Neutron energy spectra and differential cross sections from (p,n) reaction(S. Nishihara et a., Phys. Lett. B 160 (1985) 369

  18. Excitation with strong interaction V(q=0) (MeVfm3) voc v v v

  19. Ground-state γ-decay of the GDR

  20. Reaction kinematics IVGDR

  21. Schematiclayout of thesetup

  22. Geometrical arrangement

  23. Efficiency for neutrons

  24. The liquid hydrogen target

  25. Beam time estimates Counting rate for the IVGDR ≈ 250 count/h 9 shift / beam Althogether 29 shifts for 116Sn, 124Sn and 208Pb

  26. SIS18 ASY-EOS experiment S394 Spoakpersonsof ASY-EOS experimentR. Lemmon and P. Russotto (approvedby 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 Institute of Nuclear Research (ATOMKI), Debrecen, Hungary Kolkata, India NSCL-MSU, Rochester, USA

  27. Au+Au @ 400A MeV (increased statistics) 96Zr+96Zr @ 400A MeV 96Ru+96Ru@ 400A MeV Lund-SdC Califa } (increased isospin sensitivity) MSU miniball .5 m IPJ phoswich GSI LAND LNS Chimera SIS18 ASY-EOS experiment S394 Main observable: n/p differential flow Detect: n, p, t, 3He, N/Z of light IMFs Determine: reaction plane, reaction centrality Improve: statistics and neutron background determination + code clusterization algorithm

  28. Towards FAIR 132Sn, 106Sn beams

  29. Conclusion • New experimental data for the symmetry energy term of theEoS. • Nuclear structure data (Giant resonances) for ρ ≈ ρ0 • Nuclear reaction data (elliptic flow differences) for ρ ≈ 2ρ0  new predictions for neutron rich isotopes and neutron stars.

  30. Thank you for your attention !

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