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Constraining the symmetry energy of the EoS in relativistic energy of the EoS in relativistic heavy-ion reactions A. Krasznahorkay, ATOMKI, Debrecen Introduction The neutronskin thickness ( r )


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

  2. Introduction The neutron�skin thickness ρ ( r ) �������� ������� ( ) 2 ≡ ∫ ρ 2 r r r dv r � =< =< > > − − < < > > =< =< > > − − < < > > 2 1 / 2 2 1 / 2 R r r 2 n p

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

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

  5. The symmetry energy in nuclear matter Bethe – Weizsäcker mass formula B ( N,Z ) = a A - a A 2/3 – a Z ( Z - 1)/ A 1/3 - 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 ) ( N – Z ) 2 / A + Δ ( A ) a sym = 23.7 MeV ( ) ( ) ( ) ( ) ρ α = ρ + ρ α + α + 2 4 E , E , 0 S O ... − � Z α = A ∂ ρ α 2 1 E ( , ) p ( ) ... ρ = = + ρ − ρ + 0 S ( ) a 4 0 ∂ α ρ 2 α = 2 2 0 0

  6. ��������������� • The density dependence of al., PRL 102 (2009) 062502 symmetry energy is largely largely largely unconstrained unconstrained unconstrained. • What is “stiff” or “soft” “stiff” or “soft” “stiff” or “soft” Z. Xiao et al., (curvature) is density (curvature) is density dependent ��������������������������������� ������������������� �������������� ���������������������

  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. 2010 at RIKEN, Wako, Japan. � Probing the Equation of State of "eutron�Rich Matter with Heavy�Ion Reactions � Properties of Asymmetric nuclear matter within Extended BHF Approach � Determining the "uclear Symmetry Energy of "eutron�Rich Matter and its Impacts on Astrophys ics � The Nuclear Symmetry Energy and Neutron Star Crusts

  8. ������� ��� �������� Nuclear structure Pygmy Dipole Resonance Nuclear reactions Supernova collapse

  9. ������������ ������������������������������������ !���"�#�$ � ��� ��������� � Stability Stability Stability against gravitational collapse � Radial density profile density profile density profile � Internal structure � structure structure, ��������� composition and evolution � Cooling Cooling Cooling mechanism

  10. ������������������� BINARY OBJECTS � Cooling rates of proto- neutron star R & M coupled � Cooling rates for X-ray observables bursters � NS masses, radii and PULSAR moments of inertia “SQM” vs. “normal” matter EOS � “SQM” vs. “normal” matter EOS � ����������������������������������������� !���"�#�$ Quark Stars still theoretical, but evidence continues to accumulate to support them Quark Stars would offer unique opportunities to study exotic matter

  11. �������������� ��� Nuclear structure data p, n π π π π ± + � � � � Intermediate & relativistic Intermediate & relativistic energy HIC energy HIC Isospin sensitive observables Isospin sensitive observables - n/p differential flow - n/p differential flow - meson production, π + /π - ,K 0 /K + - meson production, π + /π - ,K 0 /K + - etc. - etc. Lack of data, but … %��&'(��������)������������������ - ASY-EOS experiment @ GSI - SAMURAI @ RIKEN

  12. ������ ���� ������������� � ����������!"� Spoakperson: A. Krasznahorkay (approved by GSI-PAC) R3B , EXL, ALADIN, … collaborations 1. Institute of Nuclear Research (ATOMKI), Debrecen, Hungary 2. GSI, Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany 3. 3. IFIC (CSIC-Univ. Valencia), Valencia, Spain IFIC (CSIC-Univ. Valencia), Valencia, Spain 4. Kernfysisch Versneller Instituut, Groningen, The Netherlands 5. Daresbury, Liverpool, United Kingdom

  13. Sum rule for the SDR strength Neutron-skin � =< =< =< =< 2 > > > > 1 / 2 − − − − < < < < 2 > > > > 1 / 2 R r r n p thickness  → →  a σ ⊗ ∑ τ τ r ±     a a a     JM ( ) 9 Bohr, Mottelsson Nuclear − − + = 〈 〉 − 〈 〉 2 2 S S � r Z r SDR SDR n p π 2 Structure (1969) Vol. 2 2 1 / 2 ασ − − − < > ( 1 B ) ( � Z ) r < > − < > = 2 1 / 2 2 1 / 2 r r exp p = = + + + + − − − − = = B S / S n p 2 1 / 2 < > 2 � r p 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 � ���������������� Σ[ r (i)x σ � ���������������� Σ[ r (i)x σ σ( i ) ] τ σ( i ) ] τ τ (i) τ − (i) σ σ σ σ τ τ τ τ Σ τ τ τ τ − (i) � IAS � The QFC background is not precisely defined 14

  15. ������������������������������������������������������ ����������������������������� ������������������� ����������������������� !�������������� �����������������������"����#��"�� !�������������� �����������������������"����#��"�� ���������������������

  16. Advantages of the proposed GDR method � Very little quenching, and it is precisely known for the whole nuclear chart � Normalisation can be more precise � ���� Σ r (i) τ τ τ τ − (i) => � L =1 � $%�� Στ τ τ τ − (i) => � L =0 � In coincidence with γ-decay no QFC background is expected 16

  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 &�'()���*�&�� + � � � � � στ στ στ στ � τ τ τ τ � σ σ σ σ

  19. Ground-state γ-decay of the GDR 19

  20. Reaction kinematics IVGDR

  21. Schematic layout of the setup

  22. �����������������������

  23. Efficiency for neutrons

  24. The liquid hydrogen target

  25. Beam time estimates I = 10 6 particles/s E = 600 A.MeV d(target) = 100 mg/cm 2 1.5 cm long liquid hydrogen LENA (ToF neutron spectrometer) ε≈ 0.15 CB (γ-spectrometer) CB (γ-spectrometer) ε≈ 0.2 ε≈ 0.2 ALADIN (dipole magnet) Counting rate for the IVGDR ≈ 250 count/h 9 shift / beam Althogether 29 shifts for 116 Sn, 124 Sn and 208 Pb

  26. ������#�$������ ����������%&! 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 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. ������#�$������ ����������%&! %�,%�� @ -))%�*�&����� ���������������������� 1 ./ 0�, ./ 0�� @ -))%�*�&� ������������������������������� ./ ��, ./ �� @ 400A MeV IPJ phoswich MSU miniball Main observable: n/p differential flow GSI LAND Detect: n, p, t, 3 He, N/Z of Detect: Detect: M light IMFs light IMFs GS Determine: Determine: Determine: reaction plane, reaction centrality Improve: Improve: Improve: statistics and neutron background Lund-SdC Califa determination LNS Chimera + .5 m code clusterization algorithm

  28. '�������(#�) 132 Sn, 106 Sn beams

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