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

2 neutrons protons Introduction The neutron-skin thickness

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

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

The symmetry energy in nuclear matter 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 a sym = 23.7 MeV

Symmetry energy The asymmetry term contributes a greater uncertainty than does the symmetric matter EOS. Z. Xiao et al., PRL 102 (2009)

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 Astrophys ics The Nuclear Symmetry Energy and Neutron Star Crusts

Where E sym shows up Nuclear structure Nuclear reactions Supernova collapse Pygmy Dipole Resonance

Neutron star E sym dependent J.M. Lattimer and M. Prakash, Science 304 (2004) 536

N-star observations PULSAR BINARY OBJECTS R & M coupled observables J.M. Lattimer and M. Prakash, Science 304 (2004) 536 “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  Cooling rates of proto- neutron star  Cooling rates for X-ray bursters  NS masses, radii and moments of inertia

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 p, n Intermediate & relativistic energy HIC Isospin sensitive observables - n/p differential flow - meson production, π + /π -,K 0 /K + - etc. Nuclear structure data By HIC in the Fermi energy regime

SIS18 EOS- neutron-skin experiment S408 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.IFIC (CSIC-Univ. Valencia), Valencia, Spain 4.Kernfysisch Versneller Instituut, Groningen, The Netherlands 5.Daresbury, Liverpool, United Kingdom

Sum rule for the SDR strength Neutron-skin thickness Bohr, Mottelsson Nuclear Structure (1969) Vol. 2 A. Krasznahorkay et al., Phys. Rev. Lett. 82 (1999) 3216.

Problems with the SDR method Quenching of the SDR is not known Normalization of the strength is not solved – Spin-Dipole Res.  r(i)x  i  ]  − (i) – IAS   − (i) The QFC background is not precisely defined 14

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

Advantages of the proposed GDR method Very little quenching, and it is precisely known for the whole nuclear chart Normalisation can be more precise – GDR  r(i)  − (i) =>  L  – IAS  − (i) =>  L  In coincidence with γ-decay no QFC background is expected 16

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

Excitation with strong interaction v  vv vocvoc vv V(q=0) (MeVfm 3 )

Ground-state γ-decay of the GDR 19

Reaction kinematics IVGDR

Schematic layout of the setup

Geometrical arrangement

Efficiency for neutrons

The liquid hydrogen target

Beam time estimates E = 600 A.MeVI = 10 6 particles/s d(target) = 100 mg/cm cm long liquid hydrogen LENA (ToF neutron spectrometer)ε≈ 0.15 CB (γ-spectrometer)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

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 Institute of Nuclear Research (ATOMKI), Debrecen, Hungary 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

Conclusion New experimental data for the symmetry energy term of the EoS. – Nuclear structure data (Giant resonances) for ρ ≈ ρ 0 – Nuclear reaction data (elliptic flow differences) for ρ ≈ 2ρ 0  new predictions for neutron rich isotopes and neutron stars.

Thank you for your attention !