The Equation of State of Asymmetric Matter

1. The Equation of State of Asymmetric Matter E/A (, ) = E/A (,0) + 2S()  = (n- p)/ (n+ p) = (N-Z)/A1 ? ? ? ? B.A. Brown,PRL85(2000)5296 Tsang et al,PRL102,122701(2009) • Tsang et al., PRC 86, 015803 (2012) At r<r0 density, consistent constraints have been obtained from different experiments: Heavy Ion Collisions (HIC), Giant Dipole Resonances, Isobaric Analog States (IAS), Finite Range Droplet model (FRDM), Pygmy Dipole Resonances (PDR), Proton elastic scattering on Pb, and neutron star (n-star) radius. • Future Directions • EoS of asymmetric matter at high density using heavy ion collisions with rare isotope beams at high incident energy.

2. Heavy Ion Collisions at high density with RIB E/A (, ) = E/A (,0) + 2S()  = (n- p)/ (n+ p) = (N-Z)/A1 ? ? ? ? ? ? ? ? B. Liu et al. PRC 65(2002)045201 B.A. Brown,PRL85(2000)5296 Tsang et al,PRL102,122701(2009) At r<r0 density, consistent constraints Effect of mass splitting increase with density and asymmetry Large uncertainties in the symmetry energy high density.

3. Importance of 3-body neutron-neutron force in the Equation of State of pure neutron matter Summary of 208Pb n-skin thickness constraints neutron star Model calculations with and without 3nn forces: BHF: PRC80,045806 (2009) Brueckner-Hartree-Fock DBHF: arXiv:1111.0695 Dirac Brueckner-Hartree-Fock CEFT :PRL105,161102(2010) Chiral Effective Field Theory QMC :PRC85,032801R(2012) Quantum Monte Carlo Tsang et al.PRC (in print) arXiv:1204.0466

4. MSU’09- GSI’10 RIBF’12, FRIB’20, KoRIA? FAIR Symmetry Energy Project International collaboration to determine the symmetry energy over a range of density Require: New Detectors (TPC), & theory support

5. SAMURAI-TPC • Time-projection chamber (TPC) will sit within SAMURAI dipole magnet • Auxiliary detectors for heavy-ions and neutrons, and trigger Nebula (neutron array) SAMURAI-TPC beam Hodoscope SAMURAI dipole magnet and vacuum chamber Drawing courtesy of T. Isobe

6. Experiments at RIKEN Beams are limited to the primary beams developed at RIKEN and that stable beams are produced as secondary beams. There is no advantage of using stable beams. Furthermore, stable beams are not in the priority list as they are not “unique”. Strategies: Use very neutron rich and n-poor radioactive beams. Propose several reactions to take advantage of the campaign mode. Use Sn targets (available in RIKEN): 112Sn (expensive), 124Sn Primary Beams (site not up to date) http://www.nishina.riken.jp/RIBF/BigRIPS/intensity.html 238U, 124Xe (not updated), 48Ca TPC considerations: Space-charge effect and track multiplicity considerations favor light Z beams for commissioning

7. Proposed reactions at RIKEN Proposed Symmetric and Asymmetric systems: Possible beams: 238U fission: 132Sn(10^4.8), 124Sn (10^4.7), 112Sn (10^4.2), 112Ru(4.7) 90Zr(4.8), 96Zr(4.9), 100Zr(5.5), 96Ru(4), 108Ru(5), 197Au(??10^4.2) 136Xe: 132Sn(??) 70Zn: 68Ni, 58Ni – suggested by Sukurai-san Targets available : 112Sn, 124Sn in RIKEN ; 96Zr, 96Ru in GSI, 58Ni, 64Ni Physics goal: Extract Symmetry energy constraints at high density & determination of effective nucleon masses Experimental Observables: p-/ p+ ratios n/p, t/3He ratios p,d,t,3He, 4He flow

8. 124Sn+124Sn Elab=120 MeV/A b = 1fm • p-/ p+ ratios Bickley et al., private comm. (2009) Jun Hong, private comm. (2012) BUU from: Danielewicz, NPA673, 375 (2000). gi gi S(r)=12.5(r/ro)2/3+C(r/ro) • p-/p+ ratios show a strong dependence on the symmetry energy at low incident energies and low pion energies. • p-/p+ ratios are lower at high energy because later pion collisions and pion production dilutes the sensitivity to the symmetry energy. • First experiments, use high energy beam to increase pion production.

9. 124Sn+124Sn Elab=120 MeV/A b = 1fm • p-/ p+ ratios Bickley et al., private comm. (2009) Jun Hong, private comm. (2012) BUU from: Danielewicz, NPA673, 375 (2000). gi gi S(r)=12.5(r/ro)2/3+C(r/ro) • What are the best systems? • Calculations: 132Sn+124Sn; 112Sn+112Sn, 112Sn+112Ru at 300 MeV/u • Experiments: 132, 124, 112Sn + 124,112Sn, 112Sn+112Ru at 300 MeV/u • Experiments: 56Ni, 58Ni, 64Ni, 68Ni + 58Ni, 64Niat 300 MeV/u

10. n/p ratios to probe mn* and mp* and Esym • Previous data (to be published) • 124Sn+124Sn;112Sn+112Sn,E/A=120 MeV • 48Ca+124Sn; 40Ca112Sn,E/A=140 MeV Zhang, private communications Coupland et al, 124Sn+124Sn;112Sn+112Sn,E/A=120 MeV • Experiments: 132, 124, 112Sn + 124,112Sn, 112Sn+112Ru at 200 MeV/u • : 56Ni, 58Ni, 64Ni, 68Ni + 58Ni, 64Ni at 200 MeV/u • Will require nebula neutron array

11. Summary Propose experiments Symmetric systems: 132,124,112Sn+124,112Sn; 112Ru+112Sn; E/A=300 MeV, Asymmetric systems: 56-68Nii+124,112Sn; and 56-68Nii+58-64Ni Other Possible beams or reaction combinations?? Possible targets: 124,112Sn, 58,64Ni, 96Zr, 96Ru, 58-64Ni Physics goals: Extract Symmetry energy constraints at high density determination of effective nucleon masses Information about 3n forces in pure neutron EoS at high density Experimental Observables: p-/ p+ ratios; (E/A=300 MeV) n/p, t/3He ratios; p,d,t,3He, 4He flow (E/A=200 MeV) Auxiliary detectors Nebula neutron array + scintillation array.