The Equation of State of Asymmetric Matter

The Equation of State of Asymmetric MatterE/A (, ) = E/A (,0) + 2S() = (n- p)/ (n+ p) = (N-Z)/A1

B.A. Brown,PRL85(2000)5296

Tsang et al,PRL102,122701(2009)

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At <0 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 DirectionsEoS of asymmetric matter at high density using heavy ion collisions with rare isotope beams at high incident energy.

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Heavy Ion Collisions at high density with RIBB.A. Brow

n,PRL85(2000)5296Tsang et al,PRL102,122701(2009)

At <0 density, consistent constraints Effect of mass splitting increase with density and asymmetry

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Large uncertainties in the symmetry energy high density.

E/A (, ) = E/A (,0) + 2S() = (n- p)/ (n+ p) = (N-Z)/A1

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B. Liu et al. PRC 65(2002)045201

Summary of 208Pb n-skin thickness constraints

Model calculations with and without 3nn forces:

BHF: PRC80,045806 (2009)Brueckner-Hartree-Fock

DBHF: arXiv:1111.0695Dirac Brueckner-Hartree-Fock

CEFT :PRL105,161102(2010)Chiral Effective Field Theory

QMC :PRC85,032801R(2012)Quantum Monte Carlo

Importance of 3-body neutron-neutron force in the Equation of State of pure neutron matter

Tsang et al.PRC (in print)arXiv:1204.0466

neutron star

Symmetry Energy Project International collaboration to determine the symmetry energy over a range of densityRequire: New Detectors (TPC), & theory support

FAIR

MSU’09-

RIBF’12, FRIB’20, KoRIA? GSI’10

facility Probe Beam Energy

Travel (k) $ year density

MSU n, p,t,3He 50-140 0 2009 <o

GSI n, p, t, 3He 400 25 2010/2011 2.5 o

MSU iso-diffusion 50 0 2010/2011 <o

RIKEN iso-diffusion 50 25 2010 <o

MSU p+,p- 140 0 2012-2014 1-1.5 o

RIKEN n,p,t, 3He,p+,p- 200-300 85 2014 2o

GSI n, p, t, 3He 800 25 2014 2-3o

FRIB n, p,t,3He, p+,p- 200 0 2018- 2-2.5 o

FAIR K+/K- 800-1000 ? 2018 3o

• Time-projection chamber (TPC) will sit within SAMURAI dipole magnet

• Auxiliary detectors for heavy-ions and neutrons, and trigger

Hodoscope

Nebula(neutron array)

SAMURAI dipole magnet and vacuum chamber

SAMU

RAI-TPC beam

Drawing courtesy of T. Isobe

SAMURAI-TPC

Experiments at RIKENBeams 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.html238U, 124Xe (not updated), 48Ca

TPC considerations: Space-charge effect and track multiplicity considerations favor light Z beams for commissioning

Proposed reactions at RIKENProposed 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+ ratiosn/p, t/3He ratiosp,d,t,3He, 4He flow

p-/ p+ ratios124Sn+124SnElab=120 MeV/Ab = 1fm

BUU from

: Danielewicz, N

PA673, 375 (2000).

Bickley et al., private comm. (2009)

• 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.

Jun Hong, private comm. (2012)

S()=12.5(/o)2/3 +C (/o) gi

gi

p-/ p+ ratios124Sn+124SnElab=120 MeV/Ab = 1fm

BUU from

: Danielewicz, N

PA673, 375 (2000).

Bickley et al., private comm. (2009)

• 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, 64Ni at 300 MeV/u

Jun Hong, private comm. (2012)

S()=12.5(/o)2/3 +C (/o) gi

gi

n/p ratiosto 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

124Sn+124Sn;112Sn+112Sn,E/A=120 MeV

Coupland et al,

Zhang, private communications

Experiments: 132, 124, 112Sn + 124,112Sn, 112Sn+112Ru at 200 MeV/u: 56Ni, 58Ni, 64Ni, 68Ni + 58Ni, 64Ni at 200 MeV/uWill require nebula neutron array

SummaryPropose experimentsSymmetric systems:132,124,112Sn+124,112Sn; 112Ru+112Sn; E/A=300 MeV, Asymmetric systems:56-68Nii+124,112Sn; and 56-68Nii+58-64NiOther Possible beams or reaction combinations??

Possible targets: 124,112Sn, 58,64Ni, 96Zr, 96Ru, 58-64Ni

Physics goals:Extract Symmetry energy constraints at high densitydetermination of effective nucleon massesInformation 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 detectorsNebula neutron array + scintillation array.