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)

...183

2

0

0

0

0

BsymB

osym

KLSE

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.

?? ??

Phys. Rev. C 86, 015803 (2012)Ts

ang

et a

l., P

RC

86,

015

803

(201

2)

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

?? ??

Large uncertainties in the symmetry energy high density.

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

?? ??

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

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 http://www.nishina.riken.jp/RIBF/BigRIPS/intensity.html238U, 124Xe, 48Ca, 86Kr (?), 18O, 76Ge(?)

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)48Ca fragmentation: 46Ar (8.24), 34Ar(5.64) or 47K and 37K86Kr (??) fragmentation: 56Ni (6), 64Ni(8), 70Ni(5.0), 60Zn(5.5), 76Zn(5)

Targets available : 112Sn, 124Sn in RIKEN ; 96Zr, 96Ru in GSI

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)

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

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

• 132Sn+124Sn; 112Sn+112Sn, 112Sn+112Ru at 200 MeV/uWill require nebula neutron array

Ecm (MeV)

protons

neutrons

overlap and cut

Particles Distributions Detector mismatch

γ

H n

RejectedHe

50 MeV

120 MeV

Fraction of n decreases and rejected particles increases with incident energy !

Can we detect both n and p with same detector?

θ cm

Proposed solution with veto arrays1. Need efficient

veto arrays.2. Use veto+n-wall

to identify p 3. New technical

development for a large scintillator array to detect p?

p

t

d

apt

SummaryPropose experimentsSymmetric systems:132,124,112Sn+124,112Sn; 112Ru+112Sn; E/A=300 MeV, 56-68Ni+56,64Ni;Asymmetric systems:56-68Ni+124,112Sn;

Possible beams:??

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

Physics goals: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

Auxiliary detectorsNebula neutron array + scintillation array