Determination of the Equation of State of Asymmetric Nuclear MatterNSCL MSU, USA: B. Tsang & W. Lynch,E. Brown, Zibi Chajecki, Pawel Danielewicz, A. Steiner, Gary Westfall. Texas A&M University, College Station: Sherry Yennello, A. McIntoshWestern Michigan University: Michael Famiano GSI,DE: Wolfgang Trautmann , Yvonne LeifelsDaresbury Laboratory, UK: Roy Lemmon INFN LNS, Catania, IT: Giuseppe Verde, Angelo Pagano, Paulo Russotto, Massimo di Toro, Maria Colonna, Aldo Bonasera, Vincenzo GrecoSUBATECH, FR: Christoph HartnackGANIL, FR: Abdou Chbihi, John Frankland, Jean-Pierre WieleczkoChina Institute of Atomic Energy: Yingxun Zhang, Zhuxia Li, Fei Lu (Peking University), Y.G. Ma, Wendong Tian (Chinese Shanghai Academy of Sciences)Brazil: Sergio Souza, Raul Donangelo, Brett Carlson

RIKEN, JP: Hiroshi Sakurai, Shunji Nishimura, Yoichi Nakai, Atsushi TaketaniKyoto University: Tetsuya Murakami Tohoku University: Akira Ono Rikkyo University: Jiro Murata, K. Ieki

Symmetry Energy Project (SEP)http://groups.nscl.msu.edu/hira/sep.htm

http://nscl.msu.edu/~tsang

Betty Tsang, NSCL, MSU

Symmetry Energy Project (SEP)http://groups.nscl.msu.edu/hira/sep.htm

http://nscl.msu.edu/~tsang

OutlineI. Introduction of NSCL, FRIBII. Equation of State of Symmetric Nuclear MatterIII. Symmetry energy in EoS of Asymmetric Matter

A. Constraints from HICa) n/p ratiosb) Isospin diffusion

B. Constraints from other observables from finite nucleia) Nuclear masses Isobaric Analog Statesb) Neutron skin thicknessesc) Pygmy Dipole Resonancesd) Giant Dipole Resonancese) Current Status of the Symmetry Energy Project

IV. Current Status of the Symmetry Energy ProjectV. Summary & Conclusion

NSCL

Michigan State University

The National Superconducting Cyclotron Laboratory

@Michigan State University

431 employees, including 35 faculty, 70 graduate and 59 undergraduate studentsas of December 7, 2010

The National Superconducting Cyclotron Laboratory

@Michigan State University

A national user facility for rare isotope research and education in nuclear science, astro-nuclear physics, accelerator physics, and societal applications

Facility for Rare Isotope Beams (FRIB)

FRIB will provide intense beams of rare isotopes (that is, short-lived nuclei not normally found on Earth). FRIB will enable scientists to

make discoveries about the properties of these rare isotopes in order to better understand the physics of nuclei, nuclear astrophysics,

fundamental interactions, and applications for society.Cost: $640M; construction start: 2013; completion: 2020

Neutron Number N

Prot

on N

umbe

r Z

From Elements to Rare isotopesFrom periodic table to chart of nuclei

Equation of State (EoS)

Ideal gas: PV=nRT

-20

-10

0

10

20

30

0 0.1 0.2 0.3 0.4 0.5 0.6

EOS for Asymmetric Matter

Soft (β=0, K=200 MeV)asy-soft, β=1/3 (Colonna)asy-stiff, β=1/3 (PAL)

E/A

(M

eV)

ρ (fm-3)

β=(ρn-ρ

p)/(ρ

n+ρ

p)

(0.16, -16)

How to determine nuclear EOS• Measure collisions• Simulate collisions with transport theory (BUU)• Identify observables that are sensitive to EOS

– Directed transverse flow (in-plane)– “Elliptical flow” out of plane, e.g. “squeeze-out”– …

• Find the mean field(s) that describes the data. • Constrain the relevant input variables in the transport models by

additional data. • Use the mean field potentials to calculate the EOS.

Constraining the EOS using Heavy Ion collisions

Two observable due to the high pressures formed in the overlap region:– Nucleons deflected sideways in the reaction plane. – Nucleons are “squeezed out” above and below the reaction plane. .

pressure contours

density contours

Au+Au collisions E/A = 1 GeV)

Determination of symmetric matter EOS from nucleus-nucleus collisions

The curves represent calculations with parameterized Skyrme mean fields

They are adjusted to find the pressure that replicates the observed flow.

yApx

∂∂ /

Danielewicz et al., Science 298,1592 (2002).

O

in plane

out of plane

The boundaries represent the range of pressures obtained for the mean fields that reproduce the data.

They also reflect the uncertainties from the input parameters in the model.

1

10

100

1 1.5 2 2.5 3 3.5 4 4.5 5

symmetric matter

RMF:NL3Fermi gasBogutaAkmalK=210 MeVK=300 MeVexperiment

P (M

eV/fm

3 )ρ/ρ

0

Nuclear Equation of State of asymmetric matterE/A (ρ,δ) = E/A (ρ,0) + δ2⋅S(ρ)δ = (ρn- ρp)/ (ρn+ ρp) = (N-Z)/A

...183

)(2

0

0

0

0 +

−+

−+=

ρρρ

ρρρρ sym

o

KLSS symB

sym PE

LB 0

033

0ρρ

ρρρ

=∂

∂=

=

Density dependence of symmetry energy

Symmetry Energy Project (SEP)http://groups.nscl.msu.edu/hira/sep.htm

http://nscl.msu.edu/~tsang

OutlineI. Introduction of NSCL, FRIB, rare isotopesII. Equation of State of Symmetric Nuclear MatterIII. Symmetry energy in EoS of Asymmetric Matter

A. Constraints from HICa) n/p ratiosb) Isospin diffusion

B. Constraints from other observables from finite nucleia) Nuclear masses Isobaric Analog Statesb) Neutron skin thicknessesc) Pygmy Dipole Resonancesd) Giant Dipole Resonancese) Current Status of the Symmetry Energy Project

IV. Current Status of the Symmetry Energy ProjectV. Summary & Conclusion

Strategies used to study the symmetry energy with Heavy Ion collisions

• Vary the N/Z compositions of projectile and targets124Sn+124Sn, 124Sn+112Sn,

112Sn+124Sn, 112Sn+112Sn• Measure N/Z compositions

of emitted particles n & p yields isotopes yields – isospin

diffusionResults interpreted with

transport models that simulate the collisions.

Neutron Number N

Prot

on N

umbe

r Z

δ+−= 3/2AaAaB SV 3/1

)1(AZZaC

−−

AZAasym

2)2( −−

Isospin degree of freedom

Hub

ble

ST

Crab Pulsar

Two observables: n/p ratios and isospin diffusion

E/A (ρ,δ) = E/A (ρ,0) + δ2⋅S(ρ)δ = (ρn- ρp)/ (ρn+ ρp) = (N-Z)/A

Projectile

Target

124Sn

112Sn-100

-50

0

50

100

0 0.5 1 1.5 2

Li et al., PRL 78 (1997) 1644

V asy (M

eV)

ρ / ρο

NeutronProton

u =

stiff

soft

Y(n)/Y(p); t/3He, π+/π- Isospin Diffusion; low ρ, Ebeam

Vary N/Z of projectile & target

80-380

420-620

n/p Experiment 124Sn+124Sn; 112Sn+112Sn; E/A=50 MeV

Scattering Chamber

Famiano et al

Isotope Distribution ExperimentMSU, IUCF, WU collaboration

Sn+Sn collisions involving 124Sn, 112Sn at E/A=50 MeV

Miniball + Miniwall4 π multiplicity arrayZ identification, A<4

LASSASi strip +CsI array Good E, position,isotope resolutions

Xu et al, PRL, 85, 716 (2000)

...183

)(2

0

0

0

0 +

−+

−+=

ρρρ

ρρρρ sym

o

KLSS

Constraints from np ratios and two isospindiffusion measurements

0.4≤γi ≤10.4≤γi ≤1.05 0.45≤γi ≤0.95

S(ρ)=12.5(ρ/ρo)2/3 +C (ρ/ρo) γi

Symmetry Energy Project (SEP)http://groups.nscl.msu.edu/hira/sep.htm

http://nscl.msu.edu/~tsang

OutlineI. Introduction of NSCL, FRIB, rare isotopesII. Equation of State of Symmetric Nuclear MatterIII. Symmetry energy in EoS of Asymmetric Matter

A. Constraints from HICa) n/p ratiosb) Isospin diffusion

B. Constraints from other observables from finite nucleia) Nuclear masses Isobaric Analog Statesb) Neutron skin thicknessesc) Pygmy Dipole Resonancesd) Giant Dipole Resonances

IV. Current Status of the Symmetry Energy ProjectV. Summary & Conclusion

Neutron Number N

Prot

on N

umbe

r Z

δ+−= 3/2AaAaB SV 3/1

)1(AZZaC

−−

AZAasym

2)2( −−

Symmetry Energy in Nuclei

Hub

ble

ST

Crab Pulsar

asym (volume) =S(ρo)asym (surface) S(ρ) at sub-saturation densities ρ ≈ 1/2ρo .

(Danielewicz, NPA727 (2003) 233)

Nuclear masses and the EoS

• Fits of the binding energy formula to experimental masses to provide values for av, as, ac, asym and δ using AME2003, NPA 729, (2003) 129, 337.

• Problems: The binding energy formula is not unique

• Problems: asym is small compared to other terms. ac, asym are strongly correlated & shell effects are large.

• The best fits may not give reasonable parameters.• Can we isolate asym from the rest of formula?

( )2 2 2A,Z p n A,ZM c Zm c A Z m c B= + − −

( ) ( )( )( )

( )2

2

3/12

23/2

2S1V2

2

sym AZN

A1A RO

AZNAbaba RO

AZNAa −

βα+α−

+−−

−OR OR

δ+−= 3/2AaAaB SV 3/1

)1(AZZaC

−−

AZAasym

2)2( −−

Symmetry coefficient from Isobaric Analog States

micaCSV EA

ZNaAZaAaAaE +

−+++−=

2

3/1

23/2 )(

P. Danielewicz & J. Lee, NPA 818, 36 (2009)

Charge invariance: invariance of nuclear interactions under rotations in n-p space

Symmetry energy on vastly differing length scales

208Pb

extrapolation from 208Pb radius to n-star radiusC.J. Horowitz, J. Piekarewicz, Phys. Rev. Lett. 86 (2001) 5647

~10-15 m ~104 m

Neutron Star

Extrapolation from 208Pb radius to n-star radius

Measurements of radii

• Proton elastic scattering is sensitive to the neutron density, but the results can be ambiguous.

• Parity violating electron scattering may provide strong constraints on <rn

2>1/2- <rp2>1/2 and on S(ρ) for

ρ< ρs. Expected uncertainties are of order 0.06 fm. (Horowitz et al., Phys. Rev. 63, 025501(2001).)

θcm (deg)

208Pb(p,p)Ep =200 MeV

<rn2>1/2=5.6 fm

<rn2>1/2=5.7 fm

Karataglidis et al., PRC 65 044306 (2002)

O

Pygmy Dipole Resonance Giant Dipole Resonance

Symmetry Energy from Nuclear collective motion

Pygmy Dipole Resonance Giant Dipole Resonance

Collective oscillation of neutron skin against the Core n-skin thickness

Collective oscillation of neutrons against protons

From Angela Bracco

Symmetry Energy from Nuclear collective motion

...183

2

0

0

0

0 +

−+

−+=

ρρρ

ρρρ BsymB

osym

KLSE symB

sym PE

LB 0

033

0ρρ

ρρρ

=∂

∂=

=

GDR: Trippa, PRC77, 061304

Skin(Sn): Chen et al., arXiv:1004/4672 (2009)

IAS : Danielewicz, Lee, NPA 818, 36 (2009)

PDR: A. Klimkiewicz, PRC 76, 051603 (2007)A.Carbone, O.Wieland PRC81,041301(2010)

Constraints on symmetry energy at subnormal density from existing data

Tsang et al., PRL 102, 122701 (2009)

Tsang et al., PRL 102, 122701 (2009)S(ρ)=12.5(ρ/ρo)2/3 + 17.6 (ρ/ρo)γ

Acknowledgements

NSCL SEP journal ClubZibi Chajecki, Dan Coupland, Rachel Hodges, Micha

Kilburn, Fei Lu, Mike Youngs, Jack Winkelbauer

ExperimentersMichigan State University

T.X. Liu (thesis), W.G. Lynch, Z.Y. Sun, W.P. Tan, G. Verde, A. Wagner, H.S. XuL.G. Sobotka, R.J. Charity (WU)

R. deSouza, V. E. Viola (IU)M. Famiano: (Western Michigan U)

Y.X. Zhang (ImQMD), P. Danielewicz, W.A. Friedman, Jenny Lee, A. Ono, L.J. Shi, Andrew Steiner,

Constraints on the density dependence of symmetry energy at supra normal density

Au+Au experiments in high energy are not designed to measure symmetry energy

Need better experiments

FAIR

MSU’09-

RIBF’12, FRIB’18 GSI’11

scientific program spans density range from 0.3 to 3 ρo at different facilities

Comprehensive Experimental Programs by SEP (international collaboration)

facility Probe Beam Energy

Travel (k) $ year density

MSU n, p,t,3He 50-140 0 2009 <ρo

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

MSU iso-diffusion 50 0 2011 <ρo

RIKEN iso-diffusion 50 25 2011 <ρo

MSU π+,π- 140 0 2012-2014 1-1.5 ρo

RIKEN n,p,t, 3He,π+,π- 200-300 85 2012-2014 2ρo

GSI n, p, t, 3He 800 25 2014 2-3ρo

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

FAIR K+/K- 800-1000 ? 2018 3ρo

I. Double ratio: pion production

( ) ( )( ) ( )[ ]( ) ( )[ ]112112112112

124132124132

112112124132/

Y/YY/Y

SnSn/SnSnR

++

+−

++

+−

ππ

ππππ

=

+++−

Yong et al., Phys. Rev. C 73, 034603 (2006)

SE Observables at High Energy (density)

II. n/p or t/3He flows.

B.-A. Li et al., Phys. Rep. 464 (2008) 113.

5th RIKEN PAC recommends completion of TPC in 2013 DOE FOA award

$1.2 M includes US contributions to SAMARAI TPC10/1/2010 – 9/30/2015

Symmetry Energy Project (SEP) collaborationhttp://groups.nscl.msu.edu/hira/sep.htm

Determination of the Equation of State of Asymmetric Nuclear Matter

MSU: B. Tsang & W. Lynch, G. Westfall, P. Danielewicz, E. Brown, A. SteinerTexas A&M University : Sherry Yennello, Alan McIntoshWestern Michigan University : Michael Famiano RIKEN, JP: TadaAki Isobe, Atsushi Taketani, Hiroshi SakuraiKyoto University: Tetsuya Murakami Tohoku University: Akira Ono GSI, Germany: Wolfgang Trautmann , Yvonne LeifelsDaresbury Laboratory, UK: Roy Lemmon INFN LNS, Italy: Giuseppe Verde, Paulo RussottoGANIL, France: Abdou ChbihiCIAE, PU, CAS, China: Yingxun Zhang, Zhuxia Li, Fei Lu, Y.G. Ma, W. Tian

Alan McIntoshBill LynchFei LuJimmy Dunn (UG)Jon Gilbert (UG)Jon Barney (UG)Michael Famiano

TadaAki IsobeAtsushi TaketaniHiro SakuraiTetsuya Murakami

RIKEN+ Kyoto UniversityTexas A&M + MSU+WMU

Conceptual Design of the TPC detector

TPC chamber

Field Cage

Electronics and pad plane

Alan McIntosh, Bill Lynch, Jimmy Dunn (UG), Jon Gilbert (UG), Jon Barney (UG)

Electronics on the move: Zibi Chajecki, Jack Winkelbauer

facility Probe Beam Energy

Travel (k) $ year density

MSU n, p,t,3He 50-140 0 2009 <ρo

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

MSU iso-diffusion 50 0 2011 <ρo

RIKEN iso-diffusion 50 25 2012 <ρo

MSU π+,π- 140 0 2012-2014 1-1.5 ρo

RIKEN n,p,t, 3He,π+,π- 200-300 85 2012-2014 2ρo

GSI n, p, t, 3He 800 25 2014 2-3ρo

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

FAIR K+/K- 800-1000 ? 2018 3ρo

GSI S394, May 2011

NSCL experiment 07038 Precision Measurements of

Isospin Diffusion, June 2011)

NSCL experiments 05049 & 09042Density dependence of the symmetry energy with emitted neutrons and protons& Investigation of transport model parameters (May & October, 2009 )

Current Status

n/p Experiment 124Sn+124Sn; 112Sn+112Sn; E/A=50 MeVFamiano et al

124Sn+124Sn; 112Sn+112Sn; E/A=120 MeV48,40Ca+112,124Sn; 48,40Ca+112,124Sn

Mike Youngs & Dan Coupland thesis expts

NSCL experiment 07038 & RIKEN (2012)Precision Measurements of Isospin Diffusion (Jack Winkelbauer, June 2011)

Projectile Target E/A lab

124,118,112Sn 124,118,112Sn 50 NSCL

124,112,108Sn 124,112Sn 50 RIKEN

Milestone in Management Plan

SummaryThe density dependence of the symmetry energy is of fundamental importance to nuclear physics and neutron star physics.

Observables in HI collisions provide constraints to the symmetry energy over a range of density.

Observables in HI collisions provide unique opportunities to probe the symmetry energy over a range of density especially for dense asymmetric matter.

The availability of intense fast rare isotope beams at a variety of energies at RIKEN, FRIB & FAIR allows increased precisions in probing the symmetry energy at a range of densities – Symmetry Energy Project (SEP); international collaboration of a global program.

Jimmy DunnJon Barney Jon Gilbert

Involvement of undergraduate students

http://www.nscl.msu.edu/~tsang/tsang@nscl.msu.edu