Overview of the experimental constraints on symmetry energy

Betty Tsang, NSCL/MSU

Nuclear Equation of State

Relationship between energy, temperature pressure, density in nuclear matter

E/A (,) = E/A (,0) + d2S()d = (n- p)/ (n+ p) = (N-Z)/A

Nuclear Structure – What is the nature of the nuclear force that binds protons and neutrons into stable nuclei and rare isotopes?

Nuclear Astrophysics – What is the nature of neutron stars and dense nuclear matter?

Symmetry energy calculations with effective interactions constrained by Sn masses

This does not adequately constrain the symmetry energy at higher or lower densities

E/A (,) = E/A (,0) + d2S()

d = (n- p)/ (n+ p) = (N-Z)/A

a/s

2 A/EP

Brow

n, Phys. R

ev. Lett. 85, 5296 (2001)

Symmetry energy at

0

=1

-20

-10

0

10

20

30

0 0.1 0.2 0.3 0.4 0.5 0.6

EOS for Asymmetric Matter

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

E/A

(M

eV)

(fm-3)

=(n-

p)/(

n+

p)

How does E/A depend on and ?

Symmetry energy calculations with effective interactions constrained by Sn masses

This does not adequately constrain the symmetry energy at higher or lower densities

Brow

n, Phys. R

ev. Lett. 85, 5296 (2001)

Symmetry energy at

0

=1

Overview of the experimental constraints on symmetry energy around saturation density

...183

2

0

0

0

0

BsymB

osym

KLSE

symB

sym PE

LB

00

33

0

Experimental Observables:• Heavy Ion Collisionsn/p ratiosIsospin diffusions

• Mass model (FRDM)• Isobaric Analog States (IAS)• Giant dipole Resonance (GDR)

208Pb skin measurements• PREX• antiprotonic atom systematics• 208Pb(p,p)• 208Pb(p,p’) –dipole polarizability• Dipole Pygmy Resonance (DPR)

Summary and Outlook

Introduction

Overview of the experimental symmetry energy constraints around nuclear matter density

Strategies used to study the symmetry energy with Heavy Ion collisions below E/A=100 MeV

Vary the N/Z compositions of projectile and targets

• 124Sn+124Sn, 124Sn+112Sn, 112Sn+124Sn, 112Sn+112Sn

Measure N/Z compositions of emitted particles

• n & p yields• isotopes yields: isospin

diffusion Simulate collisions with

transport theory• Find the symmetry energy

density dependence that describes the data.

• Constrain the relevant input transport variables.

Neutron Number N

Pro

ton

Nu

mb

er Z

3/2AaAaB SV 3/1

)1(

A

ZZaC

A

ZAasym

2)2(

Isospin degree of freedom

Hub

ble

S

TCrab Pulsar

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

Two HIC observables: n/p ratios and isospin diffusion

E/A (,) = E/A (,0) + d2S()d = (n- p)/ (n+ p) = (N-Z)/A

-100

-50

0

50

100

0 0.5 1 1.5 2

Li et al., PRL 78 (1997) 1644

Vasy

(MeV

)

/ o

NeutronProton

u =

stiff

soft

Y(n)/Y(p); t/3He, p+/p-

Projectile

Target

124Sn

112Sn

Isospin Diffusion; low r, Ebeam

Tsang et al., PRL 92 (2004) 062701

Experimental Layout

Courtesy Mike Famiano

Wall A

Wall BLASSA – charged particlesMiniball – impact parameter

Neutron walls – neutronsForward Array – time startProton Veto scintillators

E/A (,) = E/A (,0) + d2S()d = (n- p)/ (n+ p) = (N-Z)/A

-100

-50

0

50

100

0 0.5 1 1.5 2

Li et al., PRL 78 (1997) 1644

Vasy

(MeV

)

/ o

NeutronProton

u =

stiff

soft

Esym=12.7(r/ro)2/3 + 19(r/ro)gi

124Sn+124Sn;Y(n)/Y(p)112Sn+112Sn;Y(n)/Y(p)

Double Ratiominimize systematic errors

Two observables: n/p ratios and isospin diffusion

E/A (,) = E/A (,0) + d2S()d = (n- p)/ (n+ p) = (N-Z)/A

Esym=12.7(r/ro)2/3 + 19(r/ro)gi

124Sn+124Sn;Y(n)/Y(p)112Sn+112Sn;Y(n)/Y(p)

Double Ratiominimize systematic errors

Two observables: n/p ratios and isospin diffusion

• S() 12.3·(ρ/ρ0)2/3 + 17.6·

(ρ/ρ0) γi

• IQMD calculations were performed for i=0.35-2.0.

• Momentum dependent mean fields with mn*/mn =mp*/mp =0.7 were used.

Zhang et.al.,Phys. Lett. B 664 (2008) 145

E/A (,) = E/A (,0) + d2S()d = (n- p)/ (n+ p) = (N-Z)/A

124Sn+124Sn;Y(n)/Y(p)112Sn+112Sn;Y(n)/Y(p)

Double Ratiominimize systematic errors

Two observables: n/p ratios and isospin diffusion

0.4gi 1.05

• S() 12.3·(ρ/ρ0)2/3 + 17.6·

(ρ/ρ0) γi

• IQMD calculations were performed for i=0.35-2.0.

• Momentum dependent mean fields with mn*/mn =mp*/mp =0.7 were used.

Zhang et.al.,Phys. Lett. B 664 (2008) 145

Isospin Diffusion Projectile

Target

124Sn

112Sn

mixed 124Sn+112Snn-rich 124Sn+124Snp-rich 112Sn+112Sn

mixed 124Sn+112Snn-rich 124Sn+124Snp-rich 112Sn+112Sn

( ) / 2( ) 2 AB AA BB

i ABAA BB

R

Ri= 1 no diffusion; Ri= 0 equilibrationExtent of diffuseness reflects strength of SE

0.4gi 1

0.45gi 0.95

Consistent constraints from the 2

analysis of isospin diffusion data

S(r)=12.5(r/ro)2/3 +17.6 (r/ro)gi

Projectile

Target

124Sn

112Sn

Deg

ree

of is

ospi

n di

ffus

ion

...183

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osym

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00

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symsym

B

EL P

Symmetry energy constraints from HIC

arXiv:1204.0466S(r)=12.5(r/ro)2/3 +17.6 (r/ro)gi

0.4gi 1

Consistent with previous isospin diffusion constraints Chen, Li et al., Phys. Rev. Lett. 94 (2005) 032701

Giant Dipole ResonanceCollective oscillation of neutrons against protons

Consistency in Symmetry Energy Constraints

Trippa et al., PRC 77, 061304(R) (2008)

Tsang et al, PRL 102,122701 (2009)

Danielewicz & Lee, NPA818, 36 (2009)

Isobaric Analog States aa(A)

P. Moller et al, PRL 108,052501 (2012)

FRDM-2011a. s~0.57 MeV

Extrapolation from 208Pb radius to pressure in n-star

Typel & Brown, PRC 64, 027302 (2001) Steiner et al., Phys. Rep. 411, 325 (2005)

=L/3r00

symE

P( =0.1 r fm) (MeV/fm3)

An experimental overview of the symmetry energy around nuclear matter density

Experimental Observables:• Heavy Ion Collisionsn/p ratiosIsospin diffusions

• Mass model (FRDM)• Isobaric Analog States (IAS)• Giant dipole Resonance (GDR)

208Pb skin measurements• PREX• antiprotonic atom systematics• 208Pb(p,p)• 208Pb(p,p’) –dipole polarizability• Dipole Pygmy Resonance (DPR)

Summary and Outlook

Introduction

18

dRnp = 0.21±0.06 fm L=67±12.1 MeVSo=33±1.1 MeV

Laboratory experiments to measure the 208Pb neutron skin

Pb(p,p)

Zenihiro et al., PRC82, 044611 (2010)

Pb skin thickness from dipole polarizability

Pb(p,p’) Ebeam=295 MeV

dRnp = 0.156+0.025-0.021 fmTheoretical uncertainties underpredicted ?

Tamii et al., PRL107, 062502 (2011)

p+n

p

E

OE

p

polarizability

p+

p+

p+

J.Piekarewicz et al., arXiv:1201.3807

Reinhard & Nazarewicz ,PRC81, 051303 (R) (2010)

Summary of Pb skin thickness and symmetry energy constraints

Diverse experiments but consistent results

arXiv:1204.0466

See references inarXiv:1204.0466

Importance of 3n force in the EoS of pure n-matter

Challenge I: constraints from neutron star observations

arXiv:1204.0466 Steiner PRL108, 081102 (2012)

Challenge II: Constraints at very low density

Symmetry energy at r<0.05ro, T<10 MeV is dominated by correlations and cluster formation

J.B. Natowitz et al, PRL 104 (2010) 202501

Esy

m(n

)/E

sym

(n0)

Isospin Observables:Neutron/proton and t/3He and light isotopes energy spectra

• flow– px vs. y (v1)– Elliptic flow (v2)– Disappearance of flow (balance energy)• π+/π- spectra• π+/π- flow

Challenge III: Constraints at supra-normal densitieswith Heavy Ion Collisions

RIBF, FRIB, KoRIA

International Collaboration

ASY-EOS experiment @GSI, May 2011Au+Au @ 400 AMeV

96Zr+96Zr @ 400 AMeV 96Ru+96Ru @ 400 AMeV

~ 5x107 Events for each system

Beam Line

Shadow Bar

TofWall

Land(not splitted)

target

ChimeraKrakow array

MicroBall

Russotto & Lemmon

SAMURAI-TPC will be installed inside the SAMURAI dipole magnet in RIKEN

TPC chamber

Field Cage

Electronics and pad plane

Voltage step down

Outer enclosure

AT/TPC @ MSU

arXiv:1204.0466

NSCL/HiRA group

Acknowledgement:

A Time projection chamber is being built in the US to measure p+/p- & light charge particles in RIKEN

Nuclear Symmetry Energy (NuSym) collaboration http://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. TianKorea University, Korea: Byungsik Hong

Summary

Consistent Symmetry Energy constraints for 0.3<r/ro<1 using different experimental techniques and theories.

Importance of 3n force in the EoS of pure n-matter at high density.

arXiv:1204.0466

...183

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0

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osym

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B

sym PE

LB

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33

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Extracting the 208Pb skin thickness from HIC

Typel & Brown, PRC 64, 027302 (2001)Steiner et al., Phys. Rep. 411, 325 (2005)

0.16-0.27 fm

arXiv:1204.0466

Laboratory experiments to measure the 208Pb neutron skin

208Pb

Existence of a neutron skin3% 1% measurementPREXII approved (2013-2014)

Phys Rev Let. 108, 112502 (2012)

Neutron Number N

Pro

ton

Nu

mb

er Z

3/2AaAaB SV 3/1

)1(

A

ZZaC

A

ZAasym

2)2(

Symmetry Energy in Nuclei

Inclusion of surface terms in symmetry

2

23/2 )2()(

A

ZAAaAa SV

symsym

Hu

bb

le S

T

Crab Pulsar

)( 3/2AaAa SV

symsym

3/2AaAaB SV 3/1

)1(

A

ZZaC

A

ZACsym

2)2(

Csym=22.4 MeV

)/

(3/1

2

A

baa

Fitting of Empirical Binding Energies

Ambiquities in the volume and surface terms of asym

Finite nuclei infinite nuclear matter

Souza et al., PRC 78, 014605 (2008)

Symmetry coefficient from Isobaric Analog States aa(A)

micaCSV EA

ZNa

A

ZaAaAaE

2

3/1

23/2 )(

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

Corrections for microscopic effects + deformation

So = 31.5 MeV; L = 75.6 – 107.1 MeVSo = 33.5 MeV; L = 80.4 – 113.9 MeV

Danielewicz & Lee, NPA818, 36 (2009)

Finite Range Droplet Model (FRDM) – Peter Moller

So = 32.5 ± 0.5 MeV; L = 70 ± 15 MeV

Sophisticated mass model by adding improvementsFRDM-2011a includes symmetry energy in the fit

P. Moller et al, PRL 108,052501 (2012)

Correlation analysis of Pb skin thickness

Reinhard & Nazarewicz ,PRC81, 051303 (R) (2010)

dRnp (208Pb)= 0.20±0.02 fm L=65.1±15.5 MeVSo=32.3±1.3 MeV

Klimkiewicz et al., PRC 76, 051603(R) (2007)Wieland et al., PRL102, 092502 (2009)Carbonne et al., PRC 81, 041301 (2010)

Skin thickness from Pygmy Dipole Resonance

Collective oscillation of neutron skin against the Core dRnp

dRnp = 0.16±(0.02)stat±(0.04)syst±(0.05)theo

Systematics of anti-protonic atoms

Large experimental and theoretical uncertaintiesNeed better quality data & theory

Antiproton probe the extreme tail of nuclei.

Data from 26 nuclei: 40Ca to 238U

Strong correlation between dRnp and asymmetry d.

A. Trzcinska et al, PRL 87, 082501 (2001); M. Centelles et al, PRL 102, 122502 (2009); B.A. Brown et al., PRC 76, 034305 (2007); B. Klos et al., PRC76, 014311 (2007)

dR

np

=( - )/d N Z A

Constraining the EoS using Heavy Ion collisions

pressure contours

density contours

Au+Au collisions E/A = 1 GeV)Au+Au collisions E/A = 1 GeV)

E/A (,) = E/A (,0) + d2S(); d = (n- p)/ (n+ p) = (N-Z)/A

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

Sid

ewar

d F

lowin plane

out of plane

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.

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

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 (

MeV

/fm3 )

/0

NSCL experiments 05049 & 09042Density dependence of the symmetry energy

with emitted neutrons and protons& Investigation of transport model parameters

(May & October, 2009 )

facility ProbeBeam

EnergyTravel (k) $

year density

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

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

MSU iso-diffusion 50 0 2011 <ro

RIKEN iso-diffusion 50 25 2012 <ro

MSU p+,p- 140 0 2014-2015 1-1.5 ro

RIKEN n,p,t, 3He,p+,p- 200-300 85 2013-2014 2ro

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

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

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

GSI S394, May 2011

NSCL experiment 07038 Precision Measurements of

Isospin Diffusion, June 2011)

arXiv:1204.0466

Definition of Symmetry Energy

E/A (,) = E/A (,0) + d2S(); d = (n- p)/ (n+ p) = (N-Z)/A

3/2AaAaB SV 3/1

)1(

A

ZZaC

A

ZAasym

2)2(

-20

-10

0

10

20

30

0 0.1 0.2 0.3 0.4 0.5 0.6

EOS for Asymmetric Matter

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

E/A

(M

eV)

(fm-3)

=(n-

p)/(

n+

p)

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

Fourpi experiments are not optimized to measure symmetry energyNeed better experiments (ASYEOS & SAMURAI/TPC collaborations)

Xiao et al., PRL102, 062502 (2009)Russotto et al., PL B697 (2011) 471

How to obtain the information about EoS using heavy ion collisions?

Experiments:

Accelerator: Projectile, target, energy

Detectors: Information of emitted particles – identity, spatial info, energy, yields construct observables

Models

Input: Projectile, target, energy.

Simulate the collisions with the appropriate physics

Success depends on the comparisons of observables.

Theory must predict how reaction evolves from initial contact to final observables

Transport models (BUU, QMD, AMD)Describe dynamical evolution of the collision process

Summary of Pb skin thickness and symmetry energy constraints

arXiv:1204.0466

Hebeler et al., PRL 105, 161102 (2010)

Laboratory experiments to measure the 208Pb neutron skin

208Pb

PREX (Parity Radius experiment) measures Rnp of 208Pb

Why 208Pb? It has excess of neutrons dRnp=<rn

2>1/2 -<rp2>1/2

It is doubly-magicIts first excited state is 2.6 MeV

Expected uncertainty:APV (Parity-violating Asymmetry )~3% dRn ~1%

Ran in Jefferson Lab in Spring 2010.Phys Rev Let. 108, 112502 (2012)

Density dependence of Symmetry Energy E/A (,) = E/A (,0) + d2S(); d = (n- p)/ (n+ p) = (N-Z)/A

1

10

100

1 1.5 2 2.5 3 3.5 4 4.5 5

symmetric matter

RMF:NL3AkmalFermi gasFlow ExperimentKaons ExperimentFSU Au

P (

MeV

/fm

-3)

/0

Danielewicz, Lacey, Lynch, Science 298,1592 (2002)

Pre

ssur

e (M

eV/f

m3 )

1

10

100

1 1.5 2 2.5 3 3.5 4 4.5 5

neutron matter

Akmalav14uvIINL3DDFermi GasExp.+Asy_softExp.+Asy_stiff

P (

MeV

/fm3)

/0

??

...183

2

0

0

0

0

BsymB

osym

KLSE

symmetry energy constraints from IAS

Tsang et al, PRL 102,122701 (2009)

Equation of State (EoS)

-20

-10

0

10

20

30

0 0.1 0.2 0.3 0.4 0.5 0.6

EOS for Asymmetric Matter

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

E/A

(M

eV)

(fm-3)

=(n-

p)/(

n+

p)

Ideal gas: PV=nRT

Definition of Symmetry Energy

E/A (,) = E/A (,0) + d2S(); d = (n- p)/ (n+ p) = (N-Z)/A

3/2AaAaB SV 3/1

)1(

A

ZZaC

A

ZAasym

2)2(

B.A

. Brow

n, PR

L 85 (2000) 5296

FRDMIAS

Reactions

nuclearstructure

U.S. effort at NSCLActive Target Time Projection Chamber

(MRI)

• Two alternate modes of operation• Fixed Target Mode with target wheel inside chamber:

– 4 tracking of charged particles allows full event characterization– Scientific Program » Constrain Symmetry Energy at >0

• Active Target Mode:– Chamber gas acts as both detector and thick target (H2, D2, 3He, Ne, etc.)

while retaining high resolution and efficiency– Scientific Program » Transfer & Resonance measurements, Astrophysically

relevant cross sections, Fusion, Fission Barriers, Giant Resonances• U.S. collaboration on AT-TPC, U.S. – French GET collaboration on electronics.

S(r)=12.5(r/ro)2/3 +C (r/ro)gi

Symmetry Energy from phenomenological interactionsB

.A. B

rown, P

RL

85 (2000) 5296

...183

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arXiv:1204.0466

Acknowledgement:

NSCL/HiRA group

Giant Dipole Resonance

Collective oscillation of neutrons against protons

Symmetry Energy from Giant dipole Resonsnce

Trippa et al., PRC 77, 061304(R) (2008)

Tsang et al, PRL 102,122701 (2009)

Danielewicz & Lee, NPA818, 36 (2009)

Isobaric Analog States aa(A)

P. Moller et al, PRL 108,052501 (2012)

FRDM-2011a. s~0.57 MeV

...183

2

0

0

0

0

BsymB

osym

KLSE sym

B

sym PE

LB

00

33

0

Mini-summary of symmetry energy constraints from FRDM and IAS

An experimental overview of the symmetry energy around nuclear matter density

Experimental Observables:• Heavy Ion Collisionsn/p ratiosIsospin diffusions

• Giant dipole Resonance (GDR)• Mass model (FRDM)• Isobaric Analog States (IAS)

208Pb skin measurements• PREX• antiprotonic atom systematics• 208Pb(p,p)• 208Pb(p,p’) –dipole polarizability• Dipole Pygmy Resonance (DPR)

Summary and Outlook

Introduction

...183

2

0

0

0

0

BsymB

osym

KLSE

symmetry energy constraints from nuclear masses

Tsang et al, PRL 102,122701 (2009)

Danielewicz & Lee, NPA818, 36 (2009)Isobaric Analog States aa(A) relates the asymmetry term to isospin and energy differences of two IAS

P. Moller et al, PRL 108,052501 (2012)

Sophisticated mass model by adding improvementsFRDM-2011a includes symmetry energy in the fit. s~0.57 MeV