The National Superconducting Cyclotron Laboratory

Michigan State University

Betty Tsang

5th ANL/MSU/JINA/I

NT FRIB Workshop on

Bulk Nuclear Properties

Nov 19-22, 2008MSU

S(

Constraints on the Density dependence of Symmetry Energy in Heavy Ion Reactions

Extracting Density dependence of Symmetry Energy in Heavy Ion Reactions

F1

F3 Outline:

What does HIC have to offer?

What are the pitfalls (in theory)?

What constraints do we have now? (Are the constraints believable or reliable?)

What research directions are we going towards FRIB?

Extracting Density dependence of Symmetry Energy in Heavy Ion Reactions

F1

F3

HIC provides a range of density determined from incident energy and impact parameter

Micha Kilburn

Bulk nuclear matter properties from Heavy Ion Central Collisions

Highest density reached by central collisions depends on incident beam energy.

Types of particles formed depend on emission times and density.

Pions, n, p fragments

E/A=1600 MeV

200 MeV50 MeV

• Experiment: measure collective flow (emission patterns) of particles emitted in Au+Au collisions from (E/A~1-8 GeV).

• Transport model (BUU) relates the measurements to pressure and density.

pressure contours

density contours

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

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

Equation of State of Nuclear Matter

1

10

100

1 1.5 2 2.5 3 3.5 4 4.5 5

symmetric matter

RMF:NL3AkmalFermi gasFlow Exp.

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

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 )

•Newer calculation and experiment are consistent with the constraints.

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

Equation of State of Nuclear Matter

??

•Transport model includes constraints in momentum dependence of the mean field and NN cross-sections

Experimental Techniques to probe the symmetry energy with heavy ion collisions at 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 isotopes + & - at higher incident

energyNeutron 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

Around incident energy: E/A<100 MeV:

Reaction mechanism depends on impact parameters

Heavy Ion collision: 124Sn+124Sn, E/A=50 MeV

Neck fragmentsb=7 fm

multifragmentationb=0 fm

i=0.

5

i=2.

0

Esym=12.7(/o)2/3 + 19(/o)i

subnormal density

n & p are emitted throughout

Charged fragments (Z=3-20) are formed at subnormal density

II. Statistical models:Describe longer time scale decays from single source. •nuclear mass, •level densities, •decay ratesUncertaintiesSource parameters: Ao, Zo, Eo, Vo, JInformation obtained is for finite nuclei, not for infinite nuclear matter

I. Transport models:Describe dynamical evolution of the collision process•Self consistent mean field •n-n collisions, •Pauli exclusionUncertaintiesSemi-classicalApproximations needed to make computation feasible.

Classes of models used to interpret experimental results

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

Symmetry energy included in the form of fragment masses – finite nuclei & valid for o only. EOS extrapolated using statistical model is questionable.

Symmetry energy included in the nuclear EOS for infinite nuclear matter at various density from the beginning of collision.

xAB, yAB experimental or theoretical observable for AByAB= a xAB+bRi(xAB )= Ri(yAB )

Rami et al., PRL, 84, 1120 (2000)

BBAA

BBAAABi xx

xxxR

2/)(

2

Experimental Observable : Isospin Diffusion --Isospin Transport Ratio

No isospin diffusion between symmetric systems

124124

112112

Isospin diffusion occurs only in asymmetric systems A+B

124112

Non-isospin diffusion effects same for A in A+B & A+A ;same for B in B+A & B+B

Non-isospin transport effects are “cancelled”??

Ri = 1

Ri = -1

Experimental Observable : Isospin Diffusion

Probe the symmetry energy at subsaturation densities in peripheral collisions, e.g. 124Sn + 112Sn

Isospin “diffuse” through low-density neck region

Projectile

Target

124Sn

112Sn

BBAA

BBAAABi xx

xxxR

2/)(

2

x(calc)=

soft

stiff

Symmetry energy drives system towards equilibrium.

•stiff EOS small diffusion; |Ri|>>0

•soft EOS fast equilibrium; Ri0

Constraints from Isospin Diffusion Dataof calculation!

M.B. Tsang et. al., PRL 92, 062701 (2004) L.W. Chen, … B.A. Li, PRL 94, 032701 (2005)

pBUU: S=12.7(/o)2/3 + 12.5 (/o)

stiffness

IBUU04 : S~31.6(/o)

stiffness

Observable in HIC is sensitive to dependence of Sand should provide constraints to symmetry energy

Experimental Observables: n/p yield ratios

-100

-50

0

50

100

0 0.5 1 1.5 2

Li et al., PRL 78 (1997) 1644

Vas

y (M

eV)

/ o

NeutronProton

F1=2u2/(1+u)

F2=u

F3=u

F1F2

F3

u =

stiff

soft

Uas

y (M

eV)

=0.3

•n and p potentials have opposite sign.

•n & p energy spectra depend on the symmetry energy softer density dependence emits more neutrons.

•More n’s are emitted from the n-rich system and softer iso-EOS.

ImQMD

Y(n

)/Y

(p)

S=12.7(/o)2/3 + 17.6(/o)i

n/p Double Ratios (central collisions) 124Sn+124Sn;Y(n)/Y(p)112Sn+112Sn;Y(n)/Y(p)

Double Ratiominimize systematic errors

Data : Famiano et al. PRL 97 (2006) 052701

Will repeat experiment for better accuracy

n/p Double Ratios (central collisions)

•Effect is much larger than IBUU04 predictions inconsistent with conclusions from isospin diffusion data.

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

Double Ratiominimize systematic errors

Dou

ble

Rat

io

Center of mass EnergyFamiano et al. RPL 97 (2006) 052701

Nuclear Collisions simulations with Transport Models – Nuclear EOS included from beginning of collisions

BUU models:Semiclassical solution of one-body distribution function.ProsDerivable, approximations better understood.ConsMean field no fluctuations BUU does not predict cluster formation

QMD:Molecular dynamics with Pauli blocking.ProsPredicts cluster productionConsCluster properties (masses, level densities) approximate Need sequential decay codes to de-excite the hot fragmentsCode used: ImQMD

At high incident energies, cluster production is weak the two models yield the same results.

Clusters are important in low energy collisions.

Cluster effects

Zha ng et al. P

LB

66 4 (2 008 )1 45

Cluster effects are important for low energy nucleons but cannot explain the large discrepancy between data and IBUU04 calculations

Analysis of n/p ratios with ImQMD model Esym=12.5(/o)2/3 + 17.6 (/o)

i

i

Data need better measurements but the trends and magnitudes still give meaningful 2 analysis at 2 level

Analysis of isospin diffusion data with ImQMD model

BBAA

BBAAABi xx

xxxR

2/)(

2 i

S=12.5(/o)2/3 + 17.6 (/o)

x(data)=x(QMD)=

EquilibriumRi=0

No diffusionRi =1; Ri =-1

i

Impact parameter is not well determined in the experiment

b~5.8 – 7.2 fm

Analysis of rapidity dependence of Ri with ImQMD model

BBAA

BBAAABi xx

xxxR

2/)(

2 i

S=12.5(/o)2/3 + 17.6 (/o)

x(data)=f(7Li/7Be)x(QMD)=

EquilibriumRi=0

No diffusionRi =1; Ri =-1

i

New analysis on rapidity dependence of isospin diffusion ratios – not possible with BUU type of simulations due to lack of fragments.

b~5.8 – 7.2 fm

How to connect different representations of the symmetry energy

Consistent constraints from the 2 analysis of three observables

S=12.5(/o)2/3 + 17.6 (/o)

i

i

i

i

IBUU04 : S~31.6(/o)

approximation

For the first time, we have a transport model that describes np ratios and two isospin diffusion measurements

i

Expansion around 0: slope L & curvature Ksym

...183

2

0

0

0

0

BsymB

o

KLSS

LSymmetry pressure Psym

symB

sym PE

LB

00

33

0

S=12.5(/o)2/3 + 17.6 (/o) i

IQM

D

i

ImQMD

S~31.6(/o)

IBU

U04

IBUU04

IQM

D

IBU

U04

...183

2

0

0

0

0

BsymB

o

KLSS sym

B

sym PE

LB

00

33

0

S=12.5(/o)2/3 + 17.6 (/o) i

i

ImQMD

S~31.6(/o)

IBUU04Rnp=0.04 fm

S=12.5(/o)2/3 + Cs,p(/o) i

No constraints on So

ImQMDVary Cs,p and i

2 2 analysis

...183

2

0

0

0

0

BsymB

o

KLSS sym

B

sym PE

LB

00

33

0

Esym=12.5(/o)2/3 + Cs,p(/o) i

...183

2

0

0

0

0

BsymB

osym

KLSE sym

B

sym PE

LB

00

33

0

Constraints from masses and Pygmy Dipole Resonances

Esym=12.5(/o)2/3 + Cs,p(/o) i

...183

2

0

0

0

0

BsymB

osym

KLSE sym

B

sym PE

LB

00

33

0

Constraints from masses and Pygmy Dipole Resonances

Esym=12.5(/o)2/3 + Cs,p(/o) i

...183

2

0

0

0

0

BsymB

osym

KLSE sym

B

sym PE

LB

00

33

0

Current constraints on symmetry energy from HIC

Constraints on the density dependence of symmetry energy

Au+Au

?

No constraints between 0 and 2 0

FRIB

2020? FRIB

FAIR

Outlook

Precision measurements in FRIB

MSU

FRIB

FAIR

MSU (2009-2012) : E/A<100 MeV measure isospin diffusion, fragments, residues, p,n spectra ratios and differential flow improve constraints on S(, m*, nn, pp, np at <o

MSU (~2013) : E/A>120 MeV measure +, - spectra ratios constraints at o< <1.7o -- Bickley

Outlook

?MSU

GSI

FRIB

FAIR

GSI (2011) : E/A~400 – 800 MeV measure p,n spectra ratios and differential flow determine constraints S(, m*, nn, pp, np at 2.5o< <3o

Lemmon, Russotto et al, experimental proposal to GSI PAC

Outlook

?MSU

Riken

GSI

FRIB

FAIR

Riken (2013-2017) : E/A=200-300 MeV measure +, - spectra ratios, p,n, t/3He spectra ratios and differential flow determine S(), m*, nn, pp, np at ~2o

Riken (2011) : E/A>50 MeV measure isospin diffusions for fragments and residues determine S() at <2o.

108Sn+112,124Sn – RI beam used to increase .

Outlook

n detectors: NSCL/pre-FRIB; GSI; RIBF/Riken Pions/kaons & p, t, 3He detectors: TPC

NSCL Dual purpose AT-TPC: proposal to be submitted to DOE

RIBF TPC: SUMARAI magnet funded, TPC – Japan-US collaboration: proposal to be submitted to DOE.

AT-TPC: FRIB

~ 1.2 M

TPC ~ 0.78 MTravel: 0.37 M

Detectors needed:

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

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

Calculations suggest a number of promising observables that can probe the density dependence of the symmetry energy.

–Isospin diffusion, isotope ratios, and n/p spectral ratios provide some constraints at 0, -- refinement in constraints foreseen in near future with improvement in calculations and experiments at MSU, GANIL & Riken

– + vs. - production, n/p, t/3He spectra and differential flows may provide constraints at 20 and above, MSU, GSI, Riken

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.

Acknowledgements

NSCL Transport simulation groupBrent Barker, Abby Bickley, Dan Coupland, Krista Cruse, Pawel

Danielewicz, Micha Kilburn, Bill Lynch, Michelle Mosby, Scott Pratt, Andrew Steiner, Josh Vredevooqd, Mike Youngs, YingXun Zhang

ExperimentersMichigan State University

T.X. Liu (thesis), W.G. Lynch, Z.Y. Sun, W.P. Tan, G. Verde, A. Wagner, H.S. Xu

L.G. Sobotka, R.J. Charity (WU)R. deSouza, V. E. Viola (IU)

M. Famiano: (Westen Michigan U)

Y.X. Zhang (ImQMD), P. Danielewicz, M. Famiano, W.A. Friedman, W.G. Lynch, L.J. Shi, Jenny Lee,

How to connect different symmetry energy representations

0

10

20

30

40

50

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Total Symmetry Energy

i=0.5

i=2.0

FSU GOLDAV18skm*NL3

Esy

m (

MeV

)

/0

Value of symmetry energy at saturation

2

0

0

0

04 183

BsymB

sym

KLaE

symB

sym PE

LB

00

33

0

Expansion around 0: Symmetry slope L & curvature Ksym

Symmetry pressure Psym

40 )( aEsym

Density region sampled depends on collision observable & beamenergy• >0 examples:– Pion energy spectra– Pion production ratios– Isotopic spectra– Isotopic flow– With NSCL beams, densitiesup to 1.70 are accessible– Beams: 50-150 MeV, 50,000pps106Sn-126Sn, 37Ca-49Ca

Riken Samurai TPC

Density region sampled depends on collision observable & beamenergy• >0 examples:– Pion energy spectra– Pion production ratios– Isotopic spectra– Isotopic flow– With NSCL beams, densitiesup to 1.70 are accessible– Beams: 50-150 MeV, 50,000pps106Sn-126Sn, 37Ca-49Ca

Riken Samurai TPC

Isospin Diffusion

D

egre

e of

Asy

mm

etry

from isoscaling from Y(7Li)/Y(7Be)

Projectile

Target

124Sn

112Sn

No diffusion

Complete mixing

n-star HI collisions

/0~ 0.1 - 10 ~ 0.1-5

ye ~0.1 ~0.38-0.5

T(MeV) ~1 ~ 4-50

Extrapolate information from limited asymmetry and temperature to neutron stars!

Laboratory experiments to study properties of neutron stars

Laboratory experiments to study properties of neutron stars

208Pb

extrapolation from 208Pb radius to n-star radius

N/Z ratios from bound fragments (Z=3-8) complementary to n/p ratios

EC.M.

P T

Esym=12.7(/o)2/3 + 19(/o)i

Effects are small

Hot fragments produced in calculations.

P T

Sequential decay effects are important

Data consistent with soft EOS

N/Z ratios from bound fragments (Z=3-8) complementary to n/p ratios

Esym=12.7(/o)2/3 + 19(/o)i

Experimental Observables to probe the symmetry energy

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

• Collision systems: 124Sn+124Sn, 124Sn+112Sn, 112Sn+124Sn, 112Sn+112Sn• E/A=50 MeV• Low densities (<0):

– n/p spectra and flows; Y(n)/Y(p), Y(t)/Y(3He), – Fragment isotopic distributions,

• Isoscaling: interpretation with statistical model is incorrect• <N>/<Z> of Z=3-8 fragments• Isospin diffusion

– Correlation function, C(q)– Neutron, proton radii, E1 collective modes.

• High densities (20) – Neutron/proton spectra and flows; C(q) + vs. - production, k, hyperon production.

asy-stiff

asy-soft

Exploring Bulk properties of Nuclear Matter with Heavy Ion Collisions

High density/energy

• differential flow

• n/p, LIF ratios

• pions ratios

• kaon ratios

• neutron stars

Low density/energy

• fragments, ratios

• isospin diffusion

• isoscaling

• migration/fractionat.

• collective excitations

• surface phenomena

• phase transitions

QF Li, Di Toro

Di Toro, Lukasic

DiToro, Reisdorf, QF Li

Prassa, QF Li

BA Li, Kubis

Tsang, HW

BA Li, HW

Tsang

Di Toro

Aumann, Ducoin

Lehaut

Danielewicz

Hermann Wolter

Constraints from Isospin Diffusion Data

124Sn+112Sn data

Data:

•Collisions of Sn+Sn isotopes at E/A=50 MeV

•b/bmax>0.8 <b>~7.2 fm from multiplicity gates.

•y/yb>0.7

•Results obtained with clusters

IBUU04:

Collisions of Sn+Sn isotopes at E/A=50 MeV

b=6 fm

Projectile-like residue determined from density &

y/yb>0.5

No clusters

x=0

x=1(soft)

x=-1

x=-2

Isospin diffusion in the projectile-like region

Basic ideas:• Peripheral reactions• Asymmetric collisions

124Sn+112Sn, 112Sn+124Sn -- diffusion

• Symmetric Collisions 124Sn+124Sn, 112Sn+112Sn -- no diffusion

• Relative change between target and projectile is the diffusion effect

Projectile

Target

Density region sampled depends on collision observable & beamenergy• >0 examples:– Pion energy spectra– Pion production ratios– Isotopic spectra– Isotopic flow– With NSCL beams, densitiesup to 1.70 are accessible– Beams: 50-150 MeV, 50,000pps106Sn-126Sn, 37Ca-49Ca

• The density dependence of symmetry energy is largely unconstrained.

• Pressure, i.e. EOS is rather uncertain even at 0.

• The density dependence of symmetry energy is largely unconstrained.

• Pressure, i.e. EOS is rather uncertain even at 0.

Isospin Dependence of the Nuclear Equation of State

E/A (,) = E/A (,0) + 2S()

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

-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)

PAL: Prakash et al., PRL 61, (1988) 2518.Colonna et al., Phys. Rev. C57, (1998) 1410.

Brown, Phys. Rev. Lett. 85, 5296 (2001)

a/s

2 A/EP

Neutron matter EOS

dailygalaxy.com

• <0 – created in multifragmentation processObservables:– n/p ratios– Isotopic spectra– Beams: 50 MeV, 112Sn-124Sn

Transport description of heavy ion collisions:

,fIfUfm

p

t

fcollp

2-body hard collisions

)1)(1()1)(1(

)()2(

1

432432

43213412

124322

3

ffffffff

ppppd

dvdpdpdp

loss term gain term

11 1

12

3 4

non-relativistic: BUU

effective mass

Kinetic momentum

Field tensor

Relativistic BUU

),( fI coll

Vlasov eq.; mean field

EOS

Simulation with Test Particles:

me

an

px(

y0)

[M

eV

]

Analysis of rapidity dependence of Ri with ImQMD model Esym=12.5(/o)2/3 + 17.6 (/o)

i

New analysis on rapidity dependence of isospin diffusion ratios – not possible with BUU type of simulations due to lack of fragments.

i