Symmetry Energy in Nuclei · 5/19/2009 · spectator remnant is to shift the isotopic...

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

Hub

ble

ST

Crab Pulsar

Physics of symmetry energy

• masses

• n-skin of heavy nuclei such as 208Pb

• Fission barriers

• .

• .

• Neutron star properties

Neutron Number N

Pro

ton

Nu

mb

er Z

3/2AaAaB SV 3/1)1(

A

ZZaC

A

ZAasym

2)2(

Hub

ble

ST

Crab Pulsar

Density dependence of Symmetry Energy

Questions:

What have we learned about symmetry energy at low density?

What are the unique opportunities offered at high density?

F1

F3

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

BsymBsym

KLaE

sym

B

symP

EL

B0

0

33

0

Expansion around 0:

Symmetry slope L &

curvature Ksym

Symmetry pressure Psym

40)( aEsym

The National Superconducting

Cyclotron Laboratory

Michigan State University

Betty Tsang

Defining the neutron star crust: Giant

flares, superbursts and

x-ray bursts

May 17-21, 2009Santa Fe, NM

Learning about the EoS of Asymmetric Nuclear matter with Heavy Ion Collisiosn

How to obtain the information about EoS?

Both astrophysical and laboratory observables can constrain the EoS, (,T,) or P(,T,) indirectly.

What are the experimental uncertainties of the constraints?

What are the model uncertainties of the constraints?

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.

Transport models:

Describe dynamical evolution of the

collision process

•Self consistent mean field

•n-n collisions,

•Pauli exclusion

Uncertainties

Semi-classical

Approximations needed to make

computation feasible.

What are the uncertainties in theoretical predictions?

Symmetry energy included in the

nuclear EOS for infinite nuclear

matter at various densities from

the beginning of collision.

Low and Intermediate Energy

Heavy Ion Collisions Workshop

ECT*

5/11/2009 - 5/15/2009, Trento, Italy

Reaction mechanism of fragment

productions depends on impact

parameters

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

Neck fragments

b=7 fm

multifragmentationb=0 fm

S()=12.5(/o)2/3 +19(/o)

i

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

subnormal density

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 diffusion

p+ & p- at high incident energy

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

ST

Crab Pulsar

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

Vasy

(M

eV

)

/ o

Neutron

Proton

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 at low density.

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

ImQMD

Y(n

)/Y

(p)

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

i

80-380

420-620

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

Scattering Chamber

Famiano et al

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

Analysis of n/p ratios with ImQMD model

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

i

0.4i 1.05

Analysis of n/p ratios with ImQMD model

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

i

0.4i 1.05

Data need better measurements but the trends and

magnitudes still give meaningful 2 analysis at 2 level

Experimental Observable :

Isospin Diffusion

Isospin diffusion is measured with fragments emitted from the neck region.

Probe the symmetry energy at subsaturation densities in semi-peripheral collisions, e.g. 124Sn + 112Sn at b=6 fm

Isospin “diffuse” through low-density neck region

Symmetry energy drives system towards equilibrium.

• stiff EOS small diffusion; |Ri|>>0

• soft EOS fast equilibrium; Ri0

Projectile

Target

124Sn

112Sn

soft

stiff

BBAA

BBAAABi

xx

xxxR

2/)(2

Isotope Distribution Experiment

MSU, IUCF, WU collaboration

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

Miniball + Miniwall

4 p multiplicity arrayZ identification, A

The main effect of changing the

asymmetry of the projectile

spectator remnant is to shift the

isotopic distributions of the

products of its decay

This can be described by the

isoscaling parameters and :

)ZNexp(CZ,NY

Z,NY

1

2

Isotope distributions and isospin diffusions

1.0

0.33

-0.33

-1.0

Ri()

Isospin diffusionRi()

no diffusion

and are related to the

nucleon chemical potentials

Analysis of isospin diffusion data with ImQMD model

BBAA

BBAAABi

xx

xxxR

2/)(2 iS()=12.5(/o)

2/3 + 17.6 (/o)

x(data)=x(QMD)=

EquilibriumRi=0

No diffusionRi =1; Ri =-1

0.4i 1

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 iS=12.5(/o)

2/3 + 17.6 (/o)

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

EquilibriumRi=0

No diffusionRi =1; Ri =-1

0.4i 1

b~5.8 – 7.2 fm

For the first time, we have a transport model that describes

np ratios and two isospin diffusion measurements

Consistent constraints from the 2 analysis of three observables

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

0.4i 10.4i 1.050.45i 0.95

0.4i 1i

Expansion around 0:

slope L & curvature Ksym

...183

2

0

0

0

0

BsymBo

KLSS

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

i

IQM

D

S()~31.6(/o)

IBU

U04

LSymmetry pressure Psym

sym

B

symP

EL

B0

0

33

0

IQM

D

IBU

U04

...183

2

0

0

0

0

BsymBo

KLSS

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

i S~31.6(/o)

Rnp=0.04 fm

LSymmetry pressure Psym

sym

B

symP

EL

B0

0

33

0

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

i

No constraints on So

ImQMD

2 2 analysis

...183

2

0

0

0

0

BsymBo

KLSS sym

B

symP

EL

B0

0

33

0

Vary Cs,p and i

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

i

...183

2

0

0

0

0

BsymBosym

KLSE sym

B

symP

EL

B0

0

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

BsymBosym

KLSE sym

B

symP

EL

B0

0

33

0

Current constraints on

symmetry energy from HIC

Constraints on the density dependence of symmetry energy

?

Au+Au

Constraints on the density dependence of symmetry energy

Au+Au experiments in high energy are

not designed to measure symmetry energy

Need better experiments

1. HI collision dynamics are complex but prove to be sensitive to density dependence of symmetry energy.

2. Need multiple observables to place various constraints on the input parameters of the transport models

3. Problems still remain, e.g.

• How to extract results to T=0;

• Control of input parameters in transport models.

Low and Intermediate Energy

Heavy Ion Collisions Workshop

ECT*

5/11/2009 - 5/15/2009, Trento, Italy

Lessons learned from LE measurements:

International Collaboration

RIBF

FRIB

Outlook

MSU

GSI

FAIR

Acknowledgements

NSCL Transport simulation group

Brent 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

Experimenters


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, W.A. Friedman, A.

Ono, W.G. Lynch, L.J. Shi, Jenny Lee,

Trento workshop organizers and participants

Jorg Aichelin, Theo Gaitanos, Hermann Wolter

Summary

The 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

Need more guidance from theory regarding observables and

interpretation of experimental results.

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 – international

co-ordination of a global program.

Au+Au

Wed afternoon discussions

Au+Au

stiffness

Inconsistencies in the

constraints on symmetry energy

at high and low density?


Wednesday afternoon discussions: Experiments in RIBF

?RIBF

Isospin diffusions

for fragments and

residues with RIBF,

~2010

Riken TPC &

to measure p+/p, t/3He, p/n (Nebula),

spectra ratios

RIBF

E/A=200-300 MeV measure p+, p- spectra ratios, p,n, t/3He spectra ratios

and differential flow determine S(), m*, nn, pp, np at ~2o

E/A~50 MeV measure isospin diffusions for fragments and residues

determine S() at

Measured Isotopic yieldsT.X Liu et al. PRC 69,014603

P T

Central collisions

Similar distributionsR21(N,Z)=Y2(N,Z)/ Y1(N,Z)

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

?MSUGSI

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<

MSU

FRIB

FAIR

MSU (2009-2012) : E/A

?MSUGSI

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<

2020?

FRIB

FAIR

Outlook

Precision measurements in FRIB

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 M

Travel: 0.37 M

Detectors needed:

Density region sampled

depends on collision

observable & beam

energy

• >0 examples:

– Pion energy spectra

– Pion production ratios

– Isotopic spectra

– Isotopic flow

– With NSCL beams, densities

up to 1.7 0 are accessible

– Beams: 50-150 MeV,

50,000pps

106Sn-126Sn, 37Ca-49Ca

Riken Samurai TPC

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

Isospin Diffusion

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

Projectile

Target

124Sn

112Sn

No diffusion

Complete mixing

Au+Au

stiffness

Inconsistencies in the constraints on

symmety energy at high and low density?


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

Isotope Distribution Experiment

MSU, IUCF, WU collaboration

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

Miniball + Miniwall

4 p multiplicity arrayZ identification, A

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)/A

• Collision systems: 124Sn+124Sn, 124Sn+112Sn, 112Sn+124Sn, 112Sn+112Sn

• E/A=50 MeV

• Low densities (

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

Cluster effects

Cluster effects

are important

for low energy

nucleons but

cannot explain

the large

discrepancy

between data

and IBUU04

calculations

Constraints from Isospin Diffusion Data

124Sn+112Sn data

Data:

•Collisions of

Sn+Sn isotopes

at E/A=50 MeV

•b/bmax>0.8

~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 & beam

energy

• >0 examples:

– Pion energy spectra

– Pion production ratios

– Isotopic spectra

– Isotopic flow

– With NSCL beams, densities

up to 1.7 0 are accessible

– Beams: 50-150 MeV,

50,000pps

106Sn-126Sn, 37Ca-49Ca

• 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

•

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

p

loss term gain term

11 1

1

2

3 4

non-relativistic: BUU

effective mass

Kinetic momentum

Field tensor

Relativistic BUU

),( fIcoll

Vlasov eq.; mean field

EOS

Simulation with Test Particles:

me

an

px(y

0)

[Me

V]

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.

0.45i 0.95

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

The National Superconducting

Cyclotron Laboratory


Betty Tsang

RIBF Mini-workshop on

Nuclear Collisions and

Nuclear Matter

Dec 16-17, 2008Riken

Learning about the Density dependence of Symmetry Energy in Heavy Ion Reactions

?RIBF


•Effect is much larger

than IBUU04

predictions

inconsistent with

conclusions from

isospin diffusion data.



Double

Rat

io

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

What are the densities created in Heavy Ion 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)/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


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


•Newer calculation and

experiment are consistent with

the constraints.

E/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

EOS: symmetric matter and neutron matter

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

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

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

Neutron matter EOS

-20

0

20

40

60

80

100

120

0 1 2 3 4

symmetric matter

NL3Bog1:e/aBog2:e/aK=300, m*/m=70Akmal_corr.

E/A

( M

eV)

/0

•The density dependence

of symmetry energy is

largely unconstrained.

N-detection – neutron wall

p-detection: Scattering Chamber

3 particle telescopes

(p, d, t, 3He, …)

WU MicroBall

(b determination)

~6in

2.0ˆ b

# of charged particles

central




Double

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.

Pros

Derivable, approximations

better understood.

Cons

Mean field no fluctuations

BUU does not predict cluster

formation

QMD:

Molecular dynamics with

Pauli blocking.

Pros

Predicts cluster production

Cons

Cluster properties (masses,

level densities) approximate

Need sequential decay codes

to de-excite the hot fragments

Code used: ImQMD

At high incident energies, cluster production is weak

the two models yield the same results.

Clusters are important in low energy collisions.

y/ybeam

QMDisoscaling

R7

R7Ri()=Ri()

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? What is the origin of elements heavier than iron in the

cosmos? What are the nuclear reactions that drive stars and stellar

explosions?

Tests of Fundamental Symmetries – Why is there now more matter

than antimatter in the universe?

Examples of possible research areas in FRIB

Learning about the Equation of State of Asymmetric

Nuclear Matter with Heavy Ion Collisions

Nuclear Equation of State

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

= (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? What is the origin of elements heavier than iron in the

cosmos? What are the nuclear reactions that drive stars and stellar

explosions?

Tests of Fundamental Symmetries – Why is there now more matter

than antimatter in the universe?

Examples of possible research areas in FRIB

xAB, yAB experimental or

theoretical observable for AB

yAB= a xAB+b

Ri(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 systems124

124112

112

Isospin diffusion occurs only

in asymmetric systems A+B124

112

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

0.4i 1

0.4i 1.050.45i 0.95

Trautmann et al

Betty Tsang

Learning about Symmetry Energy at Low Density with Heavy Ion Reactions

Defining the neutron star crust: Giant

flares, superbursts and

x-ray bursts

May 17-21, 2009Santa Fe, NM

Constraints from Isospin Diffusion Dataof calculation!

M.B. Tsang et. al., arXive:0811.3107 L.W. Chen, … B.A. Li, PRL 94, 032701 (2005)

iQMD:S()=12.5(/o)2/3 + 19.6 (/o) IBUU04 : S()~31.6(/o)

stiffness

Are these constraints consistent? What are the model uncertainties?

How to connect different representations of the symmetry energy

stiffness

0.69 1.05i ~0.7

Symmetry Energy in Nuclei · 5/19/2009 · spectator remnant is to shift the isotopic...

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