Charges: Provide background information on isoscaling ...

The National Superconducting

Cyclotron Laboratory@Michigan State University

Bet ty Tsang, MSU Theory luncheon talk 3/18/05

Isoscaling in Heavy Ion Reactions

Isoscaling 101??

Charges: Provide background information on isoscaling.

•What is isoscaling? Where is it observed?

–From multifragmentation to binary reactions

•What is the origin of isoscaling? What can we learn?

–Density dependence of symmetry energy.

Neutron Number N

Pro

ton

Nu

mb

er Z 3/2

AaAaB SV 3/1

)1(

A

ZZaC

A

ZAasym

2)2(

asym=30-42 MeV for infinite NM

Inclusion of surface

terms in symmetry

2

23/2 )2()(

A

ZAAaAa SV

symsym

5o

EOS ? ?

0 o

exotics10 km

Relevance to dilute and dense n-rich objects

Sizes of nuclei with

n-halo and n-skin

Stability of Neutron

Star and its structure

P T

Multifragmentation Scenario

--consistent with mixed phase

Time Sequence

--System expands

-- light particle emitted

-- Fragments form

-- Fragments decouple

Time Dependence

--Initial compression and

energy deposition

-- Expansion

-- Cooling

-- Disassembly and freezeout

Different Approaches

Dynamical (AMD,BNV); Rate equations (EES);

Equilibrium at freeze-out density (BUU-SMM)

Micha Kilburn, REU 2003

Density for (/0)2 and 0.0 Impact Parameter


Experimental setup

MSU, IUCF, WU collaboration

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

Miniball + Miniwall

4 multiplicity array

Z identification, A<4

LASSA

Si strip +CsI array

Good E, position,

isotope resolutions

Ring Counter

Annular Si+CsI array

Z of projectile-like residue

HiRA group picture, 1999

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

P T

Isoscaling from Relative Isotope Ratios

R21=Y2/ Y1

TZTN pne//

MB Tsang et al. PRC 64,054615

112Sn+58Ni and 124Sn+64Ni at 35 AMeV; Central collisions, CHIMERA-REVERSE experiment

E. Geraci et al., Nucl. Phys. A732 (2004) 173

Simple derivation of the isoscaling law

• Basic trends from Grand Canonical ensemble:

– Yields term with exponential dependence on the chemical potentials.

• Ratios to reduce sensitivity to secondary decays:

• Scaling parameters C,

),(),(),(

)/exp(12

),(/),(exp),(

*

int

int

ZNfZNYZNY

TEJZwhere

ZNZTZNBZNZNY

HOTCOLD

i

ii

pnHOT

feeding correction

TZTNC

ZNY

ZNYZNR

//

1

221

pne),(

),(,

TT pn /,/

PRL, 85, 716 (2000)

Isospin Factionation

en

Enrichment of

n in the gas

ep

Depletion of

p in the gas

112Sn+112Sn1ˆ

1ˆ

112

112

p

n

903.0ˆ

078.1ˆ

124

124

p

n

124Sn+124Sn

Gain 24 n’s

Isoscaling in statistical models

Primary distributions show good isoscaling

A2=186, Z2=75; A1=168, Z1=75

WCI statistical model working group (2004)

Isoscaling observed in many reactions

Y2/ Y1

TZN pne/)(

Tsang et al, PRL, 86, 5023 (2001)

86Kr+116Sn,124Sn86Kr+58Ni,64NiE/A=35 MeV

More Data

58Ni+58Ni58Fe+58FeE/A=30,40,47

Souliotis et al(2003)

Shetty et al (2003)

p,4He+116Snp,4He+124SnE/A>1 GeV

Botvina,Trautmann (2002)

b

P T

P T

P T

Q Value, Sep. E

ECoul Esym

Separation Energy

ECoul Esym

Chemical Potentials

ECoul Esym p n

R21exp[(-Sn·N- Sp·Z)/T]

R21exp[((-Sn+ fn*)·N+(-Sp +fp

*+ )·Z)/T]

R21exp[(-n·N- p·Z)/T]

Origin of isoscaling

Origin of isoscaling

Isoscaling disappears

when the symmetry

energy is set to zero

Provides an

observable to study

symmetry energy

Temperature Dependence of

E*, temperature

DV Shetty et al. PRC 68,021602 (2004)

Effects of sequential decay on isoscaling

Isoscaling in

Antisymmetrized

Molecular Dynamical

model

A. Ono et al. PRC 68,051601 (2003)

Symmetry energy from AMD

depends on symmetry term interactions

A. Ono et al. PRC 68,051601 (2003)

40Ca+40Ca

48Ca+48Ca

60Ca+ 60Ca

Effects of sequential decays in AMD

Contrary to

statistical models,

sequential decay

effects are large

and may obscure

the sensitivity to

symmetry energy

Tsang et al., PRL92(2004)Lijun Shi

Isospin diffusion

BUU predictionsLijun Shi

Experimental

results are in

better

agreement with

predictions

using hard

symmetry

terms

E, E, 0Ssym( 2

Ssym(

Tsang et al., PRL92(2004)

Relevant Physics from isoscaling in

multifragmentation

1. Isospin fractionation.

2. Exploration of the density dependence of the

symmetry energy

3. Isospin diffusion

Problems:

1. Sequential decays.

2. Probably should avoid statistical models.

3. Need good dynamical calculations that have

correct fragment formation, include momentum

dependence mean field corrections etc.

Other types of “isoscaling”

1. Deeply inelastic inside the grazing

angles (charge equilibrations).

2. Projectile fragmentation at MSU and

GSI energies.

3. Spallation (Should be 2).

4. Fission ??

p, He induced reactions on 112Sn and 124Sn

Reasonable agreements

with isoscaling but

questionable data

quality.

Botvina et al, PRC 65 044610

Isoscaling in deeply inelastic reactions

86Kr+124Sn, 112Sn

86Kr+124Sn, 112Sn

86Kr+64Ni, 58Ni

86Kr+124Sn, 112Sn

Z~36, short reaction time, little

movement of p/n from targets.

Z small, long reaction time, exchange

of p/n from targets.

Evolution of N/Z equilibrium

G. Souliotis et al. PRC 68,024605

Fragmentation of 40Ca and 48Ca

Isoscaling not strictly observed especially for high Z

Slope changes with Z, higher T for small Z

H. Hua, M. Mocko et al. 2004

Isoscaling in spallation processM. Andronenko & L. Andronenko (PNPI, 2004)

Found isoscaling behaviors in

spallation processes for p+54,56Fe, 58,60,62,64Ni,70,76Ge, Rh, Ag, Cs

Detailed examinations suggest that

isoscaling is not strictly adhered to.

However, there is an increase in

alpha with differences in N/Z

changes in targets.

Future of Isoscaling– Will it live to its promise??

Expanding Emitting Source model

W. Friedman PRC42, 667 (1990)

n, lcp

frag

men

ts

15 MeV 14 MeV

13 MeV

11 MeV

multifragmentation

evap.

vaporization

Thermal instability

at low density.

Density dependence of asymmetry energy

S()=23.4(/o)

Results depends on fragment formation!

Strong

influence of

symmetry

t erm on

isoscaling

=0.36 =2/3

Consistent with

many body

calculations

with nn

interactions

Tsang et al, PRL, 86, 5023 (2001)

Isospin diffusion

P

T

P

T

Peripheral Collisions

P

T

Symmetric

system

Mixed

system

Isoscaling of mixed systems

Y21 exp(N+Z)

Tsang et al., PRL92(2004)

Experimental Results

124112

112

1240.13

0.44

112

112 0.0

124

124 0.57

b=>0.8

Y/ybeam>0.7

Experimental: isoscaling;Y21 exp(N+Z)

Theoretical : = (N-Z)/(N+Z)

x=experimental or theoretical isospin

observable

x=x124+124 Ri = 1.

x=x112+112 Ri = -1.

112112124124

1121121241242

xx

xxxR

i

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

Isospin Transport Ratio

1 – 2 (EES,SMM,AMD)

BUU calculations

-- effects of neck fragmentationE, E, 0Ssym( 2

Ssym( (

Including the Neck

fragmentation

changes the BUU

results by about

10%.

BUU calculations E, E, 0Ssym( 2

Ssym( (

Including the

momentum

dependence in the

mean-field in BUU

changes the

agreement.

Existence of neck

fragments changes

results by 10%

Estimates of symmetry

energy DependenceE, E, 0Ssym( 2

Ssym( (

Including the momentum dependence in the mean-field in BUU changes the agreement.BA Li et al, PRL (2005)

Need better theoretical

calculations.

EE

S c

entr

al

coll

isio

ns

Limit is consistent

with EES result from

central collisions

Best guess: ~0.6-1.6

Existence of neck

fragments changes

results by 10%

0.1

1

10

100

0 0.5 1 1.5

Esym() = )( 0

32

25.12

MeVekin

symee sym

kin

sym

int

30MeV (/00.530MeV (/0

1.5

/0

Esy

m (

MeV

)

0.1

1

10

100

0 0.5 1 1.5

Esym() = )( 0

32

25.12

MeVekin

symee sym

kin

sym

int

38.5(/021(/02

30MeV (/02

30MeV (/00.530MeV (/0

1.5

/0

Esy

m (

MeV

)

Summary

A lot of work has been done on isoscaling.

Robust observable

Seen in many different reactions

Promising tool to study symmetry energy with

heavy ion collisions – Isospin Diffusion

Current Best estimate: Esym ~ C(/00.51.5

Isoscaling in Fission

Fission: Binary process with mass, charge conservation.

Fragment z dependence of (z) – Friedman PRC69, 031601(2004)

Shell effects affect isoscaling fits

Friedman:

(z) 8(Csym/T)*(Ah-Al)

*[2ZU/(Ah+Al)]3/(ZU-z)

~ (Csym/T)

*A/<AU>3*1/(1-z/ZU)

Use isoscaling for high

Z to study symmetry

energy information

M. Veselsky et al. PRC 69,044607

Can we study symmetry energy from fission isoscaling ?

Friedman:

(z) (Csym/T)*A/<A>3

15 MeV n+U isotopes

Promising but need more study

~2<A> ~2<A>

Observation

Non-linear increase with A

Increase with <A>

Sensitivity to the isospin terms in the EOS

Y(N,Z)

R21(N,Z)

Data

BUUF1,F3

N/ZSMMP

T Freeze-outsource

Pros : Minimize sequential decay effects

Cons : need two systems

Sensitivity to the isospin terms in the EOS

Mirror

Nuclei

Data

BUUF1,F3

N/ZSMMP

T Freeze-outsource

Pros : Only one system is needed

Cons : Residual sequential decay effects

Gain = 24 Neutrons

124Sn+124Sn112Sn+112Sn

1ˆ

1ˆ

112

112

p

n

903.0ˆ

078.1ˆ

124

124

p

n

Varying the neutron contents

System 112Sn+

112Sn

124Sn+

124Sn

(N/Z)0 1.24 1.48

A0 224 248

Z0 100 100

N0 124 148

n-enhancements observed from isotopes ratios

en

Enrichment of n

in the gas

ep

Depletion of p in

the gas

PRL, 85, 716 (2000)

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