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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)
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
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
Isoscaling disappears
when the symmetry
energy is set to zero
Provides an
observable to study
symmetry energy
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
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.
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)
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