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7/16/2018 IWND2018 1
International Workshop on Nuclear Dynamics IWND2018
Hozhou, China, June 10-14, 2018
THANNAMANDI , JAMMU & KASHMIR, INDIA
7/16/2018 IWND2018 2
Symmetric and asymmetric fragmentation reactions at intermediate energy heavy-ion collisions using isospin-
dependent quantum molecular dynamics model
International Workshop on Nuclear Dynamics IWND2018
Hozhou, China, June 10-14, 2018
Arun Sharma
(In collaboration with Prof. Rajeev K. Puri, Panjab University, Chandigarh, India)
Department of Physics, Govt. Degree College Thannamandi, J&K, India
By
7/16/2018 IWND2018 3
Points to discuss
Dynamics of nearly symmetric and asymmetric nuclear reactions.
Confrontation of Isospin-dependent quantum molecular dynamics model results with measurements as well as with other available calculated results using different models. Isospin Effects via Coulomb forces and momentum-dependent interactions on the onset of multifragmentation.
7/16/2018 IWND2018 4
Symmetric Nuclear Reactions
Asymmetric Nuclear Reactions
Significant Share of Excitation
energy is stored in the form of
compressional energy
Significant Share of Excitation
energy is stored in the form of
thermal energy
Asymmetric nuclear matter has gained interest because the dynamics of asymmetric collisions is different from that of symmetric reactions
“η” is the mass asymmetry (= [AT -AP ] / [AT +AP]; AT /AP are the masses of the target/projectile)
7/16/2018 IWND2018 5
M O T I V A T I O N
QMD type models face problems to handle dynamics of asymmetric reactions but they work well for symmetric reactions.
7/16/2018 IWND2018 6
Isospin-Dependent Quantum Molecular Dynamics (IQMD) Model
• Initialization: Generate the Projectile/Target (P/T).
• Propagation: Nucleons of P/T propagate under the
influence of mean field.
• Nucleon-Nucleon (nn) Collisions: Nucleons scatter
if they come too close.
Ch. Hartnack, Rajeev K. Puri, J. Aichelin, J. Konopka, S.A. Bass, H. StÄocker, W. Greiner2, EPJA 1, 151 (1998).
PRINCIPLE: RUNS
INITIALIZATION
COLLISION PART
PROPAGATION PART
i
i
i
i
H
td
d
H
td
d
r
p
p
r
∑ t
10,000-10,00,000
Store at 0.1 fm/c time difference from initial to final time
7/16/2018 7 IWND2018
pdpdrdrdtprfrrVtprfm
pj
i ij
ij
i
ii
i
),,(),(),,(2
2
C. Hartnack et al., Eur. Phys. J A 1, 151 (1998).
Propagation
ij
sym
ij
MDI
ij
Coul
ij
Yukawa
ij
Skyrme
ijVVVVVrrV ),(
VTH P.E. K.E.
,r
Hp;
p
Hr
i
i
.
i
i
.
7/16/2018 8 IWND2018
7/16/2018 IWND2018 9
0 3 6 9 12 1510
1
103
105
107
109
1011
1013
1015
1017
1019
1021
1023
1025
1027
Present
Data
30 MeV
(x 106 )
25 MeV
(x 104 )
115 MeV
(x 1022
)
105 MeV
(x 1020
)
95 MeV
(x 1018
)
45 MeV
(x 1010
)
65 MeV
(x 1012
)
75 MeV
(x 1014
)
85 MeV
(x 1016
)
35 MeV
(x 108 )
20 MeV
(x 102 )
dN
/dZ
f (m
b)
40
18Ar+
45
21Sc
Zf
E / A
15 MeV
( x 100 )
Nearly symmetric reactions
The Charge distributions become steeper with increase in beam energy reflecting the violence of collisions. This behavior is opposite to that with increase of impact parameter
The charge distributions are fitted with power law
∝ Z -ɽ from 3≤Z≤12
T. Li et al., Phys. Rev. C 49, 1630 (1994). (source of data)
7/16/2018 IWND2018 10
0 25 50 75 100 1250
1
2
3
4
5
6
Present
Data
40
18Ar+
45
21Sc
Energy (MeV/nucleon)
Ç
The extracted parameter “ɽ” is plotted against the incident energy and rather than sharp minima flatness behavior is observed at low energies.
Our calculations reproduces the experimental extracted “ɽ” values.
7/16/2018 IWND2018 11
0 10 20 30 40 50 60 70 8010
-5
10-3
10-1
101
103
IQ1
IQ2
IQ3
Present
Data
32 MeV/nucleon
129
54Xe+
120
50Sn
d
N/d
Zf
(a)
}ImQMD
0 10 20 30 40 50 6010
-5
10-3
10-1
101
103
39 MeV/nucleon
(b)
Zf
0 10 20 30 40 50 6010
-5
10-3
10-1
101
103
(c)45 MeV/nucleon
0 5 10 15 20 25 3010
-3
10-2
10-1
100
101
102
Present
AMD/DS
AMD/D
Data 50 MeV/nucleon
Zf
dN
/dZ
f129
54Xe+
120
50Sn
The results of ImQMD model have been shown for three sets of equation of state [labeled as IQ1, IQ2 and IQ3]
AMD model calculations are truncated at finite time (of 300 fm/c) and decay of excited fragments is done by statistical decay code.
Prog. Part. Nucl. Phys. 53, 501 (2004) ,Source of data
Phys. Rev. C 87, 066615 (2013) & Chin. Phys. C 37, 114101 (2013), Source of data
7/16/2018 IWND2018 12
10-3
10-2
10-1
100
101
dN/d
Zf
(a)
84
36Kr+
197
79Au
35 MeV/nucleon
Zf
55 MeV/nucleon(b)
70 MeV/nucleon(c)
0 3 6 9 1210
-3
10-2
10-1
100
100 MeV/nucleon(d)
0 3 6 9 12
200 MeV/nucleon(e)
0 3 6 9 12
400 MeV/nucleon(f)
Present
Data
0
4
8
12
(c)
(b)
(a) QMD (unfiltered)
QMD (filtered)
QMD+SMM (unfiltered)
QMD+SMM (filtered)
Data
Present
0
4
8
12
(III)
(II)
(I)
Present (IICS+RFM)
Present (WSP)
Present (RFM)
IIIII
I
30 60 100 200 4000
50
100
150
84
36Kr+
197
79Au
Present
Present (RFM)
Energy (MeV/nucleon)
<N
C>
<N
IMF
s>
<
NIM
Fs> IQMD overcomes the apprehension at low
incident energies.
INVESTIGATION OF DIFFERENT RESULTS USING QMD AND IQMD
MODELS
Phys. Rev. C 55, R2132 (1997) & Phys. Rev. C 49, R2271 (1994)
7/16/2018 IWND2018 13
10-4
10-3
10-2
10-1
100
101
102
Present
FREESCO-I
FREESCO-II
Copenhagen
Data
25 MeV/nucleon
50 MeV/nucleon16
8O+
80
35Br
dN
/dZ
f
(a) (b)
10-4
10-3
10-2
10-1
100
101
(c)
75 MeV/nucleon
Zf
(d)
150 MeV/nucleon
0 10 20 3010
-4
10-3
10-2
10-1
100
101
(e)
100 MeV/nucleon
0 10 20 30 40
(f)
200 MeV/nucleon
10-4
10-3
10-2
10-1
100
101
102
(b)(a)
dN/d
Zf
Present
FREESCO-I
FREESCO-II
Copenhagen
QMD
Data
25 MeV/nucleon
16
8O+
108
47Ag
100 MeV/nucleon
10-4
10-3
10-2
10-1
100
101
(c)
50 MeV/nucleon
Zf
(d)
150 MeV/nucleon
0 10 20 30 4010
-4
10-3
10-2
10-1
100
101
(e)
75 MeV/nucleon
0 10 20 30 40 50
(f)
200 MeV/nucleon
Calculations also include results of two statistical models i.e, FREESCO and Copenhagen, which describe the breakup of excited nuclear matter and a dynamical approach namely, quantum molecular dynamics (QMD) model.
Nu
cl. Ph
ys. A 5
09
, 19
5 (1
99
0) d
ata Sou
rce
7/16/2018 IWND2018 14
10-4
10-3
10-2
10-1
100
Present
Data
16
8O+
80
35Br
200 MeV/nucleon
dN
/dZ
f
(a)
0 5 10 15 20 25 30 3510
-4
10-3
10-2
10-1
16
8O+
108
47Ag
(b)
Zf
10-4
10-3
10-2
10-1
100
101
102
Present
GEMINI
Data
25 MeV/nucleon
197
79Au+
12
6C
25 MeV/nucleon
dN
/dZ
f
(a)
10-4
10-3
10-2
10-1
100
101
102
(b)
SMM
197
79Au+
64
29Cu
35 MeV/nucleon
0 10 20 30 40 50 60 70 8010
-4
10-3
10-2
10-1
100
101
102
197
79Au+
64
29Cu(c)
Zf
Semi-cental colliding geometry leads to less violent collisions and extended tail towards higher Zf when compared with most central collisions
Extended charge distribution tail
Nucl. Phys. A 724, 455 (2003)
7/16/2018 IWND2018 15
0 5 10 15 2010
-3
10-2
10-1
100
101
102
Present
Percolation (unfiltered)
Percolation (filtered)
Data
50 MeV/nucleon
36
18Ar+
197
79Au
0 5 10 15 20 25
80 MeV/nucleon
36
18Ar+
197
79Au
0 5 10 15 2010
-3
10-2
10-1
100
101
102
(c)
110 MeV/nucleon
36
18Ar+
197
79Au
Zf
0 5 10 15 20 25
(d)
(b)
50 MeV/nucleon
129
54Xe+
79,197Au
dN
/dZ
f
(a)
0
40
80
120
160
200(a)
<N
IMF
s><
NL
CP
s>
40
18Ar+
64
29Cu
<A
max
f>
(b) 40
18Ar+
108
47Ag
(c) 40
18Ar+
197
79Au
Energy (MeV/nucleon)
0
10
20
30
(d)
Present
SMM
Berlin
Evap.
Data
(e)
(f)
0 30 60 90 1200
3
6
9
12(g)
Present
0 30 60 90 120
(h)
0 30 60 90 120
(i)
SOME MORE CALCULATIONS
COVERING GOOD RANGE OF ASYMMETRY PARAMETER
R. Sun et al., Phys. Rev. C 61, 061601 (R) (2000).
7/16/2018 IWND2018 16
Results are published in the international Journal of Nuclear Physics A
Multifragmentation of nearly symmetric and asymmetric reactions within a dynamical model.
Arun Sharma et al.,
Nuclear Physics A 945, 95 (2016) (Elsevier-North Holland) [Impact factor- 1.98]
7/16/2018 IWND2018 17
A microscopic analysis of isospin effects on the onset of multifragmentation
in light and heavy charged systems via Coulomb forces
7/16/2018 IWND2018 18
M O T I V A T I O N
Critical energy point of the liquid-gas phase transition has been said to occur at intermediate energy and it may also be associated with the emission of fragments.
This critical energy point is related with the onset of Multifragmentation.
7/16/2018 IWND2018 19
The onset of multifragmentation and its connection to the nuclear liquid-gas phase transition has been reported both experimentally and theoretically.
Also both Coulomb forces and momentum dependent interactions affect the multifragmentation phenomenon. Recent interest of the community has shifted to isospin physics. The basic cause of this shift is the availability of radioactive ion beams. Accordingly, most of the theoretical models have also been upgraded to include isospin degree of freedom.
We tried to probe the effect of Coulomb forces in the presence of momentum-dependent interactions on the onset of multifragmentation i.e., critical energy point in light and heavy colliding systems.
M O T I V A T I O N
7/16/2018 IWND2018 20
10-1
100
101
102
103
104
105
Soft
SMD
40
18Ar+
45
21Sc
E (MeV/nucleon) =
Coulomb On
15
(b)
20
(c)
25
dN
/dZ
f
(d)
30
Zf
10-1
100
101
102
103
104
(e)
35
(f)
45
(g)
65
(h)
75
0 5 1010
-1
100
101
102
103
104
(i)
85
0 5 10
(j)
95
(a)
0 5 10
(k)
105
0 5 10 15
(l)
115
Charge distributions become steeper with
increasing beam energy
Charge distributions for intermediate mass fragments are fitted
with power law
Onset of multifragmentation in light charged system
In the presence of Coulomb forces
7/16/2018 IWND2018 21
0 25 50 75 100 1250
1
2
3
4
5
6
7 Soft
SMD
40
18Ar+
45
21Sc
Energy (MeV/nucleon)
Coulomb OnValues of critical exponent for
both the equations of state increase with
incident energy
Critical exponent vs energy
Here, we do not observe any
minima in the extracted values of tau when plotted
against incident energy
Onset of multifragmentation may occur at lower incident energies
7/16/2018 IWND2018 22
Charge distributions are less steeper in
this case
10-1
100
101
102
103
104
105
Soft
SMD
40
18Ar+
45
21Sc
E (MeV/nucleon) =
Coulomb Off
15
(b)
20
(c)
25
dN
/dZ
f
(d)
30
Zf
10-1
100
101
102
103
104
(e)
35
(f)
45
(g)
65
(h)
75
0 5 1010
-1
100
101
102
103
104
(i)
85
0 5 10
(j)
95
(a)
0 5 10
(k)
105
0 5 10 15
(l)
115
In the absence of Coulomb forces
Coulomb forces can affect the
calculated charge distributions as well
as the onset of multifragmentation,
7/16/2018 IWND2018 23
0 25 50 75 100 1250
1
2
3
4
5
6
7
Soft
SMD
40
18Ar+
45
21Sc
Energy (MeV/nucleon)
Ç
Coulomb Off
Interestingly, the effect of Coulomb forces is visible
even for the light charged system
Solid arrow corresponds to the minimum in the
extracted tau values for soft equation of state
The steepening of charge distributions in the
absence of Coulomb forces gets slow down
Our calculations are consistent with T. Li et al., Phys. Rev. C 49, 1630
(1994).
7/16/2018 IWND2018 24
Accuracy of the critical energy point
10-1
100
101
102
103
104
105
Soft
SMD
40
18Ar+
45
21Sc
E (MeV/nucleon) =
Coulomb Off
15
(b)
20
(c)
25
dN
/dZ
f
(d)
30
Zf
10-1
100
101
102
103
104
(e)
35
(f)
45
(g)
65
(h)
75
0 5 1010
-1
100
101
102
103
104
(i)
85
0 5 10
(j)
95
(a)
0 5 10
(k)
105
0 5 10 15
(l)
115
0 25 50 75 100 1250.0
0.1
0.2
0.3
0.4Coulomb Off Soft 40
18Ar+
45
21Sc
Energy (MeV/nucleon)
Ç
Exponential fits are used to fit the intermediate mass
fragments
7/16/2018 IWND2018 25
Onset of multifragmentation in heavy charged system
10-3
10-2
10-1
100
101
dN/d
Zf
(a)
84
36Kr+
197
79Au
35 MeV/nucleon
Zf
55 MeV/nucleon
(b)
70 MeV/nucleon
(c)
0 3 6 9 1210
-3
10-2
10-1
100
100 MeV/nucleon(d)
0 3 6 9 12
200 MeV/nucleon(e)
0 3 6 9 12
Soft
SMD
400 MeV/nucleon(f)
Coulomb On
30 60 100 200 4001.0
1.5
2.0
2.5
3.0
Soft
SMD
Energy (MeV/A)
84
36Kr+
197
79Au Coulomb On
The distributions decrease monotonically with increase in
the fragment's charge at all incident energies
Trends in the displayed values of tau for both soft and SMD
cases are almost in accordance with those observed for light
charged systems
7/16/2018 IWND2018 26
10-3
10-2
10-1
100
101
dN
/dZ
f
(a)
84
36Kr+
197
79Au
35 MeV/nucleon
Zf
55 MeV/nucleon
(b)
70 MeV/nucleon
(c)
0 3 6 9 1210
-3
10-2
10-1
100
100 MeV/nucleon(d)
0 3 6 9 12
200 MeV/nucleon(e)
0 3 6 9 12
Soft
SMD
400 MeV/nucleon(f)
Coulomb Off
30 60 100 200 4001.0
1.5
2.0
2.5
3.0
Soft
SMD
Energy (MeV/A)
84
36Kr+
197
79Au
Coulomb Off
Both equations of state lead to the onset of
multifragmentation
7/16/2018 IWND2018 27
0 15 30 45 6010
-6
10-4
10-2
100
102
104
Present
Data
32 MeV/nucleon
129
54Xe+
119
50Sn
0 15 30 45 60
39 MeV/nucleon
0 15 30 4510
-6
10-4
10-2
100
102
104
(c)
45MeV/nucleon
Zf
0 15 30 45
(d)
(b)
50 MeV/nucleon
dN
/dZ
f
(a)
Present aim is to concentrate on the yield
of intermediate mass fragments which lie in the
range 3≤Z≤12 to extract the critical exponents as well
as critical energy
Confrontation of IQMD model results with experimental measurements of INDRA collaboration for intermediate mass fragments
Calculated results for the yield of fragments are in nice
agreement with measured ones. Thus, IQMD
model is reliable in explaining the critical
exponents (first order liquid-gas phase transition in the
nuclear matter) at intermediate energy heavy-ion collisions.
Sou
rce of d
ata, Ph
ys. Rev. C
67
, 06
46
13
(20
03
).
7/16/2018 IWND2018 28
These results are published in the European Physical Journal A (Springer)
Isospin effects via Coulomb forces on the onset of multifragmentation in light and heavy charged systems.
Arun Sharma and Arun Bharti Eur. Phys. J. A. 52, 42 (2016) (Springer-Italy) [Impact factor- 2.73]
7/16/2018 IWND2018 29
It has been predicted that IQMD model with various refined ingredients is able to reproduce the measurements of asymmetric reactions and refutes the apprehension raised earlier that molecular dynamics approaches failed to give appropriate results (when compared with measurements) in the asymmetric heavy-ion collisions.
Apart from this, investigations have been made to probe the reason behind the different outcomes of a reaction for the multiplicity of intermediate mass fragments in asymmetric reaction with two different approaches (i.e., QMD and IQMD models). Interestingly, for the first time, it has been put forward that ingredients like symmetry potential and initial large Fermi-momentum of nucleons are responsible for the better reproduction of measured results for asymmetric reactions using IQMD model and these ingredients led to different results compared to results of the QMD model.
7/16/2018 IWND2018 30
It has been found that Coulomb forces influence the onset of multifragmentation and result in the shift of the critical energy point towards lower and higher incident energies with and without their presence, respectively.
It has been noted that for the highly charged system, the critical energy point is sharp when compared with light charged system.
Very interestingly, the critical energy point predicted by the IQMD model is completely consistent with the one extracted using Percolation model by other research groups. Present Status Now we are working to probe role of different clusterization algorithms (as we have good number of these algorithims) on onset of multifragmentation.
7/16/2018 IWND2018 31
It has been predicted that IQMD model with various refined ingredients is able to reproduce the measurements of asymmetric reactions and refutes the apprehension raised earlier that molecular dynamics approaches failed to give appropriate results (when compared with measurements) in the asymmetric heavy-ion collisions.
Apart from this, investigations have been made to probe the reason behind the different outcomes of a reaction for the multiplicity of intermediate mass fragments in asymmetric reaction with two different approaches (i.e., QMD and IQMD models). Interestingly, for the first time, it has been put forward that ingredients like symmetry potential and initial large Fermi-momentum of nucleons are responsible for the better reproduction of measured results for asymmetric reactions using IQMD model and these ingredients led to different results compared to results of the QMD model.
7/16/2018 IWND2018
Further Reading: (http://www.worldscientific.com/worldscibooks/10.1142/10429)
32
We have made significant contribution to this book
7/16/2018 IWND2018 33
7/16/2018 IWND2018 34
Edited the abstract book (comprising of near about 100 abstracts) of one
day State level Science Conference held at GDC Thannamandi in Feb. 2017.
I was co-organizing secretary of the conference.
Edited the abstract book (comprising of near about 130 abstracts) of Two
day National Science Conference held at GDC Thannamandi on 19-20
March, 2018. Also I was organizing secretary of this conference.
http://gdcscienceconference.website/
Other work:
As organizing Secretary
As Co-organizing Secretary
7/16/2018 IWND2018 35
Rohit Kumar, Samiksha Sood, Arun Sharma, Rajeev K. Puri, ACTA PHYSICA
POLONICA B , Vol. 49 (2018).
Use of Simulated Annealing Technique for Finding Most Bound Structures in Nuclear Reactions
Samiksha Sood, Ishita Puri, Rohit Kumar, Arun Sharma and Rajeev K. Puri International Journal of Pure and Applied Physics. ISSN 0973-1776 Volume 13, Number 1 (2017), pp. 201-204. On the relative role of temperature of fragments within the framework of quantum molecular dynamics model
Rohit Kumar, Arun Sharma, Samiksha Sood and Rajeev K. Puri International Journal of Pure and Applied Physics. ISSN 0973-1776 Volume 13, Number 1 (2017), pp. 17-20. Isospin effects on fragmentation in the asymmetric reactions induced by neutron-rich
targets. Arun Sharma AIP Conf. Proc. 1728, 020175 (2016) .
On the cluster formation and phase transition in nuclear disassembly using variety of
clusterization algorithms (Submitted in NPA)
7/16/2018 IWND2018 36
Analysis of colliding matter in terms of symmetry energy and cross-section using computational method Arun Sharma, Sakshi Gautam and, Arun Bharti, AIP Conf. Proc. 1675, 030099 (2015). Study of Intermediate Energy Heavy-ion Collisions in Asymmetric Colliding Nuclei Using Computational Methods
Arun Sharma, Rohit Kumar, Samiksha Sood, and Rajeev K. Puri International Journal of Pure and Applied Physics. ISSN 0973-1776 Volume 13, Number 1 (2017), pp. 21-25.
7/16/2018 IWND2018 37
ACKNOWLEGEMENTS
I acknowledge the HPC team at IUAC, Delhi for giving me access of High performance computer cluster facility and being helpful in different queries regarding the use of the facility.
I would also like to thank HPC team at Department of Physics, Panjab University, Chandigarh for giving me access of the facility in the department.
I am thankful to Prof. Ch. Hartnack from Subatech, France for fruitful discussions.
I am thankful to Prof. Rajeev K. Puri, Panjab University Chandigarh for guiding me and helping me in various stages of my research work.
7/16/2018
It is not an end……It’s a first step towards new beginning…….
38 IWND2018
IWND2018
Big quark-gluon p + n low mass nuclei neutral atom star dispersion of TODAY
Bang plasma formation formation formation formation heavy elements
time 10-6s 10-4s 3 min 400,000 yr 109 yr >109yr 15x109yr
Copyright 1998 Contemporary Physics Education Project (CPEP)
...so much “heat” that we are actually forming a window back in time
7/16/2018 39
7/16/2018 IWND2018 40
In this model, baryons are represented by Gaussian-shaped density
distributions.
)2
)(exp()2
1)(exp(
1),,(
2
22
22
Ltpp
Ltrrtprf
iii
.
ij
sym
ij
Coul
ij
Yukawa
ij
Skyrme
ijVVVVrrV )(
2)()(
1
21
rrrrtrrt
)()/)((
)/)(exp(2
3rr
eZZ
rr
rrt
ji
rrPPtt '1
2
'5ln 24
).(1
33
0
6 jiji rrTTt
,
V ijmdi
+
+
+
7/16/2018 IWND2018 41
(4)
Here t6 = 4C with C = 32 MeV and Zi and Zj denote the charges of the ith and jth baryon,
and T3i and T3j are their respective T3 components (i.e. 1/2 for protons and -1/2 for
neutrons). The parameters µ and t1,....,t4 are adjusted to the real part of the nucleonic
optical potential. For the density dependence of the nucleon optical potential, standard
Skyrme-type parametrization is employed. The momentum dependence Vijmdi of the
nucleon-nucleon interactions, which may optionally be used in IQMD, is fitted to the
experimental data in the real part of the nucleon optical potential. We also use the
standard energy-dependent free nucleon-nucleon cross section. The elastic and inelastic
neutron-proton and proton-proton cross sections are discussed in detail in Ref. [33]. The
neutron-neutron cross section is taken to be equal to proton-proton cross section and
neutron-proton (np) cross section is approximated three times the proton-proton
(neutron-neutron) cross section due to the reason that proton-proton (pp) scattering
occurs only in states of total isospin T = 1 whereas np exists for T = 0 and 1. Two
particles collide if their minimum distance d fulfils
7/16/2018 IWND2018 42
Parameters corresponding to the static and momentum-dependent potentials. K (MeV) α (MeV) β (MeV) γ δ (MeV) ε EOS 200 -356 303 1.17 - - Soft 380 -124 71 2.00 - - Hard 200 -390 (-3189)† 320 (-3176)† 1.14 (1.011)† 1.57 21.54 SMD 380 -130 (-63.13)† 59 (-49.42)† 2.09 (2.12)† 1.57 21.54 HMD
7/16/2018 IWND2018 43
STABILITY TESTS
0 2 4 6 8 10 120.00
0.05
0.10
0.15
0.20
0.25
t=0fm/c
t=5fm/c
t=15fm/c
t=25fm/c
197
79Au
radius (fm)
den
sity
(r
) (f
m-3
)
0
2
4
6
8
0
2
4
6
0
2
4
6
0 50 100 150 2000
2
4
6
0.000
0.075
0.150
0.225
0.300
0.000
0.075
0.150
0.225
0 50 100 150 2000.000
0.075
0.150
0.225
0.000
0.075
0.150
0.225
rms
(r)
[fm
]
Time (fm/c)
Time (fm/c)
197
79Au
120
50Sn
6
3Li
40
20Ca
rms
(p)
[GeV
/c]
