Effect of
isospin

dependent cluster
recognition on the observables in
heavy ion collisions
Yingxun
Zhang (
张英逊
)
2012
年
8
月
10
日，
兰州
合作者：
Zhuxia
Li, (CIAE)
Chengshuang
Zhou, (CIAE, GXNU)
M.B.Tsang
(MSU)
China Institute of Atomic Energy
•
Transport model is one of the powerful methods for
understanding the mechanism of SHE synthesis and the
properties of nuclear matter
General view of transport models
Three parts in the transport models
1, Initial condition
2, Motion of equation
Cluster recognition
methods
3, Observables
1), Nucleonic potential
2), In medium XS
1),
proj
.,
targ
.,
2), density profile
3), BE,
rms
4),
Ebeam
, b
5), stability
A
, BUU type:
f(
r,p,t
)
one body phase space density
Two

body collision: occurs between test part.
Mean field
Solved with test particle methods
EOS, symmetry energy
B
, QMD type: solve N

body equation of motion
nucleon
Two body collision: occurs between nucleons
Rearrange whole nucleon

> large
flucturation
EOS, symmetry energy
Motion of Equation
also play very important roles on the final observables
as well as on EOS and in

medium XS!
Cluster recognition methods in the QMD and BUU models:
1.
MST,
Aichelin
, et.al., PR202(1991)
2.
ECRA,
C. O.
Dorso
and J.
Randrup
, Phys.
Lett
. B
301, 328 (1993).
3.
SACA,
R. K.
Puri
and J.
Aichelin
, J.
Comput
. Phys.
162, 245 (2000).
4.
MSTB,
P. B.
Gossiaux
, R. K.
Puri
, C.
Hartnack
, and J.
Aichelin
,
Nucl
. Phys. A
619,
379 (1997).
5.
Cluster Correlation
,
Danielewicz et al., NPA533 (1991) 712
,
A.Ono
, 2012
6.
Coalescence model
,
LWChen
, et.al., NPA 2004
Cluster recognition methods
Problems in current QMD models
simualtions
:
1 Z=1 largely overestimated, Z=2, underestimated,
A. Ono
K.
Zbiri
, A Le Fever, J.
Aichelin
, et.al, PRC75, 2007
2, Enhancements of the productions of neutron

rich isotopes observed in
isoscaling
,
Y
2
/ Y
1
T
Z
N
p
n
e
/
)
(
Not well predicted by the transport models
TXLiu
, et.al.,
Phys.Rev.C
69, 014603(2004)
The predicted final isotope
distributions are narrower than the
experimental data, ……
3, Strong enhancement of heavy fragments in neutron

rich reaction system,
124Sn+64Ni
112Sn+58Ni
P.Rustto
, et.al., PRC81
The result shows that the
dynamical process is about
twice as probable in the
neutron

rich system as in the
neutron

poor one.
This unexpected and significant
difference
….
~ 2 times
4, Predict more transparency than that observed experimentally in central collisions
at intermediate energy
Insufficient production of fragments in the mid

rapidity region
R.Nebauer
,
J.Aichelin
, NPA658(1999)
All the problems are not fixed by only changing the
EOS or in

medium XS in previous studies!
It naturally require an improvements on the
cluster recognition methods in the transport
models !
R
nn
0=
R
np
0=
R
pp
0=
R
0
∼
3.5 fm
In Regular MST, nucleons with relative distance of coordinate
and momentum of

r
i
−
r
j
<R
0
and p
i
−
p
j
<P
0
belong to a
fragment.
roughly be in the range of nucleon

nucleon interaction
,
and is
determined by fitting the global experimental data,
such as the IMF multiplicities.
However, previous algorithms do not address
the lack of
isospin
dependence in cluster recognition
, which is the main focus of this work.
Failed in details, such as problem 2) and 3)
Isospin
dependent MST
Rnn
0=
Rnp
0~
6.0 fm
Rpp0~3.0fm
Physical point of view:
1.
properties of neutron

rich nuclei, such as neutron skin or
neutron halo effect
2.
long

range repulsive Coulomb force between protons in
the cluster
3.
hints from neutron

rich heavy ion collisions
11Be
Isospin
dependent cluster recognition methods (
iso

MST)
Effect of
iso

MST on observables
112,124Sn+112,124Sn, b=2fm,
E_beam
=50AMeV
Reaction systems:
Transport models:
ImQMD05
Improved Quantum Molecular Dynamics model (ImQMD05)
the mean fields acting on nucleon
wavepackets
are derived
from
Skyrme
potential energy density functional
potential energy density functional:
EOS
H=
T+U+U_coul
Surface symmetry energy term
Detail of code: Zhang, et alPR
C71
(05) 024604, PR
C74
(06) 014602, PRC75,034615(07)., PL
B664
(08) 145,
PRC85(2012)024602
Isospin dependent nucleon

nucleon cross sections
are adopted, the medium corrections are
free
np
med
np
)
/
1
(
0
free
pp
nn
med
pp
nn
,
0
,
)
/
1
(
d
d
free
pp
nn
np
/
,
)
(
,
Cugnon, et al., Nucl.Instr.Meth.Phys. B111, 215(1996)
depend on the beam energy
Well reproduce the data of charge distribution, direct flow, elliptical flow and stopping
power (30

400AMeV)
Effect of
iso

MST on observables
YXZhang
,
Zhuxia
Li,
Chengshuang
Zhou,
MBTsang
, PRC85,051602(2012)(R)
1, Charge distribution
1, obviously reduce the yield of Z=1
part.
2, enhance the yield of fragments with
Z>=2.
3, strongly enhance the yield of heavy
fragments. (Z>=12)
Sn+Sn
,
Ebeam
=50AMeV
Rapidity distribution for
n,p
2,
n, p, t, He3
production
1, reduce the yield of both neutron and protons,
2, enhancement of the n/p, t/He3 ratios appears at mid

rapidity and lower kinetic
energy
n/p, DR(n/p), t/He3, DR(t/He3)
3, enhancement of the DR(n/p), DR(t/He3) ratios appears at mid

rapidity and lower kinetic energy
Zhang, et.al., PLB2008
3,isotope distribution and
isoscaling
isoscaling
YXZhang
,
Zhuxia
Li,
Chengshuang
Zhou,
MBTsang
, PRC85,051602(2012)(R)
1, enhance the production of the neutron

rich isotope, especially for neutron

rich
reaction system
2, predict larger values of
isoscaling
parameter, alpha
4, Effect of
iso

MST on equilibrium
MST:
Vartl
=0.58
Iso

MST:
Vartl
=0.62
YXZhang
,
Zhuxia
Li,
Chengshuang
Zhou,
MBTsang
, PRC85,051602(2012)(R)
•
the equilibrium or stopping power of the system
also depends on the detailed
description of cluster formation implemented in the transport models
as well as on
the mean field and the in

medium NN cross section.
Conclusion
1.
we introduce a
phenomenological
isospin
dependence in the description of
cluster formation in transport models by adopting different
R0 values for pp,
nn
, and
np
, Rpp
0= 3 fm and
Rnn
0=
Rnp
0= 6 fm.
2.
The
isospin

dependent minimum spanning tree method show
suppression of
Z = 1 particles and enhancement of fragments,
especially for heavier
fragments with
Z >=12.
3.
Furthermore,
we find
enhanced production of neutron

rich isotopes at mid

rapidity.
Consequently,
isospin

sensitive observables, such as the double
ratios,
DR(t/3He), and
isoscaling
parameter α increase to larger values.
4.
The widths of the longitudinal
and transverse rapidity distributions of
Z = 1
–
6
particles also
change,
the degree of equilibrium become higher.
5.
The
isospin
dependence of the cluster recognition can be
easily
implemented
and should be included in nuclear transport models.
Thanks
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