6 On the Fragment Production and Phase Transition Using QMD + SACA Model
67
of phase transition within QMD model and obtained no critical signal in IQMD calculations. The Coulomb forces were found to be the main reason for eliminating the
critical signal [8]. Earlier Ma et al., have obtained critical behavior within the QMD
model for the reaction of
40 Ar+
27 Al [14]. So we see that the studies with both the
statistical models and dynamical do show signatures of phase-transition. Our present
study is using the dynamical model QMD.
Further, in some experiments, the higher order correlations among fragments were
also studied to better understand the physics near the critical point. For example,
Borderie et al., studied the reactions of
129 Xe+
119 Sn at an incident energy of 32
MeV/nucleon using the 4π -multidetector at INDRA [18]. They observed an increase
in the multiplicity of equal-sized fragments as a signal of first-order phase transition.
These results evident the spinodal decomposition scenario for multifragmentation.
The studies were also extended toward N/Z dependence [19].
From the above discussion, it is clear that many facets of the liquid–gas phase
transition are already explored but still a clear picture is missing. In the present work,
we will present calculations using QMD model coupled with various definitions of
fragments for the reactions of
40 Ar+
45 Sc in the incident energy range of 10–115
MeV/nucleon. In particular, we will use energy- based clusterization algorithm, i.e.,
simulated annealing clusterization algorithm (SACA) [20]. In order to better understand this method’s utility, we will also present the calculations with the clusterization
algorithms that construct the fragments via using the local correlations among nucleons in coordinate and/or momentum space or based on binding energy conditions to
find stable fragments. The liquid–gas phase transition will be predicted using various
critical parameters. Also, we present the correlations among the fragments within
events and on event-by-event basis. This will be done to look for the behavior change
for event-by-event correlations near the critical energies.
A brief detail of the n-body model and the various clusterization is given in
Sect. 6.2. In Sect. 6.3, we will present our results and discussion. In Sect. 6.4, we will
give summary of our study.
6.2 Methodology
6.2.1 Quantum Molecular Dynamics Model
The quantum molecular dynamics (QMD) model is a dynamical model that uses
n-body theory to simulate the reactions on an event-by-event basis. In this model, the
reactions are studied via following each individual nucleon where each individual
nucleon is represented by a Gaussian wave packet of constant width in coordinate and
momentum space [21]. To propagate the nucleons, the classical Hamilton’s equations
of motion are used. These equations read as
67
of phase transition within QMD model and obtained no critical signal in IQMD calculations. The Coulomb forces were found to be the main reason for eliminating the
critical signal [8]. Earlier Ma et al., have obtained critical behavior within the QMD
model for the reaction of
40 Ar+
27 Al [14]. So we see that the studies with both the
statistical models and dynamical do show signatures of phase-transition. Our present
study is using the dynamical model QMD.
Further, in some experiments, the higher order correlations among fragments were
also studied to better understand the physics near the critical point. For example,
Borderie et al., studied the reactions of
129 Xe+
119 Sn at an incident energy of 32
MeV/nucleon using the 4π -multidetector at INDRA [18]. They observed an increase
in the multiplicity of equal-sized fragments as a signal of first-order phase transition.
These results evident the spinodal decomposition scenario for multifragmentation.
The studies were also extended toward N/Z dependence [19].
From the above discussion, it is clear that many facets of the liquid–gas phase
transition are already explored but still a clear picture is missing. In the present work,
we will present calculations using QMD model coupled with various definitions of
fragments for the reactions of
40 Ar+
45 Sc in the incident energy range of 10–115
MeV/nucleon. In particular, we will use energy- based clusterization algorithm, i.e.,
simulated annealing clusterization algorithm (SACA) [20]. In order to better understand this method’s utility, we will also present the calculations with the clusterization
algorithms that construct the fragments via using the local correlations among nucleons in coordinate and/or momentum space or based on binding energy conditions to
find stable fragments. The liquid–gas phase transition will be predicted using various
critical parameters. Also, we present the correlations among the fragments within
events and on event-by-event basis. This will be done to look for the behavior change
for event-by-event correlations near the critical energies.
A brief detail of the n-body model and the various clusterization is given in
Sect. 6.2. In Sect. 6.3, we will present our results and discussion. In Sect. 6.4, we will
give summary of our study.
6.2 Methodology
6.2.1 Quantum Molecular Dynamics Model
The quantum molecular dynamics (QMD) model is a dynamical model that uses
n-body theory to simulate the reactions on an event-by-event basis. In this model, the
reactions are studied via following each individual nucleon where each individual
nucleon is represented by a Gaussian wave packet of constant width in coordinate and
momentum space [21]. To propagate the nucleons, the classical Hamilton’s equations
of motion are used. These equations read as