66
S. Sood et al.
nuclear interactions resemble the Van der Waals forces in molecules. This leads to
the prediction of liquid–gas phase transition in nuclear matter similar to the one we
observe in classical fluids [4]. The phase transition in nuclear matter can be investigated using two different approaches: (i) kinetic methods that predict the phase
transition based on breaking of nuclei at subnormal density, and (ii) studying the
decay mechanism of the nuclei as a function of excitation energy. The former one is
purely theoretical concept, whereas later has an advantage and can be studied both
in theory and experiments. We will be sticking to the later method to understand the
liquid–gas phase transition in nuclear matter [5–8].
In heavy-ion reactions, it was observed that the fragment charge distribution
exhibits power-law fit (∝ Z
−τ
) near critical point. This behavior was in accordance
with earlier predictions by Fisher’s droplet model. The interest in this prediction
further increased when EoS collaboration observed the power-law behavior in the
nuclear fragmentation experiments of Au projectile on C target at 1 GeV/nucleon
[9]. Later, ALADIN collaboration studied the caloric curve of Au+Au reactions at
600 MeV/nucleon and found a plateau of the temperature over a wide excitation
range—the behavior in accordance with a liquid–gas system [10]. Later on, other
than power-law behavior, quantities such as normalized second moment of fragment
charges (S 2 ), variance of fragment charges (γ 2 ), charge of the second largest cluster (< Z max2 >, normalized variance of the charge of the largest cluster, derivative
of the largest fragment size, and multiplicity derivative of the fragments were also
introduced to search critical behavior in multifragmentation [6–8, 11–14]. These
quantities show enhanced fluctuations near the critical point.
Various studies have been conducted using the above-mentioned critical parameters to understand the liquid–gas phase transition in nuclear matter, e.g., Li et al.
using Michigan State University 4π Array have performed a study of
40 Ar+
45 Sc
reactions in the incident energy of 15–115 MeV/nucleon [5]. They have fitted the
charge spectra of IMFs [3 ≤ Z ≤ 12] and plotted the τ values as a function of
incident energy of the projectile. They have predicted the critical point to occur at
23.9±0.7 MeV/nucleon. They have also presented the Percolation model calculations
for theoretical explanation. In the other study, Belkacem et al., studied the Au+Au
reactions at 35 MeV/nucleon for complete impact parameter range using MULTICSMINIBALL apparatus to investigate critical behavior [15]. They predicted the critical
behavior at peripheral geometry. In other study, Ma et al., investigated the reactions of
40 Ar+
27 Al,
48 Ti, and
58 Ni at an incident energy of 47 MeV/nucleon using Neutron Ion
Multi-detector for Reaction Oriented Dynamics (NIMROD) experimental setup [12].
They have analyzed all the critical exponents simultaneously to predict the critical
behavior. Very recently, Lin et al., have investigated the critical behavior within the
statistical multifragmentation model (SMM) [16]. In another study, Liu et al., studied
the total multiplicity derivative, second normalized moment, intermediate mass fragments (IMFs) multiplicity, power-law exponents, Zipf’s law, etc. [17]. They found a
strong correlation of critical signals with the source size. In our previous attempt, we
have studied the central reactions of
40 Ar+
45 Sc using the isospin-dependent quantum
molecular dynamics (IQMD) model and its isospin independent version (QMD) coupled with spatial clusterization algorithm to obtain fragments [7]. We obtain signal
S. Sood et al.
nuclear interactions resemble the Van der Waals forces in molecules. This leads to
the prediction of liquid–gas phase transition in nuclear matter similar to the one we
observe in classical fluids [4]. The phase transition in nuclear matter can be investigated using two different approaches: (i) kinetic methods that predict the phase
transition based on breaking of nuclei at subnormal density, and (ii) studying the
decay mechanism of the nuclei as a function of excitation energy. The former one is
purely theoretical concept, whereas later has an advantage and can be studied both
in theory and experiments. We will be sticking to the later method to understand the
liquid–gas phase transition in nuclear matter [5–8].
In heavy-ion reactions, it was observed that the fragment charge distribution
exhibits power-law fit (∝ Z
−τ
) near critical point. This behavior was in accordance
with earlier predictions by Fisher’s droplet model. The interest in this prediction
further increased when EoS collaboration observed the power-law behavior in the
nuclear fragmentation experiments of Au projectile on C target at 1 GeV/nucleon
[9]. Later, ALADIN collaboration studied the caloric curve of Au+Au reactions at
600 MeV/nucleon and found a plateau of the temperature over a wide excitation
range—the behavior in accordance with a liquid–gas system [10]. Later on, other
than power-law behavior, quantities such as normalized second moment of fragment
charges (S 2 ), variance of fragment charges (γ 2 ), charge of the second largest cluster (< Z max2 >, normalized variance of the charge of the largest cluster, derivative
of the largest fragment size, and multiplicity derivative of the fragments were also
introduced to search critical behavior in multifragmentation [6–8, 11–14]. These
quantities show enhanced fluctuations near the critical point.
Various studies have been conducted using the above-mentioned critical parameters to understand the liquid–gas phase transition in nuclear matter, e.g., Li et al.
using Michigan State University 4π Array have performed a study of
40 Ar+
45 Sc
reactions in the incident energy of 15–115 MeV/nucleon [5]. They have fitted the
charge spectra of IMFs [3 ≤ Z ≤ 12] and plotted the τ values as a function of
incident energy of the projectile. They have predicted the critical point to occur at
23.9±0.7 MeV/nucleon. They have also presented the Percolation model calculations
for theoretical explanation. In the other study, Belkacem et al., studied the Au+Au
reactions at 35 MeV/nucleon for complete impact parameter range using MULTICSMINIBALL apparatus to investigate critical behavior [15]. They predicted the critical
behavior at peripheral geometry. In other study, Ma et al., investigated the reactions of
40 Ar+
27 Al,
48 Ti, and
58 Ni at an incident energy of 47 MeV/nucleon using Neutron Ion
Multi-detector for Reaction Oriented Dynamics (NIMROD) experimental setup [12].
They have analyzed all the critical exponents simultaneously to predict the critical
behavior. Very recently, Lin et al., have investigated the critical behavior within the
statistical multifragmentation model (SMM) [16]. In another study, Liu et al., studied
the total multiplicity derivative, second normalized moment, intermediate mass fragments (IMFs) multiplicity, power-law exponents, Zipf’s law, etc. [17]. They found a
strong correlation of critical signals with the source size. In our previous attempt, we
have studied the central reactions of
40 Ar+
45 Sc using the isospin-dependent quantum
molecular dynamics (IQMD) model and its isospin independent version (QMD) coupled with spatial clusterization algorithm to obtain fragments [7]. We obtain signal