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S. Sood et al.
largest cluster, on the other hand it is also able to explain physics of event-by-eventbased observables such as multiplicity probability and probability distribution of the
first three largest clusters. The bottleneck of this algorithm is its capacity to reduce
the freeze-out time down to ∼60 fm/c. The gain by a factor of six in time compared to MST method and its variants also allow one to understand the fragments
when they are well within high-density region. The only reason for lesser utility of
the SACA method is its running time. We will be utilizing the MST and its variants, MSTP, MSTBT (local correlations), and SACA (global correlations) methods
to understand liquid–gas phase transition and fragment-fragment correlations at and
near the critical energy.
6.3 Results and Discussion
For the present study, we have simulated the reactions of
40 Ar+
45 Sc in the incident
energy range of 10–115 MeV/nucleon for central geometries using soft equation of
state. The energy-dependent nucleon-nucleon cross-section is used in the present
work. Throughout the article, we will restrict our discussion at freeze-out time only.
For the MST, MSTP, MSTBT, and SACA methods, the freeze-out times are 300
fm/c and 60 fm/c, respectively. Before discussing the results let us understand the
mechanism of fragment formation within different clusterization methods.
In a typical heavy-ion collision, the nuclei approach each other and pump the
energy into the system with which they are boosted initially. The nuclear matter then
compresses and excites. The hot piece of matter then releases its energy via rapid
expansion. The matter then shatters into correlated nucleons. The clusterization methods based on local correlations are not applicable untill the nuclear matter is well
diluted. The MST method uses spatial information and may form fragments if consecutive nucleons are within defined distances. Therefore, can form fragments even
if the nucleons are spread over space, leading to lesser stability. The MSTP method
puts additional cuts on nucleons and excludes the fast moving nucleons from fragments. This de-excites the fragments to some extend and saturates its structure early
in time. It also helps to separate the overlapping fragments. In MSTBT method, the
thermal binding cut is implemented on MST fragments to sort the stable fragments.
It removes the fragments which are loosely bound. Whereas, in SACA method, the
coordinate and momentum space nucleons are used to obtain stable fragments. As
in this method, one minimizes the binding energy of the clusters, therefore, the final
cluster configuration is obtained at early times as soon as fragments are formed. All
the above-discussed clusterization methods will be used to analyze the signals of
phase transition in fragmentation.
S. Sood et al.
largest cluster, on the other hand it is also able to explain physics of event-by-eventbased observables such as multiplicity probability and probability distribution of the
first three largest clusters. The bottleneck of this algorithm is its capacity to reduce
the freeze-out time down to ∼60 fm/c. The gain by a factor of six in time compared to MST method and its variants also allow one to understand the fragments
when they are well within high-density region. The only reason for lesser utility of
the SACA method is its running time. We will be utilizing the MST and its variants, MSTP, MSTBT (local correlations), and SACA (global correlations) methods
to understand liquid–gas phase transition and fragment-fragment correlations at and
near the critical energy.
6.3 Results and Discussion
For the present study, we have simulated the reactions of
40 Ar+
45 Sc in the incident
energy range of 10–115 MeV/nucleon for central geometries using soft equation of
state. The energy-dependent nucleon-nucleon cross-section is used in the present
work. Throughout the article, we will restrict our discussion at freeze-out time only.
For the MST, MSTP, MSTBT, and SACA methods, the freeze-out times are 300
fm/c and 60 fm/c, respectively. Before discussing the results let us understand the
mechanism of fragment formation within different clusterization methods.
In a typical heavy-ion collision, the nuclei approach each other and pump the
energy into the system with which they are boosted initially. The nuclear matter then
compresses and excites. The hot piece of matter then releases its energy via rapid
expansion. The matter then shatters into correlated nucleons. The clusterization methods based on local correlations are not applicable untill the nuclear matter is well
diluted. The MST method uses spatial information and may form fragments if consecutive nucleons are within defined distances. Therefore, can form fragments even
if the nucleons are spread over space, leading to lesser stability. The MSTP method
puts additional cuts on nucleons and excludes the fast moving nucleons from fragments. This de-excites the fragments to some extend and saturates its structure early
in time. It also helps to separate the overlapping fragments. In MSTBT method, the
thermal binding cut is implemented on MST fragments to sort the stable fragments.
It removes the fragments which are loosely bound. Whereas, in SACA method, the
coordinate and momentum space nucleons are used to obtain stable fragments. As
in this method, one minimizes the binding energy of the clusters, therefore, the final
cluster configuration is obtained at early times as soon as fragments are formed. All
the above-discussed clusterization methods will be used to analyze the signals of
phase transition in fragmentation.