54
P. Bansal et al.
|r i − r j | ≤ R clus , ,
(5.3)
where r i and r j are the spatial positions of the two nucleons. Here, it is worth mentioning that the distinctive values of R clus do not affect the structure of cluster at the
freeze-out stage, where all movements and binary NN collisions cease to exist [33].
The value of R clus can vary between 2 and 4 fm. In the present work, the clusterization
distance is considered to be 2.8 fm.
5.3 Results and Discussion
To study the role of isospin effects and to see how the maximal production alters
with neutron content of the colliding pairs, we simulated several thousand events for
the semi-central collisions of isotopic pairs of
40 Ca +
40 Ca (N/Z = 1.0),
48 Ca +
48 Ca
(N/Z = 1.4), and
60 Ca +
60 Ca (N/Z = 2.0) and isobaric pairs of
48 Cr +
48 Cr (N/Z
= 1.0),
48 Ca +
48 Ca (N/Z = 1.4), and
48 S +
48 S (N/Z = 2.0) at different incident
energies between 30 and 150 AMeV using soft equation of state.
In Fig. 5.1, we display the center-of-mass energy dependence of production of
heavy mass fragments (HMFs) for the isotopic and isobaric reactions. The circles
correspond to our theoretical calculations and lines signify quadratic fits to the theoretical points. We observed a rise and fall behavior in the production of HMFs
with incident energy. This rise and fall behavior can be understood in terms of compressional energy. At low energies, the HMF emission is very minute. This may be
because the system does not have enough energy to break a colliding pair into a large
number of HMFs since the larger fraction of the initial energy is carried away by
the emission of pre-equilibrium nucleons. With the increment in the beam energy,
more energy is available to break the colliding nuclei into a large number of HMFs.
With further increment in the energy, much more energy will be accessible causing
breakage of HMFs into light clusters and free nucleons. For isotopic reaction pairs,
it is noticed that when we go from
40 Ca +
40 Ca to
48 Ca +
48 Ca, the energy corresponding to peak production of HMFs increases. This is because with an increase in
system mass, more energy is required to break the colliding matter into HMFs while
moving toward
60 Ca +
60 Ca, the energy of peak production of HMFs decreases which
is contrary to system mass effects. The factor responsible for such behavior can be
repulsive symmetry potential which pushes the system to boil at lower energy value
which will be discussed in detail in Fig. 5.4. In isobaric reaction pairs, we noticed
that the energy of peak production decreases on moving from
48 Cr +
48 Cr to
48 S +
48 S and the peak production is not varying much with an increase in neutron content.
As each colliding pair has same mass, therefore, the decrease in peak energy can be
because of symmetry potential or Coulomb potential. Going from
48 Cr +
48 Cr to
48 S
+
48 S, the repulsive symmetry potential increases and Coulomb potential decreases.
Since the decrease in peak energy production signifies the dominance of symmetry
potential over Coulomb potential which will be discussed in detail later. We additionally see that the maximum yield of HMFs is almost two for all cases which indicates
P. Bansal et al.
|r i − r j | ≤ R clus , ,
(5.3)
where r i and r j are the spatial positions of the two nucleons. Here, it is worth mentioning that the distinctive values of R clus do not affect the structure of cluster at the
freeze-out stage, where all movements and binary NN collisions cease to exist [33].
The value of R clus can vary between 2 and 4 fm. In the present work, the clusterization
distance is considered to be 2.8 fm.
5.3 Results and Discussion
To study the role of isospin effects and to see how the maximal production alters
with neutron content of the colliding pairs, we simulated several thousand events for
the semi-central collisions of isotopic pairs of
40 Ca +
40 Ca (N/Z = 1.0),
48 Ca +
48 Ca
(N/Z = 1.4), and
60 Ca +
60 Ca (N/Z = 2.0) and isobaric pairs of
48 Cr +
48 Cr (N/Z
= 1.0),
48 Ca +
48 Ca (N/Z = 1.4), and
48 S +
48 S (N/Z = 2.0) at different incident
energies between 30 and 150 AMeV using soft equation of state.
In Fig. 5.1, we display the center-of-mass energy dependence of production of
heavy mass fragments (HMFs) for the isotopic and isobaric reactions. The circles
correspond to our theoretical calculations and lines signify quadratic fits to the theoretical points. We observed a rise and fall behavior in the production of HMFs
with incident energy. This rise and fall behavior can be understood in terms of compressional energy. At low energies, the HMF emission is very minute. This may be
because the system does not have enough energy to break a colliding pair into a large
number of HMFs since the larger fraction of the initial energy is carried away by
the emission of pre-equilibrium nucleons. With the increment in the beam energy,
more energy is available to break the colliding nuclei into a large number of HMFs.
With further increment in the energy, much more energy will be accessible causing
breakage of HMFs into light clusters and free nucleons. For isotopic reaction pairs,
it is noticed that when we go from
40 Ca +
40 Ca to
48 Ca +
48 Ca, the energy corresponding to peak production of HMFs increases. This is because with an increase in
system mass, more energy is required to break the colliding matter into HMFs while
moving toward
60 Ca +
60 Ca, the energy of peak production of HMFs decreases which
is contrary to system mass effects. The factor responsible for such behavior can be
repulsive symmetry potential which pushes the system to boil at lower energy value
which will be discussed in detail in Fig. 5.4. In isobaric reaction pairs, we noticed
that the energy of peak production decreases on moving from
48 Cr +
48 Cr to
48 S +
48 S and the peak production is not varying much with an increase in neutron content.
As each colliding pair has same mass, therefore, the decrease in peak energy can be
because of symmetry potential or Coulomb potential. Going from
48 Cr +
48 Cr to
48 S
+
48 S, the repulsive symmetry potential increases and Coulomb potential decreases.
Since the decrease in peak energy production signifies the dominance of symmetry
potential over Coulomb potential which will be discussed in detail later. We additionally see that the maximum yield of HMFs is almost two for all cases which indicates