76
S. Sood et al.
radii in coordinate (r i j ) and momentum space ( p i j ) as a function of product of the
corresponding charges of the fragments. The results are displayed in Fig. 6.4 for the
fragments of the reactions of
40 Ar+
45 Sc at the corresponding critical energies with
the MSTP and SACA methods. The left and right panels correspond to the results
of the MSTP and SACA methods, respectively. One can see from the figure, that the
spatial radii (r) of fragments from the center-of-mass of the system is larger for the
MSTP method compared to the SACA method, whereas opposite behavior is seen
in momentum space. We have maximum value of radius in coordinate (momentum)
space near to ∼40 fm (∼40 MeV/c). On the other hand, the SACA method has
radius values in coordinate (momentum) space equal to ∼7.5 fm (∼250 MeV/c). The
difference in the values is due to the structure of the algorithms and their freeze-out
times. For both algorithms, we see that with the increase in the size of the fragment,
the radii have comparatively lesser values (larger values) in coordinate (momentum)
space.
In Fig. 6.4e–h, we presented the values of the relative difference between the radii
of the fragments within each event in coordinate (r i j ) (Fig. 6.4e, g) and momentum
space ( p i j ) (Fig. 6.4f, h) as a function of the product of their corresponding charges.
The smaller and larger values of the radii correspond to the fragments that are the
closest neighbors and originated from spectator parts and participant parts, respectively. Also, one can see that the trends of the distributions are horizontal, reflecting
the fact that even if the fragment sizes are different, the average relative distances are
almost same in coordinate space. In momentum space, the fragments have large relative momentum in case of SACA compared to MSTP methods. Again showing that
the SACA fragments are identified much earlier in momentum space. These results
may look surprising, but, reflects the formation of fragments from non- equilibrated
source. Earlier, the same kind of non-equilibrium condition is also observed by Furuta
and Ono for the reactions of
40 Ca+
40 Ca at an incident energy of 35 MeV/nucleon by
studying the kinetic energy and radial size of the reaction system [31].
Lastly, we construct the fragment-fragment within the events. As we mentioned
in the introduction, these correlations are used to find out the criticality signals,
i.e., equal-sized fragments. For this, we constructed the correlation function among
fragment charges Z 1 and Z 2 as
1 + R(Z 1 , Z 2 ) =
Y (Z 1 , Z 2 )
Y (Z 1 , Z 2 )
,
(6.9)
here, Y (Z 1 , Z 2 ) is the yield of the events where charges Z 1 and Z 2 appear within
the events and Y
(Z 1 , Z 2 ) is the yield of the correlated and uncorrelated events. The
results of correlation function using MSTP and SACA methods are displayed in
Fig. 6.5. We see a large difference for the correlation function for the two clusterization algorithms. In the MSTP method, we see lesser correlated events, whereas
in the SACA method we see a strong correlations for the lower charge values. We
also note that the correlations are more distributed in MSTP fragments compared to
SACA fragments.
S. Sood et al.
radii in coordinate (r i j ) and momentum space ( p i j ) as a function of product of the
corresponding charges of the fragments. The results are displayed in Fig. 6.4 for the
fragments of the reactions of
40 Ar+
45 Sc at the corresponding critical energies with
the MSTP and SACA methods. The left and right panels correspond to the results
of the MSTP and SACA methods, respectively. One can see from the figure, that the
spatial radii (r) of fragments from the center-of-mass of the system is larger for the
MSTP method compared to the SACA method, whereas opposite behavior is seen
in momentum space. We have maximum value of radius in coordinate (momentum)
space near to ∼40 fm (∼40 MeV/c). On the other hand, the SACA method has
radius values in coordinate (momentum) space equal to ∼7.5 fm (∼250 MeV/c). The
difference in the values is due to the structure of the algorithms and their freeze-out
times. For both algorithms, we see that with the increase in the size of the fragment,
the radii have comparatively lesser values (larger values) in coordinate (momentum)
space.
In Fig. 6.4e–h, we presented the values of the relative difference between the radii
of the fragments within each event in coordinate (r i j ) (Fig. 6.4e, g) and momentum
space ( p i j ) (Fig. 6.4f, h) as a function of the product of their corresponding charges.
The smaller and larger values of the radii correspond to the fragments that are the
closest neighbors and originated from spectator parts and participant parts, respectively. Also, one can see that the trends of the distributions are horizontal, reflecting
the fact that even if the fragment sizes are different, the average relative distances are
almost same in coordinate space. In momentum space, the fragments have large relative momentum in case of SACA compared to MSTP methods. Again showing that
the SACA fragments are identified much earlier in momentum space. These results
may look surprising, but, reflects the formation of fragments from non- equilibrated
source. Earlier, the same kind of non-equilibrium condition is also observed by Furuta
and Ono for the reactions of
40 Ca+
40 Ca at an incident energy of 35 MeV/nucleon by
studying the kinetic energy and radial size of the reaction system [31].
Lastly, we construct the fragment-fragment within the events. As we mentioned
in the introduction, these correlations are used to find out the criticality signals,
i.e., equal-sized fragments. For this, we constructed the correlation function among
fragment charges Z 1 and Z 2 as
1 + R(Z 1 , Z 2 ) =
Y (Z 1 , Z 2 )
Y (Z 1 , Z 2 )
,
(6.9)
here, Y (Z 1 , Z 2 ) is the yield of the events where charges Z 1 and Z 2 appear within
the events and Y
(Z 1 , Z 2 ) is the yield of the correlated and uncorrelated events. The
results of correlation function using MSTP and SACA methods are displayed in
Fig. 6.5. We see a large difference for the correlation function for the two clusterization algorithms. In the MSTP method, we see lesser correlated events, whereas
in the SACA method we see a strong correlations for the lower charge values. We
also note that the correlations are more distributed in MSTP fragments compared to
SACA fragments.