86
S. Sharma et al.
cases, exponent τ is almost same. One can notice that in the reactions of
124 Sn and
197 Au the behavior of the maximum IMFs multiplicity is independent of the target
for the same projectile. While in symmetric reactions of
197 Au +
197 Au, the value of
< N
max
I M Fs > is higher than
124 Sn +
124 Sn which is obvious due to the increase in the
total system mass.
Now, we further extend the above study for various fragments consisting of free
nucleons (FNs), fragments with mass A=2, light charged particles (LCPs) [2≤A≤4],
medium mass fragments (MMFs) [5≤ A≤9] as well as heavy mass fragments (HMFs)
[10≤A≤A total /6]. The behavior of these fragments at the peak energy of IMF’s
production is explored here for
124 Sn and
197 Au target reactions. The results are
displayed in Fig. 7.2. We observe the system mass dependence of these quantities
and follow the power law of the form A
τ
tot for both
124 Sn and
197 Au target reactions.
The exponent τ is very close to unity for the case of FNs, A=2 and LCPs. Here
the linear dependence indicates the vanishing surface and Coulomb effects. In all
these cases, the slope of
197 Au target reactions is slightly higher than that of
124 Sn.
The factor responsible for the increment of slope of these quantities is the high peak
IMFs energy for
197 Au target reactions with same projectile. It is well known that
with rise in incident energy more correlations are broken, thus the production of
these fragments rise more sharply. Correspondingly, the increased pumped energy
causes less production of MMFs and HMFs, as a result their slope rises less sharply.
To extract information about hot and dense nuclear matter, maximum density
achieved in reaction acts as an important variable. We calculate matter density as
ρ =
A tot
i=1
1
(2π L) 3/2 e
{−[ − → r − − → r i (t)]
2 /2L}
.
(7.1)
Here, A tot is the total system mass. To calculate the density, we take a sphere
of 2 fm radius around the center of mass of two colliding nuclei. The average
density (< ρ
avg
>/ρ 0 ) is calculated over the whole sphere and maximum density
(< ρ
max
>/ρ 0 ) reached anywhere in this sphere. In Fig. 7.3, we display the various
quantities such as average and maximum density as a function of time for both
124 Sn
and
197 Au target reactions at their respective peak energies. It is evident that the maximal of < ρ
avg
>/ρ 0 and < ρ
max
>/ρ 0 is delayed for symmetric reactions compared
to asymmetric reactions. Also, the density zone is wider for symmetric reactions
indicating that hot and dense matter exists for longer time. After the compressional
phase, the density in central region falls sharply to lower values. In asymmetric reactions the fall is sharp as compared to symmetric reactions. Also, the density profile of
197 Au target reactions is wider than
124 Sn target reactions reflecting the bulk effects.
Another quantity linked with the density is the collision rate (displayed in lower
panel). The collision rate (dN coll /dt) is displayed as a function of reaction time. In
case of symmetric reactions, the interaction among nucleons continue for longer time
thus, the collision rate is high. Whereas in case of asymmetric reactions, due to lesser
interaction region the collision rate is less. Again, the difference we see for the
124 Sn
and
197 Au target is due to the difference in their nucleon number and corresponding
S. Sharma et al.
cases, exponent τ is almost same. One can notice that in the reactions of
124 Sn and
197 Au the behavior of the maximum IMFs multiplicity is independent of the target
for the same projectile. While in symmetric reactions of
197 Au +
197 Au, the value of
< N
max
I M Fs > is higher than
124 Sn +
124 Sn which is obvious due to the increase in the
total system mass.
Now, we further extend the above study for various fragments consisting of free
nucleons (FNs), fragments with mass A=2, light charged particles (LCPs) [2≤A≤4],
medium mass fragments (MMFs) [5≤ A≤9] as well as heavy mass fragments (HMFs)
[10≤A≤A total /6]. The behavior of these fragments at the peak energy of IMF’s
production is explored here for
124 Sn and
197 Au target reactions. The results are
displayed in Fig. 7.2. We observe the system mass dependence of these quantities
and follow the power law of the form A
τ
tot for both
124 Sn and
197 Au target reactions.
The exponent τ is very close to unity for the case of FNs, A=2 and LCPs. Here
the linear dependence indicates the vanishing surface and Coulomb effects. In all
these cases, the slope of
197 Au target reactions is slightly higher than that of
124 Sn.
The factor responsible for the increment of slope of these quantities is the high peak
IMFs energy for
197 Au target reactions with same projectile. It is well known that
with rise in incident energy more correlations are broken, thus the production of
these fragments rise more sharply. Correspondingly, the increased pumped energy
causes less production of MMFs and HMFs, as a result their slope rises less sharply.
To extract information about hot and dense nuclear matter, maximum density
achieved in reaction acts as an important variable. We calculate matter density as
ρ =
A tot
i=1
1
(2π L) 3/2 e
{−[ − → r − − → r i (t)]
2 /2L}
.
(7.1)
Here, A tot is the total system mass. To calculate the density, we take a sphere
of 2 fm radius around the center of mass of two colliding nuclei. The average
density (< ρ
avg
>/ρ 0 ) is calculated over the whole sphere and maximum density
(< ρ
max
>/ρ 0 ) reached anywhere in this sphere. In Fig. 7.3, we display the various
quantities such as average and maximum density as a function of time for both
124 Sn
and
197 Au target reactions at their respective peak energies. It is evident that the maximal of < ρ
avg
>/ρ 0 and < ρ
max
>/ρ 0 is delayed for symmetric reactions compared
to asymmetric reactions. Also, the density zone is wider for symmetric reactions
indicating that hot and dense matter exists for longer time. After the compressional
phase, the density in central region falls sharply to lower values. In asymmetric reactions the fall is sharp as compared to symmetric reactions. Also, the density profile of
197 Au target reactions is wider than
124 Sn target reactions reflecting the bulk effects.
Another quantity linked with the density is the collision rate (displayed in lower
panel). The collision rate (dN coll /dt) is displayed as a function of reaction time. In
case of symmetric reactions, the interaction among nucleons continue for longer time
thus, the collision rate is high. Whereas in case of asymmetric reactions, due to lesser
interaction region the collision rate is less. Again, the difference we see for the
124 Sn
and
197 Au target is due to the difference in their nucleon number and corresponding