3 Statistical and Dynamical Bimodality in Multifragmentation Reactions
31
Fig. 3.1 Comparison of
mass distribution calculated
according to the existing
(blue-dotted lines) and the
modified (red solid lines)
BUU prescription. The
average value of 5 mass units
are shown. The cases are for
central collision of mass 40
on mass 40 for two different
beam energies a 25 and b 50
MeV/nucleon calculated at
t = 200 fm/c
Hence, in the modified calculation, the total number of combinations for two-body
collision is reduced by a factor of 1/N
2
test . Since typically N test is of the order of 100
this is a huge saving in computation and has allowed us to treat reactions at different
projectile energies and impact parameter described in the next sections. One bonus of
this prescription is that one sees some common ground between the BUU approach
and the “quantum molecular dynamics” approach [31].
At the end of the transport calculation, i.e., at freeze-out stage, we get different
clusters of a finite number of test particles with known position and momenta. By
knowing the number of test particles present in the cluster, one can get the mass, and
by knowing the position and momenta of these test particles, one can calculate the
potential and kinetic energies, respectively. By adding kinetic and potential energy,
the excited state energy of the cluster can be obtained. However, to know excitation,
one needs to calculate the ground-state energy also. This is done by applying the
Thomas–Fermi method for a spherical (ground state) nucleus having a mass equal to
the cluster mass. Knowing PLF mass and its excitation, the freeze-out temperature as
well as decay of excited clusters are calculated by using the canonical thermodynamic
model CTM [32] which is described in Chap. 2.
3.3 Identification of Freeze-Out
Our first aim is to identify the freeze-out time when one can safely stop transport
calculation and switch over to the statistical model. In order to do that, we have investigated the time dependence of (i) mass of the largest and second largest clusters and
(ii) isotopy of momentum distribution in the largest and second largest clusters from
BUU calculation. Indeed in the binary collisions, we consider the largest and second
largest clusters are always the residues of projectile and target. The first signal can
therefore help us to determine the time when the projectile and target are completely
separated, while the second one will point to the attainment of thermalization of these
residues.
The dependence of average size of the largest and the second largest clusters with
time for symmetric system
40 Ca +
40 Ca at projectile beam energy 100 MeV/nucleon
31
Fig. 3.1 Comparison of
mass distribution calculated
according to the existing
(blue-dotted lines) and the
modified (red solid lines)
BUU prescription. The
average value of 5 mass units
are shown. The cases are for
central collision of mass 40
on mass 40 for two different
beam energies a 25 and b 50
MeV/nucleon calculated at
t = 200 fm/c
Hence, in the modified calculation, the total number of combinations for two-body
collision is reduced by a factor of 1/N
2
test . Since typically N test is of the order of 100
this is a huge saving in computation and has allowed us to treat reactions at different
projectile energies and impact parameter described in the next sections. One bonus of
this prescription is that one sees some common ground between the BUU approach
and the “quantum molecular dynamics” approach [31].
At the end of the transport calculation, i.e., at freeze-out stage, we get different
clusters of a finite number of test particles with known position and momenta. By
knowing the number of test particles present in the cluster, one can get the mass, and
by knowing the position and momenta of these test particles, one can calculate the
potential and kinetic energies, respectively. By adding kinetic and potential energy,
the excited state energy of the cluster can be obtained. However, to know excitation,
one needs to calculate the ground-state energy also. This is done by applying the
Thomas–Fermi method for a spherical (ground state) nucleus having a mass equal to
the cluster mass. Knowing PLF mass and its excitation, the freeze-out temperature as
well as decay of excited clusters are calculated by using the canonical thermodynamic
model CTM [32] which is described in Chap. 2.
3.3 Identification of Freeze-Out
Our first aim is to identify the freeze-out time when one can safely stop transport
calculation and switch over to the statistical model. In order to do that, we have investigated the time dependence of (i) mass of the largest and second largest clusters and
(ii) isotopy of momentum distribution in the largest and second largest clusters from
BUU calculation. Indeed in the binary collisions, we consider the largest and second
largest clusters are always the residues of projectile and target. The first signal can
therefore help us to determine the time when the projectile and target are completely
separated, while the second one will point to the attainment of thermalization of these
residues.
The dependence of average size of the largest and the second largest clusters with
time for symmetric system
40 Ca +
40 Ca at projectile beam energy 100 MeV/nucleon