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S. Sood et al.
˙
r i =
∂ H
∂p i
; ˙
p i = −
∂ H
∂r i
,
(6.1)
where H represents the average Hamiltonian and consists of kinetic energy and potential terms. During the propagation, the nucleons interact with each other via two- and
three-body mean field interactions and collisions, therefore, move at curved trajectories. Within this model, large fluctuations are allowed for nucleons in coordinate
and momentum space necessarily for realistic description for cluster formation.
Over the last three decades using this model, various experimental observations over a wide range of entrance channel have been explained. In particular, this
model is applicable for incident energy of projectile starting from approximately 10
MeV/nucleon–2 GeV/nucleon. One can find the detailed formulation of this model
in [21].
6.2.2 Fragment Recognition
It is well known now that as soon as the nucleons come out of the condensed phase
via adiabatic expansion and ultimately reaches a stage of ‘freeze-out’ the clusterization algorithms are evoked to obtain the fragments. Here, we use two different
types of clusterization algorithms, i.e., minimum spanning tree (MST), minimum
spanning tree with momentum cut (MSTP), minimum spanning tree with binding
energy check (MSTB), minimum spanning tree with thermal binding cut (MSTBT),
and simulated annealing clusterization algorithm (SACA). The former ones use the
local correlations among the nucleons in spatial and/or momentum space, whereas
the latter one uses correlations at global level. Let us understand few details of these
clusterization methods.
• Fragments using local correlations: In this category, local correlations among the
nucleons are checked to sort fragments. If r i ( p i ) and r j ( p j ) are the centroids of
the ith and jth nucleon in coordinate (momentum) space, respectively, then the
following conditions are implemented
|r i − r j | ≤ 4 f m,
(6.2)
| p i − p j | ≤ P Fermi .
(6.3)
If only first condition is evoked, the method is dubbed as minimum spanning tree
(MST) [21]. If nucleons fulfill this condition, they are said to be part of the same
cluster C s , whereas if both the conditions are implemented simultaneously, the
method is dubbed as minimum spanning tree with momentum cut (MSTP) [22].
We choose P Fermi equal to average momentum of the nucleons within the nucleus,
i.e., 150 MeV/c. Due to additional cut, the later method identifies the fragments
much faster compared to former method.
S. Sood et al.
˙
r i =
∂ H
∂p i
; ˙
p i = −
∂ H
∂r i
,
(6.1)
where H represents the average Hamiltonian and consists of kinetic energy and potential terms. During the propagation, the nucleons interact with each other via two- and
three-body mean field interactions and collisions, therefore, move at curved trajectories. Within this model, large fluctuations are allowed for nucleons in coordinate
and momentum space necessarily for realistic description for cluster formation.
Over the last three decades using this model, various experimental observations over a wide range of entrance channel have been explained. In particular, this
model is applicable for incident energy of projectile starting from approximately 10
MeV/nucleon–2 GeV/nucleon. One can find the detailed formulation of this model
in [21].
6.2.2 Fragment Recognition
It is well known now that as soon as the nucleons come out of the condensed phase
via adiabatic expansion and ultimately reaches a stage of ‘freeze-out’ the clusterization algorithms are evoked to obtain the fragments. Here, we use two different
types of clusterization algorithms, i.e., minimum spanning tree (MST), minimum
spanning tree with momentum cut (MSTP), minimum spanning tree with binding
energy check (MSTB), minimum spanning tree with thermal binding cut (MSTBT),
and simulated annealing clusterization algorithm (SACA). The former ones use the
local correlations among the nucleons in spatial and/or momentum space, whereas
the latter one uses correlations at global level. Let us understand few details of these
clusterization methods.
• Fragments using local correlations: In this category, local correlations among the
nucleons are checked to sort fragments. If r i ( p i ) and r j ( p j ) are the centroids of
the ith and jth nucleon in coordinate (momentum) space, respectively, then the
following conditions are implemented
|r i − r j | ≤ 4 f m,
(6.2)
| p i − p j | ≤ P Fermi .
(6.3)
If only first condition is evoked, the method is dubbed as minimum spanning tree
(MST) [21]. If nucleons fulfill this condition, they are said to be part of the same
cluster C s , whereas if both the conditions are implemented simultaneously, the
method is dubbed as minimum spanning tree with momentum cut (MSTP) [22].
We choose P Fermi equal to average momentum of the nucleons within the nucleus,
i.e., 150 MeV/c. Due to additional cut, the later method identifies the fragments
much faster compared to former method.