44
A. Sharma et al.
Here, Z i and Z j denote the charges of ith and jth baryon, and T 3i and T 3 j are their
respective T 3 components (i.e., 1/2 for protons and −1/2 for neutrons). The parameters μ and t 1 ,....,t 6 are adjusted to the real part of the nucleonic optical potential.
For the density dependence of the nucleon optical potential, standard Skyrme-type
parametrization is employed. We also use the isospin and energy-dependent cross
section σ = 0.8 σ
f ree
nn . The details about the elastic and inelastic cross sections for
Proton–proton and proton–neutron collisions can be found in [22]. The cross sections
for neutron–neutron collisions are assumed to be equal to the proton–proton cross
sections. Explicit Pauli blocking is also included, i.e., Pauli blocking of the neutrons
and protons is treated separately. We assume that each nucleon occupies a sphere
in coordinate and momentum space. This trick yields the same Pauli blocking ratio
as an exact calculation of the overlap of the Gaussians will yield. We calculate the
fractions P 1 and P 2 of the final phase space for each of the two scattering partners
that are already occupied by other nucleons with the same isospin as that of scattered
ones. The collision is blocked with the probability
P block = 1 − [1 − min(P 1 , 1)][1 − min(P 2 , 1)],
(4.5)
and, correspondingly is allowed with the probability 1 - P block . For a nucleus in its
ground state, we obtain an averaged blocking probability P block = 0.96. Whenever an
attempted collision is blocked, the scattering partners maintain the original momenta
prior to scattering. The IQMD model briefly discussed above is a primary code and
it only generates phase space of nucleons. Therefore, after generating phase space,
there is a need for secondary models to clusterize the nucleons into fragments. In this
article, we use a minimum spanning tree (MST) method [8, 23, 25] for this purpose.
The basic procedure of this method to clusterize the nucleons into fragments is very
simple as it considers two nucleons share the same fragment if their centroids are
closer than a distance R clus , i.e.,
| r i − r j | ≤ R clus ,
(4.6)
where r i and r j are the spatial positions of both nucleons.
4.3 Results and Discussion
In the present chapter, we study some of the isospin effects on the dynamics of fragmentation in asymmetric reactions. To check the effects of isospin degree of freedom
(as it leads to refine ingredients), in IQMD model, first of all, we will robust IQMD
model against the available experimental data of emulsion experiments for asymmetric reactions [26, 27]. The data of emulsion experiments is of particular interest
because it validates any theoretical model designed for studying multifragmentation phenomenon at intermediate energies as a range of beam energies taken for
these experiments cover fusion, multifragmentation, and vaporization phenomenon.
A. Sharma et al.
Here, Z i and Z j denote the charges of ith and jth baryon, and T 3i and T 3 j are their
respective T 3 components (i.e., 1/2 for protons and −1/2 for neutrons). The parameters μ and t 1 ,....,t 6 are adjusted to the real part of the nucleonic optical potential.
For the density dependence of the nucleon optical potential, standard Skyrme-type
parametrization is employed. We also use the isospin and energy-dependent cross
section σ = 0.8 σ
f ree
nn . The details about the elastic and inelastic cross sections for
Proton–proton and proton–neutron collisions can be found in [22]. The cross sections
for neutron–neutron collisions are assumed to be equal to the proton–proton cross
sections. Explicit Pauli blocking is also included, i.e., Pauli blocking of the neutrons
and protons is treated separately. We assume that each nucleon occupies a sphere
in coordinate and momentum space. This trick yields the same Pauli blocking ratio
as an exact calculation of the overlap of the Gaussians will yield. We calculate the
fractions P 1 and P 2 of the final phase space for each of the two scattering partners
that are already occupied by other nucleons with the same isospin as that of scattered
ones. The collision is blocked with the probability
P block = 1 − [1 − min(P 1 , 1)][1 − min(P 2 , 1)],
(4.5)
and, correspondingly is allowed with the probability 1 - P block . For a nucleus in its
ground state, we obtain an averaged blocking probability P block = 0.96. Whenever an
attempted collision is blocked, the scattering partners maintain the original momenta
prior to scattering. The IQMD model briefly discussed above is a primary code and
it only generates phase space of nucleons. Therefore, after generating phase space,
there is a need for secondary models to clusterize the nucleons into fragments. In this
article, we use a minimum spanning tree (MST) method [8, 23, 25] for this purpose.
The basic procedure of this method to clusterize the nucleons into fragments is very
simple as it considers two nucleons share the same fragment if their centroids are
closer than a distance R clus , i.e.,
| r i − r j | ≤ R clus ,
(4.6)
where r i and r j are the spatial positions of both nucleons.
4.3 Results and Discussion
In the present chapter, we study some of the isospin effects on the dynamics of fragmentation in asymmetric reactions. To check the effects of isospin degree of freedom
(as it leads to refine ingredients), in IQMD model, first of all, we will robust IQMD
model against the available experimental data of emulsion experiments for asymmetric reactions [26, 27]. The data of emulsion experiments is of particular interest
because it validates any theoretical model designed for studying multifragmentation phenomenon at intermediate energies as a range of beam energies taken for
these experiments cover fusion, multifragmentation, and vaporization phenomenon.