5 Isospin Effects: Nuclear Fragmentation as a Probe
61
Next, we will check the role of isospin degree of freedom via symmetry potential
and NN scattering cross section on the cross-over energy. Here, we simulated the
reactions without considering symmetry potential and results are shown in Fig. 7.
From the figure, we see that the individual gas content is diminished without symmetry potential. One can clearly see from the figure that the cross-over is acquired
at higher energies when we neglect symmetry potential, as expected.
Next, we will explore the role of NN scattering cross section by considering
isospin-independent cross section in Fig. 8. Again, the yield of individual gas content
is suppressed by considering σ non−iso and in this way increment in cross-over energy
is observed for every asymmetric reaction pair.
Next, we will summarize our results of isospin effects on the cross-over energy
for mass asymmetric reactions in Fig. 9. Here, solid circles correspond to default
calculations. Open circles and half filled circles represent calculations without symmetry potential and isospin independent cross-section, respectively. We found that
the cross-over energy is increased in absence of symmetry potential as well as by
utilizing isospin independent cross-section. Here, we notice that the rise in crossover energy is almost comparable when calculations are performed in absence of
symmetry potential or for isospin-independent cross-section, for each colliding pair,
independent of its mass asymmetry.
Next, we check the role of density dependence of nuclear symmetry energy on
cross-over energy for the reactions of
31 P +
69 Ga (η = 0.4) and
20 Ne +
80 Kr (η =
0.6) by simulating these reactions with soft (γ = 0.5) and stiff (γ = 1.5) forms of
nuclear symmetry energy. In Fig. 10, we show the energy dependence of gas and
liquid yield for the reaction of 31P + 69Ga and 20Ne + 80Kr with soft form of
symmetry energy (upper panel) and stiff form of symmetry energy (lower panel).
Here, diamonds correspond to the reaction of
31 P +
69 Ga and triangles represent the
reaction of
20 Ne +
80 Kr. From the figure, we see that the cross-over occurs at lower
energy for stiff symmetry energy when contrasted with soft symmetry energy. The
occurrence of cross-over at higher energy for soft symmetry energy is because of the
fact that the effective strength of symmetry energy is weak in case of soft density
dependence at supra-saturation densities (which come into the picture in present
collisions) and in this way, weak repulsive forces in case of soft symmetry energy
will make the system to break at higher energy. In case of stiff symmetry energy,
the system requires a lesser amount of energy to break down because of stronger
(repulsive) symmetry potential. It is also clear from the figure that the cross-over
energy value is higher for the reaction of
20 Ne +
80 Kr (η = 0.6) in contrast with
31 P +
69 Ga (η = 0.4), as expected. Further, we observed that with increment in
mass asymmetry, the sensitivity of density dependence of nuclear symmetry energy
on cross-over energy is increased. Thus, we conclude that cross-over energy is a
sensitive probe to study nuclear symmetry energy as well as its density dependence
at supra-saturation densities.
61
Next, we will check the role of isospin degree of freedom via symmetry potential
and NN scattering cross section on the cross-over energy. Here, we simulated the
reactions without considering symmetry potential and results are shown in Fig. 7.
From the figure, we see that the individual gas content is diminished without symmetry potential. One can clearly see from the figure that the cross-over is acquired
at higher energies when we neglect symmetry potential, as expected.
Next, we will explore the role of NN scattering cross section by considering
isospin-independent cross section in Fig. 8. Again, the yield of individual gas content
is suppressed by considering σ non−iso and in this way increment in cross-over energy
is observed for every asymmetric reaction pair.
Next, we will summarize our results of isospin effects on the cross-over energy
for mass asymmetric reactions in Fig. 9. Here, solid circles correspond to default
calculations. Open circles and half filled circles represent calculations without symmetry potential and isospin independent cross-section, respectively. We found that
the cross-over energy is increased in absence of symmetry potential as well as by
utilizing isospin independent cross-section. Here, we notice that the rise in crossover energy is almost comparable when calculations are performed in absence of
symmetry potential or for isospin-independent cross-section, for each colliding pair,
independent of its mass asymmetry.
Next, we check the role of density dependence of nuclear symmetry energy on
cross-over energy for the reactions of
31 P +
69 Ga (η = 0.4) and
20 Ne +
80 Kr (η =
0.6) by simulating these reactions with soft (γ = 0.5) and stiff (γ = 1.5) forms of
nuclear symmetry energy. In Fig. 10, we show the energy dependence of gas and
liquid yield for the reaction of 31P + 69Ga and 20Ne + 80Kr with soft form of
symmetry energy (upper panel) and stiff form of symmetry energy (lower panel).
Here, diamonds correspond to the reaction of
31 P +
69 Ga and triangles represent the
reaction of
20 Ne +
80 Kr. From the figure, we see that the cross-over occurs at lower
energy for stiff symmetry energy when contrasted with soft symmetry energy. The
occurrence of cross-over at higher energy for soft symmetry energy is because of the
fact that the effective strength of symmetry energy is weak in case of soft density
dependence at supra-saturation densities (which come into the picture in present
collisions) and in this way, weak repulsive forces in case of soft symmetry energy
will make the system to break at higher energy. In case of stiff symmetry energy,
the system requires a lesser amount of energy to break down because of stronger
(repulsive) symmetry potential. It is also clear from the figure that the cross-over
energy value is higher for the reaction of
20 Ne +
80 Kr (η = 0.6) in contrast with
31 P +
69 Ga (η = 0.4), as expected. Further, we observed that with increment in
mass asymmetry, the sensitivity of density dependence of nuclear symmetry energy
on cross-over energy is increased. Thus, we conclude that cross-over energy is a
sensitive probe to study nuclear symmetry energy as well as its density dependence
at supra-saturation densities.