Connecting the nuclear equation of state to the interplay between fusion and quasifission processes in low-energy nuclear reactions

Within the time-dependent Hartree-Fock (TDHF) approach, we investigate the impact of several ingredients of the nuclear effective interaction, such as incompressibility, symmetry energy, effective mass, derivative of the Lane potential, and surface terms on the exit channel (fusion vs quasifission) observed in the reaction ${}^{238}\mathrm{U}+{}^{40}\mathrm{Ca}$, close to the Coulomb barrier. Our results show that all the ingredients listed above contribute to the competition between fusion and quasifission processes; however, the leading role in determining the outcome of the reaction is played by incompressibility, symmetry energy, and the isoscalar coefficient of the surface term. This study unravels the complexity of the fusion and quasifission reaction dynamics and helps us to understand the microscopic processes responsible for the final outcome of low-energy heavy-ion collisions in terms of relevant features of the nuclear effective interaction and associated equation of state (EOS).

Figure 1

Density contour plot at different time instants for the tip collision of the reaction ${}^{238}\mathrm{U}+{}^{40}\mathrm{Ca}$ (tip orientation) at $E_{\mathrm{c}.\mathrm{m}.}=203$ MeV and $b=0$ fm. The SAMi-$J31$ interaction is employed.

Figure 2

The quadrupole moment time evolution of the reaction ${}^{238}\mathrm{U}+{}^{40}\mathrm{Ca}$ (side orientation) at $E_{\mathrm{c}.\mathrm{m}.}=203$ MeV and $b=0$ fm, for three SAMi-$J$ EOS.

Figure 3

Same as in Fig. 1, but for the side collision.

Figure 4

Same as in Fig. 1, but for the side collision, with SAMi-$J35$.

Figure 5

The symmetry energy dependence of the quadrupole moment evolution of the reaction considered (same as in Fig. 2). All reactions are performed at $E_{\mathrm{c}.\mathrm{m}.}=203$ MeV and $b=0$ fm.

Figure 6

Surface effects on the quadrupole moment evolution of the reaction considered (same as in Fig. 2). All reactions are performed at $E_{\mathrm{c}.\mathrm{m}.}=203$ MeV and $b=0$ fm.

Figure 7

The incompressibility dependence of the quadrupole moment evolution, for the same reaction as in Fig. 2. All reactions are performed at $E_{\mathrm{c}.\mathrm{m}.}=203$ MeV and $b=0$ fm.

Figure 8

The dependence of the quadrupole moment evolution on the isoscalar effective mass. Same reaction system as in Fig. 2. All reactions are performed at $E_{\mathrm{c}.\mathrm{m}.}=203$ MeV and $b=0$ fm.

Figure 9

The $f_I$ dependence of the quadrupole moment evolution of the system considered (same as in Fig. 2). All reactions are performed at $E_{\mathrm{c}.\mathrm{m}.}=203$ MeV and $b=0$ fm.