Medium dependent relativistic NN potential: Application to the fusion dynamics

In-medium effects are introduced in the microscopic description of the effective nucleon-nucleon (NN) interaction potential entitled DDR3Y in terms of the density-dependent nucleon-meson couplings within the Relativistic-Hartree-Bogoliubov (RHB) approach. The nuclear densities of the interacting target and projectile nuclei and NN potentials are obtained for non-linear NL3$^*$ and TM1 parameter sets within the relativistic mean-field approach and density-dependent DDME1 and DDME2 parameter sets within the Relativistic-Hartree-Bogoliubov (RHB) formalism. The DDR3Y NN potential and the densities are used to obtain the nuclear potential by adopting the double folding approach. This nuclear potential is further used to probe the fusion dynamics within the $\ell-$summed Wong model for a few {\it even-even} systems leading to the formation of light, heavy and superheavy nuclei. The calculations are also performed for the relativistic R3Y, density-dependent and independent M3Y interaction potentials for the comparison. We observed that the DDR3Y NN potential gives a better overlap with the experimental data as compared to non-relativistic M3Y and DDM3Y NN potentials. From the comparison of R3Y and DDR3Y interactions, it is manifested that the inclusion of in-medium effects in terms of density-dependent nucleon-meson couplings raises the fusion barrier and consequently decreases the fusion and/or capture cross-section. Moreover, the nuclear densities, as well as the relativistic R3Y NN potential obtained for the NL3$^*$ parameter set, are observed to give a comparatively better fit to the experimental data.