Influence of effective interactions and nuclear densities on the dynamics of heavy-ion fusion

The study aims to explore the mechanism of heavy-ion fusion using various effective nucleon-nucleon (NN) interactions and nuclear density distributions. The nuclear potentials are obtained by folding the relativistic effective NN interaction (R3Y) potential with the densities derived from the relativistic mean-field (RMF) approach. Here, we have considered the RMF formalism with a nonlinear ${\mathrm{NL}3}^{*}$ parameter set and the relativistic-Hartree-Bogoliubov (RHB) approach with the DDME2 parameter set to obtain the medium-independent R3Y and density-dependent R3Y (DDR3Y) NN potentials, respectively. The results of these relativistic effective NN interactions are compared with the well-known Reid and Paris M3Y NN interactions and their density-dependent versions. Nuclear potentials are also used to calculate the fusion barrier characteristics and cross-section within the $\ensuremath{\ell}$-summed Wong model for $^{16}\mathrm{O}+^{144}\mathrm{Sm}$, $^{48}\mathrm{Ca}+^{208}\mathrm{Pb}$, $^{16}\mathrm{O}+^{154}\mathrm{Sm}$, and $^{48}\mathrm{Ca}+^{238}\mathrm{U}$ reactions. The relativistic R3Y and DDR3Y NN potentials are noted to provide a higher cross section than both the Reid and Paris versions of the nonrelativistic M3Y (Michigan 3 Yukawa) NN potentials. Moreover, the inclusion of in-medium effects in both relativistic and nonrelativistic effective NN interactions is noted to provide relatively repulsive nuclear potentials, which lead to higher fusion barriers and hindered cross sections. The impact of nuclear shape degrees of freedom in terms of nuclear deformation is also included in the description of nuclear fusion for $^{16}\mathrm{O}+^{154}\mathrm{Sm}$ and $^{48}\mathrm{Ca}+^{238}\mathrm{U}$ reactions involving deformed target nuclei. Furthermore, the results of RMF-${\mathrm{NL}3}^{*}$ densities are also compared with those obtained using the two-parameter Fermi (2pF) formula for the representative case of the $^{16}\mathrm{O}+^{154}\mathrm{Sm}$ reaction, and the RMF-${\mathrm{NL}3}^{*}$ densities are noted to provide a higher cross section for the considered reaction. The quantitative analysis of cross sections calculated using different nuclear potentials with the available experimental data shows that the R3Y NN potential and nuclear densities calculated within the RMF formalism for the nonlinear ${\mathrm{NL}3}^{*}$ parameter set provide a reasonable agreement with the experimental data for all the considered reactions containing spherical and deformed target nuclei.