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) with densities derived from the relativistic mean-field (RMF) approach. The RMF formalism with the NL3$^*$ parameter set and the relativistic-Hartree-Bogoliubov (RHB) approach with the DDME2 parameter set are used to obtain the medium-independent R3Y and density-dependent R3Y (DDR3Y) NN potentials. The results of these relativistic interactions are compared with the Reid and Paris M3Y NN interactions and their density-dependent versions. Nuclear potentials are used to calculate the fusion barrier characteristics and cross-sections within the $\ell$-summed Wong model for $^{16}$O+$^{144}$Sm, $^{48}$Ca+$^{208}$Pb, $^{16}$O+$^{154}$Sm, and $^{48}$Ca+$^{238}$U reactions. The relativistic R3Y and DDR3Y NN potentials provide higher cross-sections than both the Reid and Paris versions. The inclusion of in-medium effects in all interactions results in more repulsive potentials, leading to higher fusion barriers and reduced cross-sections. The impact of nuclear shape degrees of freedom is included for $^{16}$O+$^{154}$Sm and $^{48}$Ca+$^{238}$U reactions involving deformed targets. Results using RMF-NL3$^*$ densities are also compared with those from the two-parameter Fermi (2pF) formula for $^{16}$O+$^{154}$Sm, showing higher cross-sections with RMF densities. A comparison of calculated cross-sections with experimental data shows that the R3Y NN potential with RMF-NL3$^*$ densities provides good agreement for reactions involving both spherical and deformed nuclei.