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Impacts of the tensor couplings of $ω$ and $ρ$ mesons and Coulomb exchange terms on super-heavy nuclei and their relation to symmetry energy

We have studied the effects of tensor coupling of $ω$ and $ρ$ meson terms, Coulomb exchange term in local density approximation and various isoscalar-isovector coupling terms of relativistic mean field model on the properties of nuclear matter, finite nuclei, and super-heavy nuclei. We found that for the same fixed value of symmetry energy $J$ or its slope $L$ the presence of tensor coupling of $ω$ and $ρ$ meson terms and Coulomb exchange term yields thicker neutron skin thickness of $^{208}$Pb. We also found that the roles of tensor coupling of $ω$ and $ρ$ meson terms, Coulomb exchange term in local density approximation and various isoscalar-isovector coupling terms on the bulk properties of finite nuclei varies depending on the corresponding nucleus mass. However, on average, tensor coupling terms play a significant role in predicting the bulk properties of finite nuclei in a quite wide mass range especially in binding energies. We also observed that for some particular nuclei, the corresponding experimental data of binding energies is rather less compatible with the presence of Coulomb exchange term in local density approximation and they tend to disfavor the presence of isoscalar-isovector coupling term with too high $Λ$ value. Furthermore, we have found that these terms influence the detail properties of $^{292}$120 super-heavy nucleus such as binding energies, the magnitude of two nucleon gaps, single particle spectra, neutron densities, neutron skin thicknesses and mean square charge radii. However, the shell closure predictions of $^{208}$Pb and $^{292}$120 nuclei is not affected by the presence of these terms.