In this theoretical study, we establish an interrelationship between the nucleon-nucleon potential and the nuclear fusion reaction cross sections at low energies. The axially deformed self-consistent relativistic mean field with nonlinear $\mathrm{NL}{3}^{*}$ and TM1 force parameters is used to calculate the density distributions of the projectile and target nuclei, which are further used in the double-folding approach to obtain the nucleus-nucleus interaction potentials. The Wong formula is used to estimate the fusion cross section and barrier distributions from the nucleus-nucleus optical potential for Ni-based systems, which are known for fusion hindrance phenomena. The results of the application of the so-obtained nucleus-nucleus potential for the fusion cross section from the recently developed relativistic effective NN interactions (R3Y) are compared with the well-known, phenomenological M3Y potential. The effect of the nucleon-nucleon interaction potential on the fusion cross section, in terms of the nuclear interaction potential, is included in the present analysis. We found relatively good results from R3Y interactions below the barrier energies as compared to the M3Y potential concerning the experimental data.

We have studied the effect of density and the nucleus-nucleus interaction potential on the fusion reaction cross section for the synthesis of heavy and superheavy nuclei within the relativistic mean field formalism. The double-folding procedure is used to obtain the nuclear interaction potential for the well-known M3Y and recently developed R3Y nucleon-nucleon potential for relativistic mean field densities. The $\mathrm{NL}{3}^{*}$ parameter set is used to calculate the density distributions for targets and projectiles and is further used to obtain the nuclear potential. The $\ell$-summed Wong formula is used to provide a transparent and analytic way to formulate the fusion cross sections for even-even ${}^{48}\mathrm{Ca}+{}^{154}\mathrm{Sm}$, ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$, ${}^{48}\mathrm{Ca}+{}^{248}\mathrm{Cm}$, ${}^{64}\mathrm{Ni}+{}^{238}\mathrm{U}$, ${}^{26}\mathrm{Mg}+{}^{248}\mathrm{Cm}$; even-odd ${}^{46}\mathrm{K}+{}^{181}\mathrm{Ta}$; and odd-odd ${}^{31}\mathrm{Al}+{}^{197}\mathrm{Au}$ and ${}^{39}\mathrm{K}+{}^{181}\mathrm{Ta}$ systems. The structural effects are also correlated with the fusion cross section through the equivalent diffuseness parameter using the densities of interacting nuclei for all nuclei (projects and targets) involved in the reactions just listed.

Background: The cluster radioactivity from the neutron-deficient trans-tin region of the nuclear landscape has given immediate attention in the nuclear structure studies. Recent prediction of the emitting clusters from the ground and intrinsic excited states of proton-rich Ba isotopes opens the direction to explore the corresponding decay characteristics. A theoretical probe is necessary for understanding the cluster decays of Ba isotopes.

Background: Isotopes of $Z=107\text{–}118$ have been synthesized using cold fusion at GSI, Darmstadt, and hot fusion reactions at JINR, Dubna. Recently theoretical models have predicted $Z=120$ with $N=184$ as an island of stability in the superheavy valley. Hence it is crucial and exciting to predict theoretically the possible combination of projectiles and targets for the synthesis of $Z=120$, which can be informative for upcoming experiments.

Background: Heavy-ion fusion reactions play a crucial role in various aspects of nuclear physics and astrophysics. The nuclear interaction potential and hence the fusion barrier formed between the interacting nuclei are the keys to understanding the complex fusion process dynamics. Thus, a theoretical investigation of fusion barrier characteristics which includes the relativistic effects is of paramount significance.

The octupole deformation $\left({\beta }_3\right)$ distorts the spherically symmetric or quadrupole deformed $\left({\beta }_2\right)$ nuclei into a pear shape. In the present work, the optimum (or uniquely fixed) orientations obtained for the ‘elongated’ and ‘compact’ fusion configurations of octupole $\left({\beta }_3\right)$ deformed nuclei differ significantly from the ones reported for the quadrupole deformed nuclei. The soft-pear shape nuclei with small ${\beta }_3$ deformations show a maximum deviation of ${20}^{\circ }$ in the elongated and compact configurations, respectively, of oblate and prolate cases, whereas for rigid-pear shape nuclei with strong ${\beta }_3$ deformation, the deviation is of ${90}^{\circ }$. The optimum orientations obtained are also dependent on ‘$+$’ and ‘$-$’ signs of ${\beta }_3$. Thus, octupole deformations significantly modify the optimum orientations for the cold and hot fusion reactions and hence leads to modification of the barrier characteristics. In addition to this, the effects of ${\beta }_3$ have also been observed in the calculation of fusion cross section for the formation of heavy $\left({}^{190}\mathrm{Ir}^{*}\right)$ and superheavy $\left({}^{268}\mathrm{Sg}^{*}\right)$ elements from the octupole-based reactions, i.e., ${}^{48}\mathrm{Ca}$(sph.)$+{}^{142}\mathrm{La}\left({\beta }_2=0.108,{\beta }_3=-0.083\right)$ and ${}^{220}\mathrm{Ra}\left({\beta }_2=0.110,{\beta }_3=-0.125\right)$, respectively.