In this theoretical study, we report an investigation on the behavior of two-neutron separation energy, a differential variation of the nucleon separation energy, the nuclear charge radii, and the single-particle energy levels along the isotopic chains of transitional nuclei. We have used the relativistic mean-field formalism with NL3 and NL3* forces for this present analysis. The study refers to the even-even nuclei such as Zr, Mo, Ru, and Pd for $N=42-86$, where a rich collective phenomena such as proton radioactivity, cluster or nucleus radioactivity, exotic shapes, island of inversion, etc. are observed. We found that there are few nonmonotonic aspects over the isotopic chain, which are correlated with the structural properties such as shell/subshell closures, the shape transition, clustering, magicity, etc. In addition to these, we have shown the internal configuration of these nuclei to get a further insight into the reason for these discrepancies.

In this theoretical study, we establish a correlation between the neutron skin thickness and the nuclear symmetry energy for the even-even isotopes of Fe, Ni, Zn, Ge, Se, and Kr within the framework of the axially deformed self-consistent relativistic mean field for the nonlinear $\mathrm{NL}{3}^{*}$ and density-dependent DD-ME1 interactions. The coherent density functional method is used to formulate the symmetry energy, the neutron pressure, and the curvature of finite nuclei as a function of the nuclear radius. We have performed broad studies for the mass dependence on the symmetry energy in terms of the neutron-proton asymmetry for mass $70\le A\le 96$. From this analysis, we found a notable signature of a shell closure at $N=50$ in the isotopic chains of Fe, Ni, Zn, Ge, Se, and Kr nuclei. The present study reveals a interrelationship between the characteristics of infinite nuclear matter and the neutron skin thickness of finite nuclei.

The effect of $$\delta${}$- and $$\omega${}\text{$-${}}$\rho${}$-meson cross couplings on asymmetry nuclear systems are analyzed in the framework of an effective field theory motivated relativistic mean field formalism. The calculations are done on top of the G2 parameter set, where these contributions are absent. To show the effect of $$\delta${}$ meson on the nuclear system, we split the isospin coupling into two parts: (i) ${g}_{$\rho${}}$ due to $$\rho${}$ meson and (ii) ${g}_{$\delta${}}$ for $$\delta${}$ meson. Thus, our investigation is based on varying the coupling strengths of the $$\delta${}$ and $$\rho${}$ mesons to reproduce the binding energies of the nuclei $^{48}\mathrm{Ca}$ and $^{208}\mathrm{Pb}$. We calculate the root mean square radius, binding energy, single particle energy, density, and spin-orbit interaction potential for some selected nuclei and evaluate the ${L}_{\mathrm{sym}}$ and ${E}_{\mathrm{sym}}$ coefficients for nuclear matter as function of $$\delta${}$- and $$\omega${}\text{$-${}}$\rho${}$-meson coupling strengths. As expected, the influence of these effects are negligible for the symmetric nuclear system, but substantial for the contribution with large isospin asymmetry.

We have calculated the binding energy, root-mean-square radius, and quadrupole deformation parameter for the recently synthesized superheavy element Z=117, using the axially deformed relativistic mean-field (RMF) model. The calculation is extended to various isotopes of the Z=117 element, starting from A=286 till A=310. We predict almost spherical structures in the ground state for almost all the isotopes. A shape transition appears at about A=292 from a prolate to an oblate shape structure of the Z=117 nucleus in our mean-field approach. The most stable isotope (largest binding energy per nucleon) is found to be the 288117 nucleus. Also, the Q$\alpha${} values and the half-life T1/2$\alpha${} for the $\alpha${}-decay chains of 293117 and 294117 are calculated, supporting the magic numbers at N=172 and/or 184.