The configuration interaction relativistic Hartree-Fock (CI-RHF) model is developed in this work. Compared to the conventional configuration interaction shell model (CISM), the CI-RHF model can be applied to study the structural properties of a wide range of nuclei without readjusting any parameters, as the effective Hamiltonian for different model spaces can be deduced consistently from a universal density-dependent Lagrangian based on the Hartree-Fock single-particle basis. The convergence of intermediate-state excitations has been examined in evaluating the effective interactions, and the core-polarization effects are illustrated, taking $ ^{18} {\rm{O}}$ as an example. Employing the CI-RHF model, both the bulk properties and low-lying spectra of even-even nuclei $^{18-28} {\rm{Ne}}$ have been well-reproduced with the model space restricted to the $ sd $ shell. Studies of the isotopic evolution concerning charge radii and low-lying spectra highlight the shell closure at $ N=14 $ for neon isotopes. Furthermore, the cross-shell calculations extending from the $ sd $ to $ pf $ shell successfully reproduced the low-lying spectra of $ ^{30} {\rm{Ne}}$ and $ ^{32} {\rm{Ne}}$ . Notably, remarkably low excitation energies $ E(2^{+}_{1}) $ of $ ^{30} {\rm{Ne}}$ suggest the disappearance of the conventional magicity $ N=20 $ .

Several studies on fusion reaction dynamics focused on the impact of quadrupole $\beta_2^{\pm}$ deformation. However, existing literature highlights the importance of the octupole $\beta_3^{\pm}$ and hexadecapole $\beta_4^{\pm}$ deformations associated with both the projectile and target nuclei. However, the collective influence of these deformations ( $\beta_2$ , $\beta_3$ , and $\beta_4$ ) on the fusion reaction dynamics has not been examined explicitly. In this study, we investigated the collective influence of higher-order deformations up to $\beta_4$ on the barrier characteristics, in particular $V_B$ , $R_B$ , and $\hbar\omega$ , and their impact on the fusion cross-sections of heavy-ion induced reactions in the mass range $163\leq{ {A}}\leq182$ . The reactions were examined at both compact and elongated configurations of the deformed nuclei. Heavy ion-induced reactions, which consist of target nuclei with higher-order deformations up to $\beta_4$ , reveal a notable alteration in the barrier characteristics $V_B$ and $R_B$ , along with a significant change in orientation $\theta_i$ for both compact and elongated configurations. In addition, the incorporation of deformations up to $\beta_4$ and their corresponding orientations $\theta_i$ contributes to enhanced capture cross-sections $\sigma_{cap}$ as well as integrated cross-sections $\sigma_{int.}$ , resulting in better agreement with experimental data for $^{16}{\rm{O}}$ -induced reactions with $^{148}{\rm{Nd}}$ , $^{149-150}{\rm{Sm}}$ , and $^{32}{\rm{S}}$ -induced reactions with $^{150}{\rm{Sm}}$ . We conclude that the incorporation of deformations of all orders up to $\beta_4$ at their optimized compact and elongated configurations is essential because it provides better outcomes compared to the optimized configurations of $\beta_2$ and $\beta_3$ deformed nuclei.

The Skyrme energy density functional was used to systematically analyze the ratio of repulsive kinetic to attractive potential energy ( $ T/U $ ) for even-even nuclei in their ground states. Notably, the nuclei with maximal value of $ T/U $ are generally stable for a certain isobaric chain with $ Z\le 82 $ . However, the known magic numbers can be more clearly observed from the $ T/U $ ratio than from nuclear binding energy, particularly for the isobaric chains with semi-magic nuclei. Combining the predicted binding energies and the $ T/U $ ratios from the Skyrme Hartree-Fock-Bogoliubov (HFB) code transformed harmoic oscilattor (HFBTHO) with the parameter set based on the Universal Nuclear Energy Density Funcitonal (UNEDF0), the possible magic numbers in super-heavy mass region were simultaneously studied. The neutron magic number $ N=184 $ can be clearly observed from the calculated values of $ T/U $ and the extracted microscopic energies of the nuclei.