In this paper, we investigate features of the ground state of some nuclei far from the stability for isotope chains with proton numbers Z=18 and 20. Our aim is to predict the eventual existence of magic numbers in these exotic nuclei. For this purpose, we use two methods: the non relativistic Hartree-Fock-Bogoliubov (HFB) approach based on SLy4 Skyrme functional and the relativistic (so-called covariant) density functional theory (CDFT) by using the DD-ME2 force parametrization. We compare our results with the available experimental data and with the predictions of other models such as Finite Range Droplet Model (FRDM). Our present investigation predicts that N=32 and N=40 are magic numbers for Ar and Ca isotopes.

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The exotic even–even isotopic chains from [Formula: see text] to [Formula: see text] are investigated by means of the relativistic Hartree–Bogoliubov (RHB) approach with the explicit Density Dependent Meson-Exchange (DD-ME2) and Density-Dependent Point-Coupling (DD-PC1) models. The classic magic number [Formula: see text] is reproduced and the new number [Formula: see text] is predicted to be a robust shell closure by analysing several calculated quantities such as: two-neutron separation energies, two-neutron shell gap, neutron pairing energy, potential energy surface and neutron single particle energies. The obtained results are compared with the predictions of finite range droplet model (FRDM) and with the available experimental data. A reasonable and satisfactory agreement between the theoretical models and experiment is established.

A systematic study of the shape evolution in Ge (Z = 32), Se (Z = 34), Kr (Z = 36) and Sr (Z = 38) isotones for N = 70, and their neighboring isotones with N = 68 and N = 72 is presented. We use, in this investigation, the covariant density functional theory (CDFT) with the explicit Density Dependent Meson-Exchange (DD-ME2) and Density-Dependent Point-Coupling (DD-PC1) models. The finite range pairing interaction separable in coordinate space which was proposed by Tian et al. has been used to treat the pairing correlations. By investigating structural properties of nuclei under consideration, it is found that N = 70 isotones are, in generally, spheric. Furtheremore, the N = 70 can be considered as magic number.