  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.
