Deformation of nuclei close to the two-neutron drip line in the Mg region

We present Hartree-Fock-Bogoliubov (HFB) calculations of the ground states of even Mg isotopes. A Skyrme force is used in the mean-field channel and a density-dependent zero-range force in the pairing channel. $^{40}$Mg and $^{20}$Mg are predicted to be at the two-neutron and two-proton drip lines respectively. A detailed study of the quadrupole deformation properties of all the isotopes shows that the ground states of $^{36,38,40}$Mg are strongly deformed with significantly different deformations for the neutrons and protons. Our study supports the disappearance of the $N$ = 28 shell gap in the Mg and Si isotopes