Superdeformed structures and low $\Omega$ parity doublet in Ne$-$S nuclei near neutron drip-line

The structure of Ne, Na, Mg, Al, Si, P and S nuclei near the neutron drip-line region is investigated in the frame-work of relativistic mean field theory and non-relativistic Skyrme Hartree-Fock formalism. The recently discovered nuclei $^{40}$Mg and $^{42}$Al, which are beyond the drip-line predicted by various mass formulae are located within these models. We find many largely deformed neutron-rich nuclei, whose structures are analyzed. From the structure anatomy, we find that at large deformation, low $\Omega$ orbits of opposite parities (e.g. $\frac{1}{2}^+$ and $\frac{1}{2}^-$) occur close to each other in energy.