The structures of Ne, Na, Mg, Al, Si, P and S nuclei near the neutron drip-line region are investigated in the frame-work of relativistic mean field theory and non-relativistic Skyrme Hartree-Fock formalism. The recently discovered nuclei 40Mg and 42Al, 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 orbits of opposite parities (e.g. $$\frac{1} {2}^ +$$ and $$\frac{1} {2}^ -$$) occur close to each other in energy.
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