Shell model study of the neutron rich isotopes from oxygen to silicon

In this paper we extend the shell model calculations previously made for the very neutron-rich nuclei with $Z>~14$ to Al, Mg, Na, Ne, F, and O, using the same valence space and effective interaction. Predictions are made for the neutron separation energies and for the location of the neutron drip line. We find that the isotopes of Ne, Na, and Mg are deformed for $N>~22.$ In ${}^{40}\mathrm{Mg},$ which is at the edge of the drip line, the $N=28\mathrm{}$ shell closure does not stand. By enlarging the valence space to include intruder states we are able to account for the vanishing of the $N=20\mathrm{}$ neutron shell closure in a small region around ${}^{31}\mathrm{Na}$ that we delineate. The dominance of the intruders explains the collective features experimentally found in this region.