Shell model study of the neutron-rich nuclei around $N=28\mathrm{}$

We describe the properties of the neutron-rich nuclei around $N=28\mathrm{}$ in the shell mode framework. The valence space includes the $\mathrm{sd}$ shell for protons and the $\mathrm{pf}$ shell for neutrons without any restriction. Good agreement is found with the available experimental data. The $N=28\mathrm{}$ shell closure persists, even if eroded by the large neutron excess. The calculations predict that ${}^{40}$S and ${}^{42}$S are deformed with $\beta =0.29\mathrm{}$ and $\beta =0.32\mathrm{}$ respectively.