The microscopic structure of neutron-rich $\mathit{sd}$-shell nuclei is investigated by using the spherical-shell model in the $\mathit{sd}$-$\mathit{pf}$ valence space with the extended pairing plus quadrupole-quadrupole forces accompanied by the monopole interaction (EPQQM). The calculation reproduces systematically the known energy levels for even-even and odd-mass nuclei including the recent data for ${}^{43}\mathrm{S}$, ${}^{46}\mathrm{S}$, and ${}^{47}\mathrm{Ar}$. In particular, the erosion of the $N=28$ shell closure in ${}^{42}\mathrm{Si}$ can be explained. Our EPQQM results are compared with other shell-model calculations with the SDPF-NR and SDPF-U effective interactions.

• Received 4 August 2010

DOI:https://doi.org/10.1103/PhysRevC.83.014320