Properties of the ground and several collective excited states of selected neutron-rich $N=28\mathrm{}$ isotones and sulfur isotopes around ${}^{44}\mathrm{S}$ are described in the framework of the angular momentum projected generator coordinate method using the quadrupole moment as collective coordinate and the Gogny force, with the D1S parametrization, as the effective interaction. Fairly good agreement with available experimental data is obtained for the $2^{+}$ excitation energies and $B\left(E2\mathrm{}\right)\mathrm{}$ transition probabilities of the $N=28\mathrm{}$ isotones. For the sulfur isotopes an acceptable agreement is found and the isotopic trend is well reproduced. It is found that the $N=28\mathrm{}$ shell closure is not preserved in the prolate ${}^{40}\mathrm{Mg},$ the oblate deformed ${}^{42}\mathrm{Si},$ and the shape coexistent isotones ${}^{44}\mathrm{S}$ and ${}^{46}\mathrm{Ar},$ whereas it is preserved (on the average) in ${}^{48}\mathrm{Ca}.$ The sulfur isotopes ${}^{38-42}\mathrm{S}$ are found to be, to some extent, prolate deformed.

• Received 20 June 2001

DOI:https://doi.org/10.1103/PhysRevC.65.024304