Description of quadrupole collectivity in $N\approx 20$ nuclei with techniques beyond the mean field

Properties of the ground and several collective excited states of the light nuclei ${}^{30,32,34}\mathrm{Mg}$ are described in the framework of the angular momentum projected generator coordinate method using the quadrupole moment as collective coordinate and the Gogny force as the effective interaction. The calculated excitation energies and $B\left(E2\mathrm{}\right)\mathrm{}$ transition probabilities agree reasonably well with experiment. The results clearly indicate that both the restoration of the rotational symmetry and the quadrupole dynamics are key ingredients for the description of the properties of the above-mentioned nuclei.