In this work we look at the low-lying nuclear structure properties of several $N=Z$ nuclei residing between the doubly magic nuclei ${}^{40}$Ca and ${}^{100}$Sn. Using large shell model codes, we calculate and discuss the systematics of energies. We show energy levels, $B\left(E2\right)$'s, static quadrupole moments, and $g$ factors of these $N=Z$ nuclei. In all cases, we compare the results of two different interactions which yield significantly different occupation numbers. We compare our shell model results with those of the rotational and vibrational models. By examining $B\left(E2\right)$'s and static quadrupole moments, we make associations with collective models and find that in the model space considered here, ${}^{88}$Ru is oblate. The quadrupole moment of the lowest 2${}^{+}$state of ${}^{92}$Pd is calculated to be very small. This would appear to support a vibrational picture and indeed recent measurements give equally spaced levels up to $J=6^{+}$ but the authors also point out that the $B\left(E2\right)$'s do not steadily increase as is required by such a model.

• Received 14 October 2013

DOI:https://doi.org/10.1103/PhysRevC.89.014316