Implications of Deformation and Shape Coexistence for the Nuclear Shell Model

The successes of the nuclear shell model in explaining the stability properties of magic nuclei are challenged by the observation of rotational bands for which the sequential filling of single-particle energy levels of the spherical shell model are not respected. This Letter proposes criteria for identifying the shell-model configurations appropriate for describing such bands of states.

Figure 1

Positive-parity energy levels of the model with $L\le 6$ for ${}^{16}\mathrm{O}$ in comparison with those observed below 15 MeV. Energy levels associated with an irrep $N(\lambda \mu )$ are shown in groups. Reduced $E2$ transition rates are indicated (in $e^2{\mathrm{fm}}^4$ units) beside the arrows. (The data are extracted from the ENSDF data base, revision of Mar 8, 2002.).

Figure 2

Spectrum of $E_{\mathrm{exc}}^{N(\lambda \mu )}/\hslash \omega$ energies for leading positive-parity lowest-grade U(3) irreps of ${}^{16}\mathrm{O}$ as functions of $\kappa$. The filled circles indicate values of $\kappa =2\chi [1-\lambda /(2N)]$.