Shell-Model Interpretation of the Collective-Model Potential-Energy Surface

The potential-energy-surface concept of the generalized collective model is given a shell-model interpretation. For deformation less than the equilibrium value, $\beta <{\beta }_0$, the shape of the potential is related to intrashell dynamics while the sharp rise for $\beta >{\beta }_0$ is shown to be an intershell phenomenon that depends on competition between major shell excitation energies and the binding energy of the residual interaction. The exclusion principle plays an essential role in the argument. Results for ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ illustrate the necessity of an open-shell picture.