Shape isomers of α -like nuclei in terms of the multiconfigurational dynamical symmetry

Abstract

Background: The shape isomers of the $N=Z=\mathrm{even}$ nuclei are known from the energy-surface calculations within the Bloch-Brink (BB) $\ensuremath{\alpha}$-cluster model and Nilsson model. As an alternative, a new method (called SCS) has been proposed recently for determining the stable shapes, which is based on the investigation of the stability and consistency of the $\mathrm{SU}(3)$ symmetry (or quadrupole deformation).Purpose: We wish to derive the shape isomers of the $\ensuremath{\alpha}$-like nuclei from the SCS method and compare them with the results of the energy-surface calculation. Furthermore, we intend to study the consequences of the stable symmetries. In particular, we investigate (i) what kind of binary clusterizations are structurally allowed for the shape isomers and (ii) if energy spectra similar to those of the BB model can be obtained with a simple dynamically symmetric Hamiltonian.Methods: We determine the stability and self-consistency of the quadrupole deformation from a systematic calculation with the Nilsson model by applying the concept of the quasidynamical $\mathrm{U}(3)$ symmetry. The allowed cluster configurations are determined from the application of the U(3) and ${\mathrm{U}}^{\mathrm{ST}}(4)$ selection rules. The forbidden ones are characterized quantitatively. The energy spectrum is calculated with a simple dynamically symmetric Hamiltonian of the multiconfigurational dynamical symmetry (MUSY), which proved to be useful for the description of some experimental spectra.Results: The shape isomers found from the SCS method are in good agreement with the results of the energy surface method (BB and Nilsson models). Their allowed binary clusterizations are obtained from structural selection rules, but they give a hint for the available reaction channels, too. Last, a very simple energy functional is able to reproduce the gross features of their energy spectra in a large range of excitation energy and deformation.Conclusions: The similarity of the shape isomers from two very different methods gives a strong support to these predictions. The reasonable reproduction of the energy distribution of the ``ground-band heads'' is especially remarkable, considering the fact that MUSY is able to produce the complete spectra in detail, not only the energy minima.