A quantal Hamiltonian ${\hat{\mathcal{H}}}_{\mathrm{coll}}$ expressed in terms of the five collective quadrupole coordinates is built for eight nuclei ${(}^{190,192,194}$Hg, ${}^{192,194,196}$Pb, and ${}^{196,198}$Po) which display secondary minima at large elongation in their potential energy surface. These surfaces as well as the tensor of inertia entering ${\hat{\mathcal{H}}}_{\mathrm{coll}}$ are deduced from constrained Hartree-Fock-Bogoliubov calculations based on Gogny force. A two-center basis method employed to solve ${\hat{\mathcal{H}}}_{\mathrm{coll}}$ is presented. The stability of predicted collective spectra is discussed. Yrast and vibrational $\pi =+$ superdeformed (SD) bands are predicted together with collective bands at normal deformation (ND). The predicted yrast SD bands at low spin display properties which compare favorably with experimental information. Quite good agreement is in particular obtained for the isomeric energies of nuclei for which the link between SD and ND levels is experimentally known. Among the excited SD bands which are here predicted, those built on top of $\beta$ vibrations are lower in energy. Only for the ${}^{196,198}$Po isotopes are these excitation energies falling in the low energy range $E\sim$0.8–1.0 MeV. These properties should favor an experimental discovery of $\beta$-vibrational SD bands in the $A\sim$190 mass region.

• Received 26 March 1999

DOI:https://doi.org/10.1103/PhysRevC.60.054301