Search for shape isomers in the Pt-Hg-Pb region

Potential-energy surfaces of nine even-even isotopes of Pt, Hg, and Pb around $^{186}\mathrm{Pt}$ are evaluated within a macroscopic-microscopic model based on the Lublin-Strasbourg-Drop macroscopic energy and the microscopic energy obtained using the Yukawa-folded mean-field potential to establish the Strutinski shell corrections and the pairing-correlation energy through the BCS approach with a monopole pairing force. The rapidly converging Fourier-over-Spheroid shape parametrization is used to describe nuclear deformations. The stability of the identified shape-isomeric states with respect to nonaxial and higher-order deformations is investigated. It is also found that in the description of nonaxial deformations special attention needs to be devoted to the orientation of the triaxial shape. For the example of the $^{186}\mathrm{Hg}$ nucleus, where three prolate shape-isomeric states are found, it is shown that the potential-energy surface obtained in our model is close to the one obtained in the Hartree-Fock-Bogoliubov theory with the Gogny energy-density fuctional.