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

TL;DR

The paper addresses shape isomerism and shape coexistence in the Pt–Hg–Pb region around $^{186}$Hg using a macroscopic-microscopic framework with the LSD energy and a Yukawa-folded mean-field potential. It introduces the Fourier-over-Spheroid deformation parametrization and a symmetrized potential-energy surface (SPES) to account for orientation and higher-order deformations, projecting onto the Bohr $\{\beta,\gamma\}$ plane. Key findings include multiple shape isomers across Pt, Hg, and Pb, notably three prolate shape isomers in $^{186}$Hg, with SPES results that are broadly consistent with self-consistent HFB-Gogny D1S calculations. The study demonstrates substantial energy gains from correctly accounting for orientation and higher-order deformations (up to about $1.5$–$2.5$ MeV), reinforcing the importance of SPES in predicting shape coexistence in heavy nuclei and guiding future explorations in nearby mass regions.

Abstract

Potential energy surfaces of nine even-even isotopes of Pt, Hg, and Pb around $^{186}$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 non-axial and higher-order deformations is investigated. It is also found that in the description of non-axial deformations special attention needs to be devoted to the orientation of the triaxial shape. For the example of the $^{186}$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 functional.

Figures (8)

• Figure 1: Illustration of the symmetry of Bohr's $\{\beta,\gamma\}$ shape parametrization.
• Figure 2: Potential energy surface (PES) obtained in the tree $(\beta,\gamma)$ sectors (upper map) and symmetrized potential-energy surface (SPES) (lower map) for the $^{186}$Hg nucleus obtained by the symmetrization procedure as explained in the text.
• Figure 3: Symmetrized potential energy surfaces for Pt isotopes.
• Figure 4: Symmetrized potential energy surfaces for Hg isotopes.
• Figure 5: Symmetrized potential energy surfaces for Pb isotopes.