Shape coexistence of neutron deficient isotopes near the Z = 82 closure with relativistic energy density functional theory.

Relativistic energy density functionals have been extensively used to describe shape transitions and coexistence. They provide a consistent framework for studying static and dynamic properties of nuclei across the nuclear chart. Presently, we explore shape coexistence/transitions in the neutron deficient side with N = 96 – 112 around the Z = 82 magic number and in particular for the Hg and Pb isotopes. This area has been extensively researched experimentally, with well-established shape coexistence observed in several isotopes, making it a suitable testing ground for theoretical approaches. Our model is based on the microscopic theory of relativistic energy density functionals. In the first step it involves calculations at the mean-field level, wherein the relativistic Hartree-Bogoliubov equations are solved under constraints on the shape parameters. This enables the construction of potential energy surfaces for the nuclei, revealing the position of the absolute minimum of the ground state and the existence, or absence, of secondary or more minima at different deformations. The second step extends beyond the static mean-field level encompassing the dynamics of rotations and vibrations as collective excitations of the system. The constrained calculations are used to derive mass, inertial parameters and the potential of a five-dimensional collective Hamiltonian (5DCH). Solving the corresponding eigenvalue problem allows for the calculation of excitation energies, of low-lying levels and B(E2) transition probabilities that can be directly compared with observations. In both steps, we demonstrate how the strength of the pairing interaction affects the theoretical description both quantitatively and qualitatively.