Abstract
The evolution of the ground-state nuclear shapes with the number of nucleons is studied within a self-consistent Hartree-Fock-Bogoliubov formalism based on Gogny and Skyrme density-dependent interactions. Potential energy surfaces including triaxial degrees of freedom are studied in various isotopic chains. Signatures for the E(5) critical point symmetry are analyzed in Pd, Xe, and Ba isotopes, while those for the X(5) are studied in Nd, Sm, Gd, and Dy isotopes. Oblate to prolate shape transitions are also studied in Yb, Hf, W, Os, and Pt isotopic chains. The transitions are discussed in terms of the deformation dependence of the single-particle energies.