Shape evolution and possible E(5) critical-point symmetry in Ti isotopes

Abstract The nuclear shape phase transitions of even-even isotopes are analyzed within the framework of relativistic Hartree-Bogoliubov (RHB) model. A detailed study of the shape evolution between the spherical U (5) and γ -unstable O (6) phases has been performed using potential energy curves derived from the density-dependent meson exchange (DD-ME2) and density-dependent point coupling (DD-PC1) interactions. The analysis of the potential energy curve indicate the prolate shape predominance in even-even isotopes. It is observed that the occupation of intruder orbits leads not only to significant quadrupole deformation but also a substantial hexadecapole deformation. The potential energy curves for point to them as possible candidates for critical-point nuclei exhibiting E (5) symmetry. Additionally, we have investigated the excitation spectra of even-even isotopes using the triaxial projected shell model (TPSM). The weak dependence of the potential on the triaxial parameter γ , along with the ratios of excitation energies and transition probabilities, suggests that 48 Ti and 52 Ti could be possible candidates for the E (5) critical-point symmetry, corresponding to a second-order shape phase transition. These predictions are supported by experimental data of energy ratios. While the E (5) symmetry is also predicted for based on nearly flat potential energy curves from the RHB model, but this prediction is not supported by the observed energy ratios.