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

The nuclear shape phase transitions of even-even ${}^{40-62}\text{Ti}$ 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 ${}^{40-62}\text{Ti}$ 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 ${}^{48,52}\text{Ti}$ point to them as possible candidates for critical-point nuclei exhibiting E(5) symmetry. Additionally, we have investigated the excitation spectra of even-even ${}^{48-56}\text{Ti}$ 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 48Ti and 52Ti 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 ${}^{54,56}\text{Ti}$ based on nearly flat potential energy curves from the RHB model, but this prediction is not supported by the observed energy ratios.