Shape phase transition atN=88–90inBa144,146

Background: The neutron-rich Ba isotopes with only six valence protons represent the beginning of the collective rotation-vibration band structure. The sharp shape phase transition at $N=88\text{--}90$ observed in Ce-Gd isotones is not exhibited in $^{144\text{--}146}\mathrm{Ba}$, which renders their analysis interesting. Also there are ambiguities in the spin and band assignments.Purpose: To study their spectra empirically and to compare with predictions from an interacting boson model and microscopic dynamic pairing plus quadrupole model to explain the smooth shape transition at $N=88\text{--}90$.Method: We compare the results of the calculation in the interacting boson models (IBM-1) and IBM-2 and the dynamic pairing plus quadrupole model with experiment and illustrate the variation in level structure of the Ba isotopes with N. The absence of sharp phase transition at $N=88\text{--}90$ is examined.Results: The ambiguous spin and parity of levels of the vibrational bands are assigned on the basis of calculated K components and the decay characteristics.Conclusion: The second ${I}^{\ensuremath{\pi}}={2}^{+}$ states in $^{144,146}\mathrm{Ba}$ have $K=0$ predominance, and ${I}^{\ensuremath{\pi}}={2}_{3}^{+}$ states are $K=2$. The smooth transition at $N=88\text{--}90$ is explained.