\begin{document}$ ^{126-136} {\rm{Ba}}$\end{document} was systematically investigated using pairing self-consistent Woods-Saxon-Strutinsky calculations combined with the total Routhian surface (TRS) method in the (\begin{document}$ \beta_2, \gamma, \beta_4 $\end{document}) deformation space. Empirical laws were applied to evaluate nuclear ground-state properties, revealing a shape evolution from axially deformed to non-axial vibrational configuration in even-even \begin{document}$ ^{126-136} {\rm{Ba}}$\end{document} isotopes. Particularly, an extreme γ-unstable shape was predicted in \begin{document}$ ^{130} {\rm{Ba}}$\end{document}. The shape transition of the ground state in these nuclei was confirmed by the TRS calculations. In addition, the evolution of the nuclear shape in high spin states with varying rotational axes associated with rotation around the medium, long, and short axes was elucidated from the TRS calculations. This variation was further characterized by the alignment of the \begin{document}$ \pi(h_{11/2})^2 $\end{document} and \begin{document}$ \nu(h_{11/2})^2 $\end{document} configurations, highlighting a preference for non-collective oblate/triaxial shapes with \begin{document}$ \gamma > 0^{\circ} $\end{document} and collective oblate/triaxial shapes with \begin{document}$ \gamma < 0^{\circ} $\end{document}, respectively."> Exploring shape (phase) evolution in even-even <sup>126−136</sup>Ba -
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