In this study, the multi-quasiparticle triaxial projected shell model (TPSM) is applied to investigate -vibrational bands in transitional nuclei of . We report that each triaxial intrinsic state has a -band built on it. The TPSM approach is evaluated by the comparison of TPSM results with available experimental data, which shows a satisfactory agreement. The energy ratios, B(E2) transition rates, and signature splitting of the -vibrational band are calculated.

The evolution of non-axial shapes and rotational structure in even–even 122–132Ba isotopes has been investigated microscopically with the application of a triaxial projected shell model (TPSM). Based on calculations, the shape instability and softness towards γ deformation are predicted for these isotopes. In the present work, the application of three-dimensional angular-momentum projection on multi-quasiparticle configurations, constructed from the triaxially deformed mean field, provides a reliable description of the yrast and near yrast structure in these nuclei. The theoretically obtained backbends demonstrate the importance of decoupling of multi-quasiparticle states for these nuclei. The uniform behaviour of transition probabilities B(E), shown by the present calculations, authenticate the global validity of Grodzin’s product rule. Besides this, the deformation systematics and odd–even staggering in γ bands have also been discussed in the present work.

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