Systematic investigation of quadrupole properties in deformed and transitional nuclei

In the present work, we address a long-standing problem in nuclear physics on how to decipher the nature of collective motion from electromagnetic transition probabilities. A systematic analysis of the $B(E2)$ transitions is performed for thirty nuclei using the triaxial projected shell model (TPSM) approach. It is shown that $I \rightarrow (I-2)$ transitions for the $\gamma$-bands depict a staggering phase and this phase reverses with the inclusion of the quasiparticle excitations for all the nuclei, except for the six nuclei of $^{76}$Ge, $^{112}$Ru, $^{170}$Er, $^{182}$Os, $^{192}$Pt and $^{232}$Th. This feature is analogous to the energy staggering phase obtained for these nuclei. It is noted that the energy staggering phase with even-spin-down (odd-spin-down), which is considered as a signature of $\gamma$-softness ($\gamma$-rigidity), corresponds to even-spin-up (odd-spin-up) staggering phase of the $B(E2)$ transitions. Further, TPSM predicted values for both energies and transition are shown to be in good agreement with the corresponding experimental values.