Microscopic investigation of $E2$ matrix elements in atomic nuclei

A systematic analysis of $E2$ matrix elements of ⁷²Ge, ⁷⁶Ge, ¹⁶⁸Er, ¹⁸⁶Os, ¹⁸⁸Os, ¹⁹⁰Os, ¹⁹²Os and ¹⁹⁴Pt nuclides is performed using the beyond mean-field approach of triaxial projected shell model (TPSM). For these nuclei, large sets of $E2$ matrix elements have been deduced from the multi-step Coulomb excitation experiments, and it is shown that TPSM approach provides a reasonable description of the measured transitions. We have evaluated 1496 $E2$ matrix elements up to spin, $I=10$ for the eight nuclei studied, and tabulate them for future experimental and theoretical comparisons. Further, shape invariant analysis has been performed with the calculated $E2$ transitions using the Kumar-Cline sum rules. It is inferred from the analysis that the resulting shape, after configuration mixing of the quasiparticle states, transforms from γ-rigid to that of γ-soft for some nuclei, in conformity with the experimental data.