Insights into Nuclear Triaxiality from Interference Effects in $E2$ Matrix Elements

Recently, we have introduced [1] a triaxial rotor model with independent inertia and $E2$ tensors. The $E2$ matrix elements [2] of the osmium isotopes (186, 188, 190, and 192) are studied in the framework of this model (59 of 84 $E2$ matrix elements deviate by 30$\%$ or less). It is shown that interference effects in the inertia tensor ($K$-mixing) and the $E2$ tensor can lead to significant reductions in the diagonal $E2$ matrix elements. In some instances, the diagonal $E2$ matrix elements may decrease with increasing spin. Additionally, a sum rule for diagonal $E2$ matrix elements is shown and used to explore missing strength from $K$-admixtures. \newline \newline [1] J.L.~Wood, A-M.~Oros-Peusquens, R.~Zaballa, J.M.~Allmond, and W.D.~Kulp, Phys. Rev. C \textbf{70}, 024308 (2004). \newline [2] C.Y.~Wu, D.~Cline, T.~Czosnyka, A.~Backlin, C.~Baktash, R.M.~Diamond, G.D.~Dracoulis, L.~Hasselgren, H.~Kluge, et al., Nucl.~Phys.~\textbf{A607}, 178 (1996).