Triaxial nuclear shapes from simple ratios of electric-quadrupole matrix elements

Theoretical models often invoke axially-asymmetric nuclear shapes to explain elusive collective phenomena, but such an assumption is not always easy to confirm experimentally. The only model-independent measurement of the nuclear axial asymmetry (or triaxiality) $\gamma$ is based on rotational invariants of zero-coupled products of the electric-quadrupole (E2) operator — the Kumar-Cline sum rule analysis — which generally requires knowledge of a large number of E2 matrix elements connecting the state of interest. We propose an alternative method to determine $\gamma$ using only two E2 matrix elements, which are among the easiest to measure. This approach is based on a standard rotational description of a nucleus with stable triaxial deformation, where all underlying assumptions are either empirically proven or unnecessary. It is applied to the 2${}^{+}$ states of the ground-state and the $\gamma$ bands of even–even nuclei and is model-independent provided these 2${}^{+}$ states have rotational nature. This technique was applied to a number of deformed even–even nuclei for which the ratio of the energies of the yrast 4${}^{+}$ and 2${}^{+}$ states was $R_{{}_{4/2}}>$ 2.4. Where sufficient experimental data were available for performing Kumar-Cline analysis, good agreement was observed between the $\gamma$ values deduced in these two approaches. The agreement shows that (i) the 2${}^{+}$ states of the selected nuclei have indeed rotational nature, and (ii) the proposed method represents a simple and reliable deduction of $\gamma$. In the present work more than 60 even–even rotating nuclei were associated with axially-asymmetric nuclear shapes.