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) γ 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 γ 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 γ 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 γ 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 γ . In the present work more than 60 even–even rotating nuclei were associated with axially-asymmetric nuclear shapes.