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

Abstract: Theoretical models often invoke triaxial nuclear shapes to explain elusive collective phenomena, but such assumptions are usually difficult to confirm experimentally. The only direct measurements of the nuclear axial asymmetry $\gamma$ is based on rotational invariants of zero-coupled products of the electric-quadrupole (E2) operator, the Kumar-Cline sum rule analysis, which generally require knowledge of a large number of E2 matrix elements connecting the state of interest. We propose an alternative assumptions-free method to determine $\gamma$ of even-even rotating nuclei using only two E2 matrix elements, which are among the easiest to measure. This approach is based on a simple description of nuclear rotation, where the underlying assumptions of the Davydov-Filippov model are either empirically proven or unnecessary. The $\gamma$ values extracted here are found in agreement with the values deduced from Kumar-Cline sum rules measurements (where available), providing further evidence that the proposed approach represents a reliable, model-independent deduction of $\gamma$. The technique was applied to more than 60 deformed even-even rotating nuclei and the results indicate that rotating nuclei generally exhibit well-defined stable axially-asymmetric shapes.