The interpretation of nuclear observables in the laboratory frame in terms of the intrinsic deformation parameters $\beta$ and $\gamma$ is a classical theme in nuclear structure. Here we use the quadrupole invariants, calculated within the framework of the configuration-interaction shell model, to clarify the meaning and limitations of nuclear shapes. We introduce a novel method that enables us to calculate accurately higher-order invariants and, therefore, the fluctuations in both $\beta$ and $\gamma$. We find that the shape parameter $\beta$ often has a non-negligible degree of softness and that the angle $\gamma$ is usually characterized by large fluctuations, rendering its effective value not meaningful. Contrary to common belief, we conclude that doubly magic nuclei are not spherical, because the notion of a well-defined shape does not apply to them.

• Received 18 June 2019
• Revised 19 February 2020
• Accepted 26 March 2020

DOI:https://doi.org/10.1103/PhysRevC.101.054307