Limits on assigning a shape to a nucleus
A. Poves, F. Nowacki, Y. Alhassid
Abstract
The interpretation of nuclear observables in the laboratory frame in terms of the intrinsic deformation parameters $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ 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 $\ensuremath{\beta}$ and $\ensuremath{\gamma}$. We find that the shape parameter $\ensuremath{\beta}$ often has a non-negligible degree of softness and that the angle $\ensuremath{\gamma}$ 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.