# Limits on assigning a shape to a nucleus

## TL;DR

This paper investigates the limitations of defining nuclear shapes using deformation parameters, revealing that many nuclei exhibit shape softness and fluctuations, challenging traditional assumptions about nuclear structure.

## Contribution

The authors introduce a new method to accurately calculate higher-order invariants, providing deeper insight into nuclear shape fluctuations and their implications.

## Key findings

- Beta often exhibits shape softness and fluctuations.
- Gamma angle is characterized by large fluctuations.
- Doubly magic nuclei are not necessarily spherical.

## Abstract

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 (Kumar), 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.