On the intersection of the shell, collective and cluster models of atomic nuclei I: Multi-shell excitations

TL;DR

This paper explores the relationships between shell, collective, and cluster models of atomic nuclei through symmetry considerations, identifying the U(3) and U(3)×U(3) symmetries as key to understanding multi-shell excitations.

Contribution

It introduces the concept of U(3)×U(3) dynamical symmetry as the intersection of models for multi-shell excitations, extending previous symmetry frameworks.

Findings

U(3) symmetry links shell, collective, and cluster models for single shells.

U(3)×U(3) symmetry describes multi-shell excitations.

Symmetry analysis clarifies model relationships in nuclear physics.

Abstract

The relation of the shell, collective and cluster models of the atomic nuclei is discussed from the viewpoint of symmetries. In the fifties the U(3) symmetry was found as their common part for a single shell problem. For multi major-shell excitations, considered here, the U(3)$\otimes$U(3) dynamical symmetry turns out to be their intersection.