The proxy-SU(3) symmetry in atomic nuclei

TL;DR

The paper reviews the proxy-SU(3) symmetry model in atomic nuclei, highlighting its theoretical foundations, validation, and predictions for nuclear shapes and phase transitions, offering a parameter-free approach to understanding nuclear structure.

Contribution

It introduces and validates the proxy-SU(3) approximation scheme, connecting it to the shell model and predicting nuclear shape phenomena without adjustable parameters.

Findings

Predicts beta and gamma deformation variables for even-even nuclei.

Explains the dominance of prolate shapes in ground states.

Identifies regions of shape coexistence and phase transitions.

Abstract

The microscopic origins and the up-to-now predictions of the proxy-SU(3) symmetry model of atomic nuclei are reviewed. Starting from the experimental evidence for the special role played by nucleon pairs with maximal spatial overlap, the proxy-SU(3) approximation scheme is introduced and its validity is demonstrated through Nilsson model calculations, as well as through its connection to the spherical shell model. The major role played by highest weight irreducible representations of SU(3) in shaping up the nuclear properties is pointed out, resulting in parameter-free predictions of the collective variables beta and gamma for even-even nuclei, in the explanation of the dominance of prolate over oblate shapes in the ground states of even-even nuclei, in the prediction of a shape/phase transition from prolate to oblate shapes below closed shells, as well as in the prediction of specific islands on the nuclear chart in which shape coexistence is confined. Further developments within the proxy-SU(3) scheme are outlined.