# Proxy-SU(3) symmetry in heavy nuclei: Foundations

## TL;DR

This paper explores an approximate SU(3) symmetry in heavy deformed nuclei by replacing intruder orbitals with proxy orbitals, testing the approximation's accuracy within the Nilsson model at large deformations.

## Contribution

It introduces a novel proxy-SU(3) symmetry approach for heavy nuclei and analyzes its validity through Nilsson model calculations.

## Key findings

- The proxy approach maintains a one-to-one orbital correspondence.
- The approximation accurately reproduces key symmetry features.
- Selection rules and avoided crossings are affected by parity differences.

## Abstract

An approximate SU(3) symmetry appears in heavy deformed even-even nuclei, by omitting the intruder Nilsson orbital of highest total angular momentum and replacing the rest of the intruder orbitals by the orbitals which have escaped to the next lower major shell. The approximation is based on the fact that there is a one-to-one correspondence between the orbitals of the two sets, based on pairs of orbitals having identical quantum numbers of orbital angular momentum, spin, and total angular momentum. The accuracy of the approximation is tested through calculations in the framework of the Nilsson model in the asymptotic limit of large deformations, focusing attention on the changes in selection rules and in avoided crossings caused by the opposite parity of the proxies with respect to the substituted orbitals.