# Evidence for Symplectic Symmetry in Ab Initio No-Core Shell Model Results for Light Nuclei

## TL;DR

This paper provides evidence that symplectic symmetry plays a significant role in the structure of low-lying states of light nuclei like carbon-12 and oxygen-16, supporting the relevance of a symplectic no-core shell model.

## Contribution

It demonstrates that a symplectic symmetry-based approach can accurately describe low-energy nuclear states without effective charges, confirming theoretical models and highlighting clustering phenomena.

## Key findings

- Eigenstates project strongly onto symplectic basis states
- Results are consistent across different interaction renormalizations
- Model reproduces experimental B(E2) values without effective charges

## Abstract

Clear evidence for symplectic symmetry in low-lying states of $^{12}$C and $^{16}$O is reported. Eigenstates of $^{12}$C and $^{16}$O, determined within the framework of the no-core shell model using the JISP16 $NN$ realistic interaction, typically project at the 85-90% level onto a few of the most deformed symplectic basis states that span only a small fraction of the full model space. The results are nearly independent of whether the bare or renormalized effective interactions are used in the analysis. The outcome confirms Elliott's \SU{3} model which underpins the symplectic scheme, and above all, points to the relevance of a symplectic no-core shell model that can reproduce experimental B(E2) values without effective charges as well as deformed spatial modes associated with clustering phenomena in nuclei.