Conservation laws in the $1f_{7/2}$ shell model of $^{48}$Cr

TL;DR

This paper explains conservation laws in the $1f_{7/2}$ shell model of $^{48}$Cr through symmetry principles and group theory, providing a theoretical foundation for previously observed numeric results.

Contribution

It offers a symmetry-based explanation for conservation laws in the $1f_{7/2}$ shell model, extending previous numeric findings with a group-theoretic framework.

Findings

Conservation laws are explained by particle-hole conjugation symmetry.

Irreducible representations of the symplectic group Sp(4) underpin these laws.

A generalization of the symmetry explanation is discussed.

Abstract

Conservation laws in the $1f_{7/2}$ shell model of $^{48}$Cr found in numeric studies by Escuderos, Zamick and Bayman [A. Escuderos, L. Zamick, and B. F. Bayman, arXiv:0506050 (2005)] and me [K. Neerg\aa rd, Phys. Rev. C \textbf{90}, 014318 (2014)] are explained by symmetry under particle-hole conjugation and the structure of the irreps of the symplectic group Sp(4). A generalization is discussed.