Partial conservation of seniority in $j=9/2$ shell: Analytic and numerical studies

TL;DR

This paper investigates the partial conservation of seniority in the $j=9/2$ shell, providing an analytic proof for special states with fixed seniority and total spin, and explores its uniqueness among similar systems.

Contribution

It offers the first analytic proof explaining the partial seniority conservation in the $j=9/2$ shell and identifies its specific occurrence for certain states.

Findings

Special states with seniority v=4 and spins I=4,6 are eigenstates of any two-body interaction.

Partial seniority conservation is unique to the $j=9/2$ shell for the studied configurations.

Analytic proof links this phenomenon to properties of fractional parentage coefficients.

Abstract

Recent studies show that for systems with four identical fermions in the $j=9/2$ shell two special states, which have seniority $v=4$ and total spins I=4 and 6, are eigenstates of any two-body interaction. These states have good seniority for an arbitrary interaction. In this work an analytic proof is given to this peculiar occurrence of partial conservation of seniority which is the consequence of the special property of certain coefficients of fractional parentage. Further calculations did not reveal its existence in systems with other $n$ and/or $I$ for shells with $j\leq15/2$.