Seniority in quantum many-body systems. I. Identical particles in a single shell

TL;DR

This paper explores the concept of seniority quantum number in many-body quantum systems, focusing on identical particles in a single shell, revealing partial conservation phenomena especially in spin-9/2 fermions and bosonic systems.

Contribution

It demonstrates the conditions under which seniority is partially conserved in systems of identical particles, highlighting its relevance to nuclear isomers and transfer reaction selection rules.

Findings

Partial conservation of seniority occurs in spin-9/2 fermions.

Seniority conservation is prevalent in bosonic systems of any spin.

Partial seniority conservation explains observed nuclear isomers and reaction rules.

Abstract

A discussion of the seniority quantum number in many-body systems is presented. The analysis is carried out for bosons and fermions simultaneously but is restricted to identical particles occupying a single shell. The emphasis of the paper is on the possibility of {\em partial} conservation of seniority which turns out to be a peculiar property of spin-9/2 fermions but prevalent in systems of interacting bosons of any spin. Partial conservation of seniority is at the basis of the existence of seniority isomers, frequently observed in semi-magic nuclei, and also gives rise to peculiar selection rules in one-nucleon transfer reactions.