Seniority in quantum many-body systems

TL;DR

This paper reviews the concept of seniority in quantum many-body systems, discussing its historical development, various extensions, and recent applications in Bose--Einstein condensates with spin.

Contribution

It provides a comprehensive overview of seniority's evolution and introduces recent advances and applications in complex quantum systems.

Findings

Seniority remains a useful quantum number in diverse many-body systems.

Extensions of seniority theory to multiple shells and mixed particles are feasible.

Recent applications demonstrate seniority's relevance in Bose--Einstein condensates.

Abstract

The use of the seniority quantum number in many-body systems is reviewed. A brief summary is given of its introduction by Racah in the context of atomic spectroscopy. Several extensions of Racah's original idea are discussed: seniority for identical nucleons in a single-$j$ shell, its extension to the case of many, non-degenerate $j$ shells and to systems with neutrons and protons. To illustrate its usefulness to this day, a recent application of seniority is presented in Bose--Einstein condensates of atoms with spin.