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

• Unified derivation of conditions for the total and partial conservation of seniority.
• General analysis of the partial conservation of seniority in boson systems.
• Why partial conservation of seniority is crucial for seniority isomers in nuclei.
• The effect of partial conservation of seniority on one-nucleon transfer intensities.

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 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.