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.