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The **Racah seniority number** (seniority quantum number) was introduced by Giulio Racah for the classification of electrons in an atomic configuration.^{[1]} The "seniority number", in a loosing statement, is quantum number additional to the total angular momentum and total spin , which gives the degree of unpaired particles.

A spin-independent interaction is assumed with the property^{[2]}

- ,

where is the combined angular momentum, magnetic quantum number, is electrons' orbital angular momenta, and is the dimensionless magnetic moment. The equation above shows there is no interaction unless the two electrons' orbital angular momenta are coupled to . The eigenvalue is the "seniority number" .

**^**Racah, Giulio (1943). "Theory of Complex Spectra. III".*Phys. Rev*.**63**(9–10): 367. doi:10.1103/physrev.63.367.**^**Isacker, P. Van (2010). "Seniority in quantum many-body systems".*Symmetries in Nature: Symposium in Memoriam Marcos Moshinsky*. AIP Conference Proceedings: 141–152. arXiv:1010.2415. doi:10.1063/1.3537842. S2CID 53417881.