The Racah seniority number (seniority quantum number) ν was introduced by Giulio Racah for the classification of electrons in an atomic configuration. The "seniority number", in a loosing statement, is quantum number additional to the total angular momentum L and total spin S , which gives the degree of unpaired particles.
A spin-independent interaction V ^ is assumed with the property
< l 2 ; L M L | V ^ | l 2 ; L M L >= g ( 2 l + 1 ) δ L 0 ,
where L is the combined angular momentum, M L magnetic quantum number, l is electrons' orbital angular momenta, and g is the dimensionless magnetic moment. The equation above shows there is no interaction unless the two electrons' orbital angular momenta are coupled to L = 0 . The eigenvalue is the "seniority number" ν .
