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The Racah seniority number ν {\displaystyle \nu } 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 {\displaystyle L} and total spin S {\displaystyle S} , which gives the degree of unpaired particles.
A spin-independent interaction V ^ {\displaystyle {\hat {V}}} is assumed with the property
where L {\displaystyle L} is the combined angular momentum, M L {\displaystyle M_{L}} magnetic quantum number, l {\displaystyle l} is electrons' orbital angular momenta, and g {\displaystyle 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 {\displaystyle L=0}. The eigenvalue is the "seniority number" ν {\displaystyle \nu }.