Racah seniority number

The Racah seniority number (seniority quantum number) $$\nu$$ 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 $$L$$ and total spin $$ S $$, which gives the degree of unpaired particles.

A spin-independent interaction $$ \hat{V} $$ is assumed with the property


 * $$ \langle l^2;LM_L|\hat{V}|l^2;LM_L \rangle = g(2l+1)\delta_{L0} $$,

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" $$\nu$$.