Racah seniority number explained

The Racah seniority number (seniority quantum number)

\nu 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 L and total spin S , which gives the degree of unpaired particles.

A spin-independent interaction

\hat{V} is assumed with the property^[2] \langle l ^{2 ;LM} _{L} \rangle = g( 2 l +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 .

Notes and References

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