Physics:Racah seniority number
The Racah seniority number (seniority quantum number) [math]\displaystyle{ \nu }[/math] 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 [math]\displaystyle{ L }[/math] and total spin [math]\displaystyle{ S }[/math], which gives the degree of unpaired particles. A spin-independent interaction [math]\displaystyle{ \hat{V} }[/math] is assumed with the property[2]
- [math]\displaystyle{ \langle l^2;LM_L|\hat{V}|l^2;LM_L \rangle = g(2l+1)\delta_{L0} }[/math],
where [math]\displaystyle{ L }[/math] is the combined angular momentum, [math]\displaystyle{ M_L }[/math] magnetic quantum number, [math]\displaystyle{ l }[/math] is electrons' orbital angular momenta, and [math]\displaystyle{ g }[/math] is the dimensionless magnetic moment. The equation above shows there is no interaction unless the two electrons' orbital angular momenta are coupled to [math]\displaystyle{ L = 0 }[/math]. The eigenvalue is the "seniority number" [math]\displaystyle{ \nu }[/math].
References
- ↑ 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. doi:10.1063/1.3537842. http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.3537842.
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