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
.
