14
A. V. Glushkov
S J
a
n 1 j 1 l 1 n 2 j 2 l 2 ; n 4 j 4 l 4 n 3 j 3 l 3
= (−1) j 4 − j 2 +J +1
j 3 j 4 J
j 2 j 1 a
×
(2 j 1 + 1)(2 j 2 + 1)(2 j 3 + 1)(2 j 4 + 1)
×
j 1 j 3 a
1/2 −1/2 0
j 2 j 4 a
1/2 −1/2 0
×
{al 1 l 3 }{al 2 l 4 }F a
n 1 j 1 l 1 n 2 j 2 l 2 ; n 4 j 4 l 4 n 3 j 3 l 3
+
l
(−1) l+a
× (2a + 1)M l
a
n 1 j 1 l 1 n 2 j 2 l 2 ; n 4 j 4 l 4 n 3 j 3 l 3
.
(18)
Here jl = j
l
and
a 1 l 1 l 3
denotes the triangle condition for moments a 1 ,l 1 ,l 3 .
The detailed expressions for the Coulomb and Breit parts can be found in Refs.
[4, 114–120, 128–130]. The quantity F is connected with the Coulomb part of the
interelectron interaction:
F a
n 1 j 1 l 1 n 2 l 2 j 2 ; n 4 l 4 j 4 n 3 j 3 l 3
= R a
n 1 j 1 l 1 n 2 j 2 l 2 ; n 4 j 4 l 4 n 3 j 3 l 3
+ R a
n 1 j 1 l 1 n 2
∼
j 2 l 2 ; n 4
∼
j 4 l 4 n 3 j 3 l 3
+ R a
n 1
∼
j 1 l 1 n 2 j 2 l 2 ; n 4 j 4 l 4 n 3
∼
l 3 j 3
+ R a
n 1
∼
j 1 l 1 n 2
∼
j 2 l 2 ; n 4
∼
j 4 l 4 n 3
∼
j 3 l 3
. (19)
The quantity M is connected with the Breit part of interelectron interaction:
M
l
a
n 1 j 1 l 1 n 2 j 2 l 2 ; n 4 j 4 l 4 n 3 j 3 l 3
= R l
n 1 j 1 l 1 n 2 j 2 l 2 ; n 4
∼
j 4 l 4 n 3
∼
j 3 l 3
× X
l
a
j 1 l 1 ; j 3 l
3
X
l
a
j 2 l 2 ; j 4 l
4
+ R l
n 1
∼
j 1 l 1 n 2
∼
j 2 l 2 ; n 4 j 4 l 4 n 3 j 3 l 3
× X
l
a
j 1 l
1 ; j 3 l 3
X
l
a
j 2 l
2 ; j 4 l 4
+ R l
n 1
∼
j 1 l 1 n 2 j 2 l 2 ; n 4
∼
j 4 l 4 n 3 j 3 l 3
× X
l
a
j 1 l
1 ; j 3 l 3
X
l
a
j 2 l 2 ; j 4 l
4
+ R l
n 1 j 1 l 1 n 2
∼
j 2 l 2 ; n 4 j 4 l 4 n 3
∼
j 3 l 3
× X
l
a
j 1 l 1 ; j 3 l
3
X
l
a
j 2 l
2 ; j 4 l 4
.
(20)