Зайцевский А.В. Релятивистская теория электронного строения молекул
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s
W
γ
l
(r)
l
P
γ
l
l γ
P
γ
l
=
l
X
m=−l
|Y
γ
lm
i hY
γ
lm
|,
W
W
γ
=
X
l
W
γ
l
(r)P
γ
l
.
j m l
ψ
′′
ljm
= (1 + N)
1/2
ϕ
lj
L
(r)Y
ljm
e
ψ
ljm
l
j
l j W
lj
(r)
W
γ
=
X
lj
W
γ
lj
(r)P
γ
lj
,
P
γ
lj
Y
ljm
m γ
l
j j = l + 1/2 j = l − 1/2
j
W
γ
=
X
l
W
γ
l,l+1/2
(r)P
γ
l,l+1/2
+ W
γ
l,l−1/2
(r)P
γ
l,l−1/2
.
l
W
γ
l
(r) =⇒ W
γ
l,l−1/2
(r), W
γ
l,l+1/2
(r)
l
W
γ
l,l−1/2
, W
γ
l,l+1/2
•
j
W
γ
l
=
(l + 1)W
γ
l,l+1/2
+ lW
γ
l,l−1/2
2l + 1
2j + 1
•
∆W
γ
l
= W
γ
l,l+1/2
− W
γ
l,l−1/2
.
W
γ
lj
=
W
γ
l
+
2
2l + 1
·
l
2
∆W
γ
l
(j = l + 1/2 )
2
2l + 1
·
(−l − 1)
2
∆W
γ
l
(j = l − 1/2 ).
j
2
= (l + s)
2
= l
2
+ s
2
+ 2(l, s),
(l, s) l j
h(l, s)i
lj
=
D
j
2
E
lj
−
D
l
2
E
lj
−
D
s
2
E
lj
2
=
l
2
(j = l + 1/2 )
(−l − 1)
2
(j = l − 1/2 ).
W
γ
lj
W
γ
lj
=
W
γ
l
+
2
2l + 1
∆W
γ
l
h(l
γ
, s)i
lj
.
W
γ
=
X
l
W
γ
l
P
γ
l
|
{z }
+
X
l
2
2l + 1
∆W
γ
l
(P
γ
l
l
γ
P
γ
l
, s)
|
{z }
W
γ
SC
W
γ
SO
H
P P
= H
SC
+ H
SO
H
SC
=
X
i
−
∆
i
2
+
X
γ
W
γ
SC
(i)
+
X
i>j
r
−1
ij
H
SO
=
X
i
X
γ
W
γ
SO
(i).
H
SC
H
SO
H
P P
H
P P
•
•
•
H
SC
1
0
0
1
H
P P
W
SO
H
SO
H
P P
H
SC
Ψ
SC
µ
= E
SC
µ
Ψ
SC
µ
Ψ
SC
µ
Λ S
Λ S
H
P P
H
SC
Ψ
SC
µ
H
[0−1]
eff
= P H
P P
P = P (H
SC
+ H
SO
)P,
P =
X
µ
Ψ
SC
µ
ED
Ψ
SC
µ
H
[0−1]
eff
D
Ψ
SC
µ
H
[0−1]
eff
Ψ
SC
ν
E
= E
SC
µ
δ
µν
+
D
Ψ
SC
µ
H
SO
Ψ
SC
ν
E
.
•
D
Ψ
SC
µ
H
SO
Ψ
SC
ν
E
Ψ
SC
µ
H
SO
•
D
Ψ
SC
µ
H
SO
Ψ
SC
κ
E
Ψ
SC
κ
D
Ψ
SC
µ
H
(2)
eff
Ψ
SC
ν
E
=
X
κ
D
Ψ
SC
µ
H
SO
Ψ
SC
κ
ED
Ψ
SC
κ
H
SO
Ψ
SC
ν
E
E
SC
ν
− E
SC
κ
.
H
SO
˜