Hyperfine and Electroweak Interactions in Heavy Finite Fermi Systems …
69
< a|P NC|b >= −
n
[
< b
eα ν A ν
n >< n
H
(1)
W
a >
ε a − ε n
+
< b
H
(1)
W
n >< n
eα ν A ν
a >
ε b − ε n
. (8)
The corresponding spin-dependent PNC contribution is:
< a|P NC|b > sd = k a < a|P NC|b > (a) +k 2 < a|P NC|b > (2) +k h f < a|P NC|b > (h f ) , (9)
where
< a|P NC|b >
(h f )
=
m =a
n =a
< a
H
(1)
W
n >< n
H
(h f )
W
m >< m|eα ν A
ν
|b >
(ε a − ε m )(ε a − ε n )
+
m =a
n =a
< a
H
(h f )
W
n >< n
H
(1)
W
m >< m|eα ν A
ν
|b >
(ε a − ε m )(ε a − ε n )
+
m =a
n =b
< a
H
(1)
W
m >< m|eα ν A
ν
|n >< n
H
(h f )
W
m >
(ε a − ε m )(ε b − ε n )
+
m =a
n =b
< a
H
(h f )
W
m >< m|eα ν A
ν
|n >< n
H
(h f )
W
b >
(ε a − ε m )(ε b − ε n )
+
m =b
n =b
< a|eα ν A
ν
|n >< n
H
(1)
W
m >< m
H
(h f )
W
b >
(ε b − ε m )(ε b − ε n )
+
m =b
n =b
< a|eα ν A
ν
|n >< n
H
(h f )
W
m >< m
H
(1)
W
b >
(ε b − ε m )(ε b − ε n )
− < a
H
(h f )
W
a >
m =a
< a
H
(1)
W
m >< m|eα ν A
ν
|b >
(ε a − ε m ) 2
−
n =b
< a|eα ν A
ν
|n >< n
H
(1)
W
b >
(ε b − ε n ) 2
< b
H
(h f )
W
b > . (10)
Here the following notations are used: |a >=|a I F F M F >, |b >=|bI F I M I >,
I—spin of a nucleus, F I,F —is a total momentum of an atom and M—its z component
(I, F are the initial and final states). It should be noted the expressions for the matrix
elements < a|P NC|b >
(a) , < a|P NC|b >
(2) are similar to Eq. (10). The full