introduction-weak-interaction-volume-one
introduction-weak-interaction-volume-one
introduction-weak-interaction-volume-one
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final state coulomb <strong>interaction</strong> between the daughter nucleus and the outgoin g<br />
electron, but, as we saw in the preceeding section, this is slight fo r<br />
light nuclei . (3 .5 .8) and (3.5 .9) yield three further relations concerning<br />
purely the axial vector and tensor couplings :<br />
= J,J' ( 1 /3)(I 1 2 ) =<br />
(Ifi )av<br />
= (~6~ ~<br />
av<br />
I ,IGTI 2<br />
(1/3)<br />
(3 .5 . 1 06 )<br />
J,J '<br />
(r%A ( 1 /3) I 'IGTI 2 i Y+A )<br />
av =<br />
d<br />
(3 .5 .10e )<br />
k ,k '<br />
i<br />
SJ,k ( 1/3) I x 2 . (3 .5 .10f )<br />
(NA vfi = (ti r<br />
u .T<br />
) av<br />
"A ) av<br />
We now writ e<br />
xunpol<br />
= (1/2) it 1 2 A + (1/6) 1 1'10111<br />
2 B , (3 .5 .11 )<br />
where, by trace evaluation (38) ,<br />
A = (Ic S 2 + c5I 2) (1 - v case) + (Icv ; 2 + ICl 2 ) (1 + v cos )<br />
t (2m/E) Re (C s C7 t CS ) , (3 .5 .12a )<br />
B = 3(ICT2 + IC .12) ( 1 + ( 1/3) v cos e) + 3(ICA I 2 +<br />
ICkI2)<br />
x<br />
x (1 - (1/3) v case) + (6m/E) Re (CT CA -r c, ca p' )<br />
(3 .5 .12b )<br />
introducing the variables 0, the angle between the electron and neutrin o<br />
momentum vectors, and v, the electron velocity . Finally, integrating ove r<br />
all plane angles except 8), and using the intensity formula (3 .5 .7a), we<br />
obtai n<br />
1 (9) ( /4i 3 ) q2 (E max - E) 2 (1 + a v cos 8 + b (2-/E)) sine de ,<br />
z (IC S 1 2 + c 2 +<br />
12 + ICV12)<br />
I , 1 2<br />
(3 .5 .13a )<br />
+ (I c T 1 2 + c112 +<br />
(IcV I2 IcI 2 _<br />
+ 1 /6 (1 02 12 + ci !2 -<br />
i<br />
i c gl 2<br />
2<br />
l * ! Cl~ I2) N 2<br />
GT I<br />
1cS12)I N,F I 2<br />
2 _ i2 I 2<br />
CAi i 0A 1 ) SGT
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