introduction-weak-interaction-volume-one

and where q is the four-momentum of the particles . By analogy with electrodynamics,
we may deduce that in (5 .5 .3) and (5 .5 .4) both hv and hA are zero .
Tests of this hypothesis are rendered difficult because the terms containin g
h are momentum-dependent, and hence are very small in most weak processes .
In (5 .2 .9) we considered the weak current of the form
component
(5 .5 .1) as anothe r
of the vector electromagnetic current . Using this approach, we may
evaluate the vector form factors occuring in the matrix element for a transitio n
between the nucleon states (i .e . neutron decay and crossed equivalent s7 ) i n
terms of the nucleon isovector electromagnetic form factors defined in (5 .4 .11) :
gv (g2 ) Fy( g2) , (5 .5 .6 )
fV ( g2) }A n)/(2 mN) G'V (g 2) • (5 .5 .7 )
We may also
write down the boundary conditions for the cas e
q = 0 (5 .5 .8 )
gV(G) = 1 , (5 .5.9 )
by the CVC hypothesis, and
fV ( 0 ) ( N p r n )/(2 DIN ) (3.7)(2 mN ) . (5 .5 .10 )
By analogy with electromagnetism, the term (5 .5 .7) is known as the weak magneti c
form factor, and its effects are known as weak magnetism (19) .
There are basically three types of reactions in which weak magnetis m
may be detected : favourable beta decays, muon capture in atoms and high-energ y
neutrino reactions . Since the term containing g V
in (5 .5 .3) is momentumdependent,
we wish to maximize this momentum in order to detect weak magneti c
effects . Thus, in order to detect weak magnetism in beta decay, we consider ,
G62 ,
as was suggested by Gell-hann (20), the A e 12 triad : B52 ,
N7- 2 , an d
assume perfect charge independence . All three members of the triad, `which have
I = 1, JP 1* in their excited level, are connected to the I = 0, JP = 0 t
C12 ground-state by allowed transitions :
B12 > C 12 t e + ve (5 .5 .11 )
N 12 "--> C l + e + ve (5 .5 .12 )
C 12 ''_>C 12 + (5 .5 .13)
(5 .5 .11) and (5 .5 .12) are allowed Gamow-Teller transitions with large energ y
releases, and (5 .5 .13) is a magnetic dipole transition . The presence of weak