introduction-weak-interaction-volume-one

magnetic effects in these decays would cause first-order forbidden transitio n
effects, which we mentioned in 3 .5 . In the absence of all forbidden transitio n
effects, we should obtain pure Fermi spectra F(E, E O ) , where E is the energy
of the electron or positron, and E O is the endpoint energy (see 3 .4), for the
B12 and N12 decays . EO is slightly different for B12 and for N12 . Experimentally ,
the decay spectra are of the form
N ( E , E0 ) = F(E, Eo) (1 ± (8/3) aE) , (5 .5 .14)
or, dividing through by F(E, E O ) ,
S(E, EO ) = N(E, E0 ) /F ( E , E0 ) _ (1-1. ( 8 /3) a E ) . (5 .5 .15 )
The term linear in E in (5 .5 .15) arises from interference between the axial
vector interaction, which causes the allowed Gamow-Teller transition, an d
the vector interaction, which is responsible for first forbidden effects, if
these are indeed present . For the decay (5 .5 .11) the last term in (5 .5 .15 )
become s
(1 - (8/3) a E) , (5 .5 .16 )
and for (5 .5 .12) :
(1 + (8/3) a E) . (5 .5 .17 )
Weak magnetism should produce a nonzero coefficient a, which is connected t o
the bandwidth or uncertainty in the energy of the photon emitted in C12 '' deca y
(5 .5 .13) . By comparing the spectra in (5 .5 .11) and (5 .5 .12) we may obtai n
a value for a . The ratio of the departures from the allowed transition spectr a
for these decays is given b y
S(E, B12)/S(E, N12) k. (1 -+ A(1 + 7A ) E ) f(E) , (5 .5 .18 )
where f(E) is a correction for the inner Bremsstrahlung8 which unavoidably
accompanies beta decay . f(E) is dependent upon the endpoint energy EO .
Weak magnetism predicts the gradient of the line in (5 .5 .18) to b e
A = (1 .33 0 .15) % NeV 1 (5 .5 .19 )
The experimental value of A obtained by Xayer-Kuckuck and Michel (21) was
A -- (1 .13 0 .2.5) % ;eV l . (5 .5 .20 )
Thus the prediction of weak magnetism is within experimental error limits .
Similar experiments have also been conducted on the A = 8 triad . Here again ,
the results favoured weak magnetism, but were not accurate enough to verify it .
The second method for detecting weak magnetic effects is to study high-energy