introduction-weak-interaction-volume-one

We are thus forced to conclude that only antineutrinos with positiv e
helicity (r= 2), and only neutrinos with negative helicity (r = 1) may
ever be produced . We may therefore reduce our usual four-componen t
neutrino spinor to a two-component one . This is known as the
neutrino hypothesis' .
'two-componen t
We now discuss the experimental determination of the neutrin o
helicity (69) . In a decay of the form
A(0) + e >B(1 )-+v >C(O') + f , (3 .8 .6 )
we see that, by angular momentum conservation, 1 the nucleus B must have
a spin opposite to that of the emitted neutrino . Furthermore, when th e
excited nuclide B returns to the ground-state C, the circular polarizatio n
of the decay photon will be by cos e), where e is the angle between
the neutrino and photon momentum vectors . In order to select only thos e
gamma rays which are emitted in a direction opposite to their associate d
neutrinos, we may employ the phenomenon of nuclear resonance scattering .
When a photon is emitted or absorbed by a nucleus, the latter recoils wit h
energy n^g/M
. Thus, when a photon is absorbed, the energy available fo r
excitation is only E O(l - EO /M) . In order to make resonance possible ,
extra energy, amounting to that lost in the nuclear recoil, must be supplied t o
the photon . This occurs if the decaying nucleus has already recoile d
in a direction opposite to that induced by gamma-ray emission . Such an
extra recoil could be provided by the emission of a neutrino whos e
direction of motion was precisely opposite to that of the photon .
The Doppler shift in the gamma-ray energy caused by the nuclear recoi l
is given b y
L'_\E _ (EO Ev cose)/ii , (3 .8 .7a )
and hence the total energy for excitation transferred by the gamma ray
will be
E EO t (E0 Ev cos e )/M - ED/i . (3 .8 .7b )
We now deduce that the condition for resonant absorption i s
Ev case = EO • (3 .8 .7c )
1 . Obviously we assume that any electrons captured from the atomic K shel l
will be s-wave .