64 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 3 



positron emission, however, a correction for twice the rest mass must be made 

 since both the positron and an orbital electron are lost. 



The emission of the hypothetical neutrino, first postulated by Pauli, 

 is required for the conservation of energy, spin, and statistics. The emission 

 of a beta particle corresponds to a transition in the excited nucleus involving 

 a discrete quantity of energy; yet the emitted particles are observed to 

 possess any energy ranging from zero up to the total transition energy, Em &% . 

 It is necessary to assume, therefore, that the neutrino carries off an amount of 

 energy in each instance equal to the difference between the beta-particle 

 kinetic energy and the transition energy. Furthermore, beta emission 

 always results in a change of spin i of the residual nucleus by integral units 

 of h/2ir, i.e., 0, ± 1, + 2, • ■ ■ , while the intrinsic spin of the beta particle is 

 only a half unit. It must be assumed, therefore, that the neutrino spin is 

 also one-half. A similar observation holds for the statistics in that residual 

 nucleus remains unaltered while the emitted electron obeys Fermi statistics. 



The properties of the neutrino deduced from these observations are then 



Mass : or <<C electron mass 



Charge : None 



Spin: k/4r 



Magnetic moment: < 1.5 X 10 -4 Bohr magneton 



Statistics: Fermi-Dirac 



With the aid of the neutrino hypothesis and the transformations (p — > n), 

 (n — > p), Fermi [10] developed a theory of beta decay analogous to that for the 

 emission of light from an atom. The theory provides a means of calculating 

 the probability of the transformation in terms of the mean life for decay, the 

 energy distribution of the particles and a set of selection rules for determining 

 if a transition is allowed or forbidden. 



Assuming the neutrino mass to be negligible, the probability of emitting 

 per unit time a beta particle with energy between E and E + dE is given 

 by Fermi's theory in the form 



PdE = £- 3 \Q\*f(Z, E)pE(E 2 - 1)X(E - E) 2 dE 



where E = energy of electron in units of m c 2 — mc 2 /m c 2 

 E = maximum energy in units of m c 2 

 g = constant 



p = momentum of electron 

 The factor Q is a matrix element involving the proper functions U n for the 

 neutron and U m for the proton to which it is transformed, integrated over-all 

 space and spin coordinates 



Q = jUtU m e- 2 - i ^"°+^ ) - T/h dv 



