66 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 3 



= A - B{E + 1) 



GT 



where iV = number of particles observed in each successive momentum 

 = interval 

 E = energy in units of m c 2 

 A, B = experimental constants 

 In terms of the number N 1 of particles per unit energy range, the "Kurie 

 plot" is 



Jef) = c ~ de 



(, 



where p = momentum in units of m c for energy E 



C, D = experimental constants 

 Plotting (N/F)W or (N l /pEF) Vl against E, a straight line of negative slope 

 is obtained if the particles follow a Fermi distribution in energy. The 

 intercept on the energy ordinate corresponds to E = %mv 2 + m c 2 . 



The theoretical mean life r for beta decay is found by integrating the 

 probability of emission per unit time over the whole range of energy. 



i-P,« j*° PdE = g>\Q\>F(Z,E ) 



where Pt = total probability that a particle of any energy is emitted per unit 

 of time 



F(Z, E ) = f^EiE* - 1)»(JE - EYf{Z, E) 



dE 



The exact form of the function F{Z, E ) is inconveniently complicated for 

 calculation, but approximations valid over certain ranges of Z and E have 

 been suggested [14,15,16]. In all cases the probable life for beta emission 

 decreases rapidly with increasing maximum energy, E . 



3.12. Selection Rules for Beta Decay. Nuclear transitions of the form 

 w— >P or P-^n involved in beta emission are classed as allowed, first, 

 second, or higher order forbidden depending upon the relative probability of 

 the process. Empirically, a transition is classed by comparison of the magni- 

 tude of its half-life and energy with those of beta emitters of nearly the same 

 atomic number. 



The product of the half-life T and the function F, defined in the preceding 

 section, is roughly constant for a particular class of transition within each of 

 the three groups formed by light, medium, and heavy nuclei. Division of 

 nuclei into at least three groups is necessary since the product FT increases 

 also with atomic number independent of the forbiddenness of a transition. 



