40 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 2 



where m = electronic rest mass 

 e = electronic charge 

 c = velocity of light 

 Z = atomic number of absorber 

 At very great energies, where kv )>> l37m c 2 Z^^, Bethe and Heitler [4] 

 have also shown that the exact formula approaches asymptotically the value 

 given by the formula 



— 27 



) 



The atomic cross section and the linear- and mass-absorption coefficients 

 for pair production are obtained from the usual relations 



Kl = pK m = pNKa = pNZK e 



When the mass-absorption coefficient is known for one substance, e.g., lead, 

 the coefficient for any other material may be found from 



. v 207.2 P Z* 



Km - Um)Pb (82)21L3 A 



where p, Z, A = density, atomic number, and atomic weight, respectively, of 

 absorber 

 lOpb = mass-absorption coefficient for pair production in lead 

 The explanation of the process of pair production is to be found in Dirac's 

 relativistic theory of the electron [7]. Dirac showed that the wave equation 

 for the electron admits negative energy states for the electron as well as those 

 of positive energy. The lowest positive state in the continuum of positive 

 energies must necessarily be that equivalent to the rest mass of the electron, 

 m c 2 , as required by Einstein's law. Similarly, a highest negative energy 

 state may exist at —m c 2 , and below this there exists an infinity of possible 

 quantum states identical to the positive energy continuum. Between 

 —m c 2 and +m c 2 there are no states in which an electron can exist. Since 

 the existence of electrons in positive states hardly needs demonstration, it 

 must be assumed on the basis of Pauli's exclusion principle that all negative 

 states are filled and, hence, that all space is occupied by an infinite density of 

 negative energy electrons. The existence of such a "sea" of electrons 

 normally could not be demonstrated because its uniformly distributed charge 

 forms a field-free region. However if an electron is raised to a positive 

 energy state, the unoccupied level or "hole" left behind behaves as a posi- 

 tively charged electron and can be detected by the ionization it produces. 

 An electron can be ejected from a negative state only by the expenditure of 

 energy at least equal to 2m c 2 , corresponding to the transition from —m c 2 to 

 -\-m c 2 . Gamma rays with energies greater than this, therefore, can excite 



