Sec. 2.4] GAMMA RAYS 39 



<T e — 8<?e + a<T ( from which the scattering coefficient s o> can be obtained by- 

 subtraction. 



The linear-, mass-, and atomic-absorption coefficients may be found from 

 the usual ratios 



<*l = P0~m = pN(Ta = pNZ<T e 



where p = density of absorber, gm per cc 



N = N / A = number of atoms per gm 

 N = Avogadro's number 

 A = atomic weight 

 Z — atomic number 

 Since the value of <r e is independent of atomic number, once it has been cal- 

 culated for a desired energy range the curve may be applied to any absorbing 

 material by multiplying it with the appropriate physical constants p, A T , and 

 Z. Stated alternatively, the absorption coefficients are directly proportional 

 to the electronic density of the medium. 



2.4. Pair Production. Pair production involves the complete absorption 

 of a gamma photon in the formation of an electron and a positron. The 

 process can take place only in the coulomb field of a nucleus although the 

 atom itself does not participate directly in the formation of the particles. 

 Its presence is necessary mainly for the conservation of momentum when the 

 gamma photon transfers its entire energy to the two light particles. 



The cross section per electron for pair production increases very nearly in 

 direct proportion to the atomic number of the absorbing atoms, but its 

 variation with the gamma-ray energy is more complicated and computations 

 with the exact formulas are inconvenient. It can be calculated, however, by 

 approximations that are valid in particular energy ranges [4,5,6]. A special 

 characteristic of pair production is the existence of a definite threshold 

 energy at 2m c 2 (1.02 mev) below which the process cannot occur. Above the 

 threshold the cross section increases rapidly for energies up to ~ 10 mev, but 

 at very high energies it increases more slowly, approximately as log E y . 

 An approximate formula for computing the cross section per electron for 

 gamma-ray energies up to 10m o c~ has been given in a form similar to that 

 below [13] 



K e = 2.87 X 10- 2s Z(E y - 1.19) 



where E y = gamma-ray energy, mev 



For high gamma energies lying within the range where m c 2 <<C hv <<C 137 

 nioC 2 Z~^, Heitler and Sauter [16] and Bethe and Heitler [4] give an approxi- 

 mate formula for the electronic cross section in the form 



/ e 2 V J^ /28 2hv 2\ 



Ke ~ \m c 2 ) 137 V 9 g Z*~~ 21/ 



