36 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 2 



the K absorption limit the cross section, or absorption coefficient, decreases 

 rapidly and smoothly. In this region the cross section per electron may be 

 calculated from a formula given by Grey [13,15] in a form similar to that 

 below. 



r e = 2.04 X 10- 30 Z 3 £ 7 - 4 (1 + 0.008Z)(£ 7 - 0.25E k - 0.422£|) 



where Z = atomic number of absorbing atoms 



E y = gamma-ray energy, mev 



E y = K x-ray absorption limit, mev 

 When Ey » E k , 



T e = 2.04 X 10- 30 Z 3 £ 7 - 3 (1 + 0.008Z) 



From T e the linear-, mass-, and atomic-absorption coefficients are obtained 

 from the relations given in Sec. 2.1. 



ti = pT m = pNr a — pNZr e 



When the electronic cross section is known for one substance, e.g., lead, it 

 may be calculated approximately for another absorbing material with atomic 

 number Z by the relation 



Z z 



Te = \Je)Vb Tcyy^Z 



Similar extrapolations may be made for the linear and mass coefficients. 

 Empirical cross section formulas, equivalent to that above, have been 

 given in the form > 



Te = AZ n \ m 



where A = constant 



X = gamma wavelength 

 As an example, for air and water the mass-absorption coefficients are 



r m = 2.33X 3 - 13 (air) 



r m = 2.54X 3 - 22 (water) 



2.3. Scattering of Gamma Rays. Gamma rays are scattered with loss of 

 energy only by electrons, and all electrons, whether bound in an atom or free, 

 have the same cross section for scattering. It is the only process in which 

 the gamma photon is not absorbed but instead undergoes a reduction in energy 

 and a deflection from its initial direction. Thus a collimated beam of 

 monoenergetic gamma rays after traversing an absorber is partially degraded 

 in energy and spread over a wide angle by scattering. 



Scattering is also the only process involving gamma rays in which both 

 energy and momentum are balanced exclusively by the scattered photon and 

 recoil electron; the atom does not participate in the interaction, and its 

 presence is unnecessary. The effect was first described by Compton [1] who, 



