PRINCIPLES OF RADIOLOGICAL PHYSICS 



105 



The chances of absorption and Compton scattering of X rays by adjacent 

 atoms are quite independent. The chance of coherent scattering depends a 

 little on the arrangement of adjacent atoms in liquid and in noncrystalline solids. 

 In crystalline solids the combined coherent scattering by many atoms gives rise 

 to the striking phenomenon of crystal diffraction. 



lO u-;-!— ;- ' -B 



2 

 O 



a. Kj 

 o: E 



o 



O 



to 



UJ 



to — 



CD O 



5 u. 



-I 9 

 < o 



l- 

 o 



I.O 



01 



001 



0.01 



10 



100 



0.1 1.0 



PHOTON ENERGY, Mev 

 Fig. 1-64. Total narrow-beam mass absorption coefficient for X rays of different 

 energies in aluminum and lead. (Courtesy G. R. White.) 



Therefore, except for crystal diffraction, the total attenuation of X rays in 

 passing through any material results very approximately from the sum of the 

 attenuations due to the separate constituent elements of the material. The 

 mass absorption coefficient of a material equals the arithmetic mean of the mass 

 absorption coefficients of its constituent elements Nos. 1, 2, 3, . . . , weighted 

 according to the crude chemical composition of the material. 



The coefficients pi, p2, 

 the material.^ 



fj. = piMi + p2fJL2 + PiiJ-i + • • • (43) 



. . . indicate the per cent by weight of each element in 



As mentioned before, the simple exponential law of attenuation, Eq. 

 (40), holds when the intensity I{x) includes only the fraction of the 

 incident X rays which has traversed a material without experiencing any 



5 For the purpose of calculating the X-ray absorption coefficient, or some other 

 atomic property, of a material containing different elements, the material is often 

 characterized by an "effective atomic number." Thus, for example, if the absorption 

 coefficient fx of each element happened to be proportional to the cube of its atomic 

 number Z, the Zeu of a mixture of elements could be defined, according to Eq. (4.3), 

 by the formula 



Zl,, = p.Zl + p,Zl + p,Zl + ■ ■ ■ 



Then the absorption coefficient of the mixture would be treated as the coefficient 

 pertaining to a single element whose atomic number equals Zett. Naturally, the 

 definition of Zen must be adapted in each case to the actual dependence of the coeffi- 

 cient under consideration upon the atomic number of each element. 



