104 RADIATION BIOLOGY 



physical standpoint the intensity is an energy flow per unit area per unit 

 time. It may also be expressed as a flow of photons, equal to the flow of 

 energy divided bj'' the energy hu oi each photon. 



According to the exponential law of penetration, Eq. (40), the intensity 

 does not vanish exactly, however large the thickness of material traversed. 

 Some minute fraction of the X-ray intensity penetrates through any 

 barrier. 



The intensity of the monochromatic beam drops to half its initial value after 

 traversing a thickness of material equal to 



x^ = In (2/m) = 0.693/m (41) 



This thickness is called a "half- value layer," and its value serves frequently as an 

 index of the penetrating capacity of X rays. Thicknesses of 2, 3, 4, . . . half- 

 value layers reduce the intensity to i.^ >^, He, . . . of its initial value. 



The reciprocal of the absorption coefficient ju corresponds to the quantity v in 

 Eq. (27) which indicates the mean distance between successive collisions along 

 the track of a particle. (The reciprocal of ju is sometimes called the "relaxation 

 length.") The absorption coefficient itself represents a reciprocal distance and is 

 expressed accordingly in inverse centimeters (cm^^). 



Frequently, however, it is convenient to express the thickness of the layers of 

 material traversed by X rays according to their mass per unit area, that is, in 

 g/cm^. The absorption coefficient is then called the "mass absorption coef- 

 ficient" and is expressed in inverse g/cm^, i.e., in cmVg- The value of /x in 

 cm-i is then referred to more specifically, as the "linear absorption coefficient." 

 The ratio of the value in cm-i to the value in cmVg is simply the density p of the 

 material in g/cm^. 



The mass absorption coefficient has a more basic significance than the linear 

 coefficient because the X-ray absorption actually depends on the amount of ma- 

 terial packed within a layer rather than on the thickness of the layer. A change 

 of density affects the linear but not the mass absorption coefficient. 



The absorption coefficient consists of three components: iiph, which corresponds 

 to the probability of photoelectric absorption, Mpair, which corresponds to the 

 probability of pair production, and jjlsc, which corresponds to the probability of 

 scattering. 



M = MpA + Mpair + Msc (42) 



Scattering arises primarily from the Compton eifect, but there is also an appreci- 

 able probability of plain scattering which exerts no effect on matter (see Sect. 

 2-3) and is called "coherent scattering." The probabiUty of photoelectric effect 

 and of Compton effect equals the sum of the probabilities that either effect 

 results from the action of X rays on each of the various atomic electrons. 



Figure 1-64 shows data on the whole absorption coefficient. (Sample data on 

 the probabiUty of various effects are also shown in Figs. 1-24, 1-29, 1-41.) The 

 mass absorption coefficient varies regularly from element to element as a function 

 of the atomic number. Detailed tabulations of the values of the absorption 

 coefficient for all elements are given by White (1951). 



