306 Molecular Action of Ionizing Radiations /I6 : 4 



Integration of Equation 1 leads to the equation 



- = e~ SD (2) 

 n 



where n is the number of molecules before receiving total dose D, and 



n is the number left unaltered afterward. 



If the number of ionizations along the track of the bombarding 



particle is sufficiently low, each may produce the destruction of one 



molecule. Then one may write 



S = Vi (3) 



where V is the critical volume of the molecule and i is the number of 

 ionizations per unit path length. (If there are too many ionizations per 

 unit path length, Equation 3 must be modified. Moreover, if several hits 

 are necessary for molecular destruction, Equation 3 must be changed in a 

 different fashion.) To further simplify Equation 3, one may define a 

 total ionization density / such that 



/ = Di (4) 



that is, /is the number of ionizations per unit volume. Using Equation 3, 

 including its implicit assumptions, and Equation 4, Equation 2 may be 

 rewritten as 



- = e~ m (5) 

 n 



"■o 



Equation 5 is in a form that can be readily tested. Graphs of lines 

 expected from this equation are shown in Figure 5. A wide variety of 

 experiments ranging from genetic effects in whole animals and plants to 

 the destruction of molecules in dried film all can be described by this 

 equation if the ionization per unit path length is sufficiently small. It 

 was used to compute the sensitive volume referred to in the discussion of 

 genetic effects in Chapter 10, and its implications were considered in 

 Chapter 14. 



If instead of sparse ionizations, one considers the limiting case of a 

 very large number of ionizations per unit path length, then Equation 2 

 can also be rewritten in a simpler form. In this case, there is certain 

 to be at least one ionization within each molecule for each incident 

 particle. Then S becomes a constant S , the cross section for destruction 

 of the molecule if ionization occurs within it. Under these conditions, 

 Equation 2 becomes 



- = e~ s o D (6) 



The calculations of the critical volume V and of the limiting cross section 

 S are shown in Figure 5. The applications of these techniques are 

 discussed in the following two sections. 



