The intensity I of a monochromatic beam passing through water 

 decreases exponentially according to 



I = Ioe 



-a X 



where I is the initial intensity, x the depth of penetration, and a the 



absorption coefficient, a is composed additively of a part due to pair 

 production and a part due to the Compton effect; 



a 



a . + a 

 pair compt 



If a represents the cross-section of one atom for one of these processes, 

 the corresponding a is given by 



a = Na 



3 

 where N is the number of atoms per cm . The cross-sections for these 



processes are given in the book by Heitler^ and will not be reproduced 



here. The expression for a 4. is considered exact, although errors 

 •^ compt 



arise in a ■ from screening by atomic electrons and use of the Born 

 pair ^ '' 



approximation. However, these errors are negligible for the present 



purpose. Since a (and a) are independent of any molecular and atomic 



interactions in the medium, a theoretical calculation of absorption from 



these two processes will be extremely accurate. 



Table lis taken from Heitler and gives a per cm for various 

 frequencies, these being expressed in units of the rest energy of the electron. 



TABLE I. ABSORPTION OF GAMMA RAYS IN H2O 



It can be seen from Table I that the absorption decreases with 



frequency up to 



hv 



mc 



100 and then starts increasing again. The fall-off 



results from a decrease in Compton scattering with frequency, while the rise 

 results from the creation of pairs. 



