Sec. 2.1] GAMMA RAYS 33 



and photons scattered by the Compton effect are regarded as lost since they 

 no longer contribute to the intensity of the collimated primary beam. Thus 

 since each absorption event involves the complete removal of a single photon, 

 the energy is not degraded as in the absorption of charged particles and the 

 cross sections, therefore, remain constant. Consequently the reduction in 

 energy flux, or intensity, is due wholly to the reduction in the number of 

 photons and not the energy per photon. The rate at which the beam 

 intensity or the number of photons decreases at any depth x in an absorber is 

 then directly proportional to the depth. 



dl 



Tx = -^ 



Therefore if the absorber is homogeneous the gamma-ray intensity decreases 

 exponentially with absorber thickness. 



/ = I e^ x 



where I = intensity at surface 

 y. = absorption coefficient 

 The physical significance of the absorption coefficient is apparent from the 

 fact that when x = 1/n the intensity is reduced to l/e of its value at the 

 surface of the absorber. When * is measured in units of length, p is referred 

 to as the linear-absorption coefficient and is expressed in cm"" 1 . Other 

 units also can be used and sometimes are found more useful. A form that is 

 frequently used is the mass-absorption coefficient p m expressed in square 

 centimeters per gram when x is measured in units of grams per square centi- 

 meter. This is related to the linear-absorption coefficient by p TO = p./p, where 

 p is the density of the absorbing material. This form of the coefficient has 

 the advantages of being an easy and more certain quantity to measure and is 

 independent of the physical state of the absorber. Two other forms are also 

 important in that they relate the linear and mass coefficients to values that 

 can be calculated. The first is the electronic coefficient p e which is simply the 

 cross section per electron, or p e = r e + a e + x-e- The second is the atomic- 

 absorption coefficient or atomic cross section p a , which is equal to \i e Z. The 

 relationship between the four coefficients is then 



ill = p/JL m = pXna = pNZfX e 



where N = N /A = number of atoms per gm 

 N = Avogadro's number 

 A = atomic weight 

 Z = atomic number 

 Instead of expressing gamma-ray absorption in terms of absorption coeffi- 

 cients it is sometimes more explicitly stated in units of half- value layers of 



