96 



RADIATION BIOLOGY 



photons. Similarly, the energy of a pair-producing photon may be shared in any 

 ratio between the electron and positron with nearly equal chance. Moreover, 

 the radiation of a high-energy photon by an electron or the pair production by a 

 photon may take place after a flight of variable length. 



Nevertheless, when a beam of high-energy electrons strikes a material, the 

 important quantity is the average number of particles which traverse each layer 

 per electron incident on the material. The order of magnitude of this number 

 may be estimated by a semiquantitative schematic discussion of the shower 

 phenomenon, disregarding statistical fluctuations. 



Assume, for the sake of the argument, that each electron or positron travels a 

 fixed distance d characteristic of each material, and then generates one photon 

 carrying half its energy. Assume also that the photon travels an equal distance 

 and then forms a pair of particles, each of which carries just half the energy of the 

 photon, etc. If there occurs one "doubling up" every path length d, a layer of 

 material located at a depth n times d is traversed by approximately 2" particles 

 or photons. The numbers of electrons, positrons, and photons tend to remain 

 equal. 



The shower multiplication stops when the energy is so subdivided that the 

 energy dissipation by electrons and positrons through inelastic collisions exceeds 

 the energy spent in producing new X rays. At this point the energy of particles 

 and photons is of the order of 10^/Z ev, according to expression (34) . 



According to this picture an electron of energy E ev gives rise to a shower which 

 develops up to a number of particles and photons of the order of EZ/ 10^. This 

 maximum number is attained at a depth of nM times the distance d, where the 

 number nu fulfills the condition 



2"^EZ/109 



(36) 



The distance d corresponds in essence to the so-called "radiation length." 

 The radiation length, in turn, equals, to within a factor of the order of 1, the 

 average distance traveled by a very-high-energy photon before producing a pair or 

 the average distance traveled by an electron or positron before radiating away 

 its energy in the form of X rays. Table 1-9 gives the values of the radiation 

 length in various materials. The results of detailed calculations or of experi- 

 ments on cascade showers are usually plotted against the depth of penetration 

 expressed in radiation lengths. For detailed results, see, for example, Janossy 

 (1948), pp. 202 ff. 



Table 1-9. Radiation Lengths in Various Materials 



These values must be divided by the density in g/cm' to obtain the length in 

 centimeters. 



Figure 1-57 shows plots of the numbers of particles against the depth 

 of penetration. The region of maximum intensity of the shower spreads 

 out over quite a thick layer of material because of the statistical fluctua- 

 tions which were disregarded in the preceding discussion. For the same 



