PRINCIPLES OF RADIOLOGICAL PHYSICS 



R = 1.25 X 10-' ^T^ 

 pZ 



cm 



93 



(32) 



Here A and Z indicate the atomic weight and the atomic number of the 

 material, p the density of the material in g/cm^ and T the electron energy 

 in thousand electron volts. This formula appears to hold satisfactorily 

 from about 10 to 200 kev in materials of low atomic weight. In "heavy" 

 materials the formula is less satisfactory in the lower portion of this range 

 since B varies more rapidly. 



Actually, throughout its range of validity, this formula nowhere repre- 

 sents the depth of penetration to be expected in a material, since it gives 

 the length of the path which is far from straight. What matters is how 

 much energy a beam of electrons dissipates in successive layers of a mate- 

 rial. Some data on this question are available (Trump et al., 1940, 1950). 

 A qualitative picture emerges, for electrons of low or moderate energies, 

 from the following very crude considerations. 



Since most electrons lose the "memory" of their initial direction before 

 they are completely slowed down, the initial penetration of a beam has 

 the main effect of "injecting" the electrons at some depth within the 

 material. Thereafter the electrons essentially diffuse away from the zone 

 of injection in random directions. This zone of injection lies in light 

 materials at a depth of a few times smaller than the true range of the elec- 

 trons and in heavy materials at a depth twenty to fifty times smaller than 

 the true range. 



The concentration of electrons is highest in the zone of injection. Con- 

 sequently a maximum of energy is dissipated in this zone rather than right 

 at the surface through which the beam enters the material. Furthermore 

 the deep-lying layers of the material 

 are traversed by electrons of lower 

 average energy which dissipate their 

 energy at a higher rate. This effect 

 shifts the point of maximum energy 

 dissipation toward greater depth. 

 (The same effect is much stronger in 

 the case of heavy particles and gives 

 rise to the maximum of the Bragg 

 curve of Fig. 1-52). Figure 1-56 gives 

 approximate data on the energy dis- 

 sipation at various depths in a heavy 



150 



< :t: 

 a. c 



— 3 



CD >% 



— i_ 



Q o 



i_ 



>^ 

 O -^ 



UJ 



100 



and a light material. 



50 100 150 200 

 DEPTH, mg/cm2 



Fig. 1-56. Diagram of energy dissi- 

 pation by an electron beam at 

 various depths of penetration within 

 a material. {Courtesy of J . Fleeman 

 and F. Frantz.) 



The shape of the curves in Fig. 1-56 depends primarily on the atomic number 

 of the material but rather little on the energy T of the incident electrons as long 

 as this energy remains well below 1 Mev. As the energy increases, other con- 

 ditions being equal, the depth of penetration increases, and therefore the scale 



