PRINCIPLES OF RADIOLOGICAL PHYSICS 99 



30 per cent below the corresponding probability for electrons (Seliger, 

 1950). 



4-2e. Penetration of Thin Foils. It is sometimes of interest to consider how 

 the passage through a thin layer of material modifies the characteristics of a beam 

 of electrons. Consider, for example, a beam of cathode rays which has been 

 accelerated to a definite energy inside an evacuated vessel and then emerges 

 from the vessel through a thin window which absorbs only a small fraction of the 

 beam energy. Most of the electrons emerge with nearly equal energies and 

 traveling approximately in the initial direction. 



The average energy loss depends on the foil thickness and on the stopping 

 power of the material and can be evaluated as indicated in Sect. 4-1. The 

 departures from the average energy loss may be subdivided into two classes. 

 Small departures, similar to the straggling of heavy charged particles (see Sect. 

 4-la), are the rule. Unusually large energy losses may arise either from an 

 occasional knock-on collision in which an atomic electron acquires a rather large 

 amount of energy or from the emission of an X-ray photon. As we know, X-ray 

 emission is quite unlikely for lower energy electrons and in light materials, but it 

 becomes increasingly frequent as the electron energy and the atomic number of 

 the material increase. 



In conclusion, it may be said that large-energy straggling constitutes an occa- 

 sional anomaly under most conditions but becomes the rule in the conditions 

 which lead to the formation of cascade showers. The accumulation of the effects 

 of small deflections proceeds for electrons in the same way as for heavy charged 

 particles (see Sect. 4-lb) . The mean square angle of deflection increases as a func- 

 tion of the thickness of the foil according to Eq. (30). Occasional sharp deflec- 

 tions are noticeable. Their probability follows, in the main, the law of Ruther- 

 ford scattering, Eq. (13), Sect. 2-2c. 



4-2f. Penetration of Thick Foils. The fraction of incident electrons that passes 

 through comparatively thick foils is frequently the object of experiments directed 

 to evaluate the energy of the beam. Aluminum foils are mostly employed in 

 these experiments, but foils of other light materials give comparable results. 



The number of electrons which penetrate, to increasing depths, a material 

 remains fairly constant during the early stages of penetration, i.e., until the effect 

 of progressive scattering becomes important. This stage lasts longer in light than 

 in heavy materials and is followed by a rapid decrease of the number of electrons 

 attaining greater and greater penetrations. Therefore the curves of Fig. 1-60 



CD 



2 



go 



»i 



1 FOIL THICKNESS 



EXTRAPOLATED 

 RANGE 



Fig. 1-60. Diagram indicating progressive reduction of the fraction of incident 

 electrons which are transmitted through foils of increasing thickness. 



