Range of Electrons and Positrons

Electrons and positrons behave in essentially the same way with regard to energy loss, slowing down, and penetration through matter. Small differences exist one was indicated when dE/dx was discussed in Sec. 4.3. Small differences in the values of the range between electrons and positrons should also be expected, and indeed this is the case. Most of the range measurements have been performed with electrons because electrons are used much more frequently than positrons in radiation measurements. For this reason, from this point on, only electrons will be discussed. The reader should be aware that the results are equally applicable for positrons, to a first approximation, but for very accurate results the references listed at the end of this chapter should be consulted. 

If the experiment shown in Fig. 4.5 and discussed in Sec. 4.6.1 is repeated with the incident beam consisting of monoenergetic electrons, the result will look as shown in Fig. 4.8. For electrons, the transmission curve does not have a flat part. It decreases gradually to a level which is the background. The range is equal to the thickness of the material, which is defined by the point where the linear extrapolation of the transmission curve meets the background. 

The semiempirical equation giving the range of electrons for the energy range 0.3 keV to 30 MeV has been developed by Tabata, Ito, and Okabe, based on the experimental results available until 1972. This equation, indicated from now on as the TIO equation, has the following form  

In the case of absorbers that are mixtures or compounds, the atomic number Z and atomic weight A to be used in Eq. 4.22 are given by 

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