Sec. 3.3] BETA PARTICLES 51 



3.2. Absorption Processes. The absorption of beta particles in matter is 

 the result of energy loss by two main processes: excitation and ionization of 

 atoms of the absorber and radiation of energy by the beta particle during 

 acceleration in close collisions with nuclei. At sufficiently high energies 

 (~ 1 mev or more) some loss occurs by nuclear excitation, but the contribu- 

 tion of this process to the stopping power of an absorber is wholly negligible 

 compared with the two processes named above. At energies less than a few 

 mev, radiative losses are also small and the principal stopping process is then 

 excitation and ionization. At very high energies, however, radiative energy- 

 loss becomes dominant. 



In principle, no clearly defined range-energy relation exists as it does for 

 heavy charged particles because of the great variation in energy loss per 

 collision, which may vary from zero to almost the total beta-particle energy, 

 and because of the more pronounced effects of scattering. In practice, 

 a maximum range can be established that is useful to dosimetry and for 

 ascertaining the maximum energy associated with beta-particle beams. 



3.3. Ionization Energy Loss. The mechanism of beta-particle energy loss 

 from ionization and excitation of the absorber atoms follows in detail the 

 corresponding processes for heavy charged particles. In brief, absorption of 

 energy takes place by repeated transfer of fractions of the beta particle's 

 kinetic energy to the orbital electrons through interaction between the field 

 of the beta particle and that of the atomic electron. The stopping formula 

 expressing the energy loss per unit length of path has been given by Bethe [2] 

 in the form 



dE __ 2Tte A NZ 

 dx m v 2 



E 3 

 log mj?(\ - P 2 )P " ^ 



where / = average excitation potential (see Alpha Particles, Chap. 4) 

 Z = atomic number 

 N — number of atoms per cc 



E — total energy of electron (kinetic plus rest mass) 

 m = electronic mass 

 e = electronic charge 

 v — velocity of electron 

 = v/c 

 The stopping formula reduces to a simple form for electrons with very high 

 energies, E ^$> m c 2 , traversing media of low density 



dE 2ve*NZ . E s 



log 



dx m„c 2 2m c i r- 



This formula is not valid, however, for electrons with high velocities travers- 

 ing dense materials since local polarization of the medium greatly alters the 



