PRINCIPLES OF RADIOLOGICAL PHYSICS 55 



Notice that the main factor ^-kzH" I mv- depends only on the charge and the 

 velocity and not on the mass of the incident particle. 



Modifications to the theory are required when the velocity of the incident 

 particle approaches the speed of light (see Sect. 2-2d), but they are not too impor- 

 tant. The necessary corrections are usually incorporated in the value of the 

 stopping number B. 



Data are also still inadequate concerning the effect upon the stopping power of 

 the presence of atoms located between the path of the incident particle and the 

 atoms which actually absorb energy. The presence of such atoms tends to 

 reduce the probability of energy absorption in proportion to the density of the 

 material, but only when the velocity of the incident particle approaches the speed 

 of light, and thus to flatten the curve of B vs. energy (see Fig. l-36a and b). 



2-4c. Prohahility of Inelastic Collisions. The energy dissipation by a 

 particle as it traverses matter results from the product of the number of 

 inelastic collisions and of the average energy dissipated per collision. 

 Since we have already given formulas for the energy dissipation, we may 

 express the number of collisions as the ratio of the total energy dissipa- 

 tion to the average energy loss per collision. 



This detour proves convenient because the average energy E dissipated 

 in a collision depends only on the relative probability of different out- 

 comes of the collision. This probability, in turn, depends primarily on 

 the characteristic reaction of atomic electrons to a sudden blow and only 

 a little on the nature and speed of the incident particle. Therefore E is 

 approximately constant for each kind of atom or molecule, and the varia- 

 tions of the expected number of collisions, 9fl, parallel the variations of the 

 energy dissipation W. We write 



91 = W/E (20) 



The mean energy transfer has different values £"1,^2, • • . , ^z for the different 

 atomic electrons 1, 2, . . . , Z. We may also consider separately the energies 

 Wi, W2, . . . , Wz dissipated to the different electrons in a whole series of col- 

 lisions and the corresponding numbers 91,, 9I2, . . • , 9lz of collisions which affect 

 the different electrons. For example, 



3l, = 5:. = iV,2«VB. (21) 



El mv^ El 



The mean energies ^1, ^2, . • • are of the same order of magnitude as the binding 

 energies of the corresponding electrons and decrease very slowly as the energy of 

 the incident particle increases. 



The expected number of collisions 9li may be further subdivided according to 

 the relative frequency with which the electron 91 1 is excited to the stationary 

 state a,b,c, . . . as a result of the collision. We indicate the relative frequency 

 as gia, gib, Qic, . . . , so that, for example, 



9l,a = 9li^ia = m ^^ ^ gia (22) 



