52 RADIATION BIOLOGY 



2irele 



2 



mv'^ 



Vmin/ 



Nt ^^^^' In ^ (15) 



Large values of the recoil energy Q correspond to knock-on collisions in 

 which the atomic electrons actually behave as free electrons. Therefore 

 the value of the maximum recoil energy Q^^^ follows from elementary con- 

 siderations on the mechanics of collisions between free particles. Low 

 values of the recoil energy Q correspond to glancing coUisions in which the 

 bond of the recoiling electron within an atom is very important. There- 

 fore the determination of the effective value of the lower limit Qmin 

 requires a more sophisticated treatment. However, any error in the 

 determination of this limit tends to have only a minor influence on the 

 final result because the logarithmic function in the formula above is a 

 slowly varying function of its variable Qmax/Qmin- 



The factor in front of the logarithm describes the principal influence of 

 the pertinent variables upon the energy dissipation by fast particles 

 traversing matter. It represents the energy absorbed by free electrons 

 in colhsions in which the recoil energy lies between two limits Qi and Q2 

 such that 



In (Q1/Q2) = 1 (16) 



This factor serves as an arbitrary standard of reference for the energy 

 dissipation. The remaining, logarithmic, factor measures the ratio of 

 the actual energy dissipation to the arbitrary standard and embodies the 

 results of the finer details of the calculation. 



In the formulas regarding the energy dissipation we shall indicate the 

 charge of the incident particle by ze, rather than by ei as in Eq. (14), 

 and its speed by v. The charge and the mass of the atomic electrons will 

 be indicated by e (instead of e?) and m, respectively, the number of elec- 

 trons per unit volume by NZ (instead of A'^) representing N atoms per 

 unit volume with Z electrons per atom. The factor In (Qmax/Qmin), which 

 represents the ratio of the actual energy dissipation to a convenient 

 standard, is often indicated by the single letter B. Using these symbols 

 we express the average energy W dissipated by a particle through inelastic 

 collision while it traverses a layer of matter of thickness t in the form 



The ratio 



W = tNZ --^ B (17) 



K = NZ?^B (18) 



t mis- 



represents the average rate of energy loss per unit distance traveled by 

 the particle and is called the "stopping power" of the material for the 

 particles under consideration. The value of B is called the "stopping 

 number" of the atomic electrons for the pertinent incident radiation. 



