Sec. 4.6] 



PROTONS, DEUTERONS, AND ALPHA PARTICLES 



85 



Recently a more general treatment of stopping for charged particles with 

 very high energies was formulated by Halpern and Hall [26]. Their theory, 

 based on a multiple-dispersion-frequency model in which the effects of oscilla- 

 tion damping and conduction electrons are also considered, is a generaliza- 

 tion of Fermi's development. The correction in energy loss when these 

 additional factors are taken into account is found to be somewhat less than in 

 the Fermi theory, but the absolute increase in the rate of energy loss is not so 

 fast as log E required by the simple stopping formulas. 



4.5. Relative Stopping Power. Calculations of the stopping power of 

 various substances relative to air are complicated by the dependence on the 

 velocity of the particle as well as on the atomic number and average excitation 

 potential of the absorber. Approximately, the ratio is given by 



N'Z' log (2mv 2 /r) 

 NZ log (2mv 2 /Ie 



where the primed letters refer to the substance and the unprimed to air. 

 Measurements of relative stopping powers of absorbers for alpha particles 

 relative to air are given in Table 10 for two energies and in Fig. 17 for various 

 energies. For heavy charged particles with energies greater than 1 mev the 

 relative stopping power changes very slowly, while above 10 mev it remains 

 essentially constant. 



Table 10. Atomic Stopping Power for Alpha Particles Relative to Air at Normal 



Temperature and Pressure 



m 



4.6. Atomic Stopping Power. The atomic stopping power a, frequently 

 termed stopping cross section, is defined as the energy loss per centimeter 



