Sec. 4.2] 



PROTONS, DEUTERONS, AND ALPHA PARTICLES 



79 



I = 11.5 Z ev. The values for 7 for various substances determined empiri- 

 cally by Mano [12] and those calculated from the Bloch- Wilson formula are 

 listed in Table 9. More recently Halpern and Hall [26] have introduced an 

 analytical expression for I derived from a theory of ionization loss based on a 

 multiple-dispersion-frequency model of the atom or molecule. In the energy 

 range where the stopping formula above is accurate, the dispersion-frequency 

 model gives the average excitation potential as the geometric mean of the 

 dispersion frequencies Vi in the form 



n 

 log V m = \ fi log Vi 



i = 



where /, is the fraction of electrons with a dispersion frequency vi and the 

 sum is taken over all dispersion frequencies in the atom or molecule. The 

 values of vi must be obtained from spectroscopic data and are expressed in 

 units of (N e e 2 firm)^ where N e is the number of electrons per unit volume. 

 The excitation potentials calculated by this method compare well with the 

 values given in Table 9 only for light atoms; for heavy atoms they are as 

 much as 20 per cent greater than the values given by Mano. 



Table 9. Average Excitation Potentials 



It is seen from the stopping formula that the rate of energy loss for particles 

 of different mass but with the same velocity is proportional to the square of 

 the particle's charge. Protons and deuterons consequently lose energy at 

 one-fourth the rate of alpha particles that have the same velocity. This 

 property of the stopping formula provides a convenient means for computing 



