72 THE PHYSICS OF VIRUSES 



of experiment and theory. Two basic relations are derived. The 

 first concerns the number, d7i, of ionizing processes (primary 

 ionizations) of energy between Wi and W2, and is 



mi- [III 11 2 J 



where z is the niim})er of elementary charges on the flying 

 particle, e is the electronic charge, A^ is the number of atoms 

 traversed per unit length, Z is the number of electrons per atom, 

 dx is the distance traveled, m is the mass of the electron, and 

 V is the velocity of the flying particle. 



If we consider energy-loss values between W and W + dW, 

 then the above formula becomes 



9,Trz'^e^ dW 



dhl - ^ NZ -ry., dx (3.2) 



mv' II ^ 



where, now, d^^n is the number of primary ionizations of energy 

 between IF and W + dW in the length of path dx. 



The rate of loss of energy is also important. In principle, it is 

 given by the integral of Eq. 3.2 over all possible values of TT^. 

 This is complicated by the fact that a somewhat different rela- 

 tion holds for excitaiions, which have discrete energies, and by the 

 fact that both an upper and a lower limit to the possible values of 

 W exist. The upper limit is set by the fact that energy transfers 

 in excess of the conservation of momentum may not take place, 

 and the lower limit by the fact that the first excited state of the 

 atom must be reached. When these are duly processed, the 

 result obtained (for heavy particles, not electrons) is, to a first 

 approximation, 



dE ^Tve'NZ , f2wf2 



dx mr- \ 1 ] 



where —dE/dx is the rate of energy loss with distance, and I is 

 an equivalent excitation potential which must be found by 

 experiment. 



