230 



THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



the two retains very nearly the constant value 3 throughout the table. 

 The fact that the ratio is substantially larger than unity is explained 

 by. the resonance feature of the ion-atom scattering process as discussed 

 in Section lA. The fact that it is constant is perhaps an indication of 

 the fact that both processes are governed by overlap conditions of 

 essentially the same wave functions. 



I would like to point out in connection with the calculations of this 

 section that the method developed is potentially of very wide applica- 

 tion. One question that comes up, for instance, is whether a careful 

 kinetics calculation is necessarily restricted to certain models or whether 

 an ion-atom cross section known numerically could be used to derive 

 therefrom kinetic properties. This is indeed possible. Suppose, for 

 instance, that the cross section (t{c) were available as a function of c for 

 collision of He "'"-ions and He-atoms and suppose that this cross section 

 were to satisfy the condition of isotropy 11 (x) = 1 to a good approxi- 



Table III 

 Cross sections for ion-atom and atom-atom collisions for the noble gases. 



mation; we may then derive for this eventuality conditions on ho(c) 

 which are more general, respectively, than (79) or (87), (80) or (88), (81) 

 or (89). Since we are outrunning here the experimental evidence we shall 

 limit ourselves to the derivation of the first of these relations. The first 

 truncated relation is exactly (50a) which, for isotropy and equal masses, 

 reads 



/ c.\_ 

 \aT{c)/ 



= 2 



(101) 



The reduction of this formula to a condition on /io(c) requires the rela- 

 tionship 1/ == of the set (46). This relation is always integrable to 

 yield hi{c) in terms of /io(c), as was pointed out early in this section. 

 For the special circumstances assumed the integrated equation 

 equation (74) 



IS 



h{c) = 3 I 



ar(7) 



dy 



(102) 



