PHYSICAL PRINCIPLES OF CHEMICAL REACTIONS 237 



themselves ejected in ionization acts and which had widely different 

 initial energies, and in the case of X or 7 radiation virtually none of the 

 ionization is primary. An analysis of these complex chains of events is 

 yet to be given. 



Perhaps the simplest average, or "index" of this complicated mixture 

 is the "mean energy per ion pair," and although the magnitude of this 

 quantity and its approximate constancy but small variation in several 

 gases are now understood in an approximate way (Fano, 1946; cf. also 

 Chap. 1, Sect. 3-lb), no quantitative treatment for even the simplest 

 cases has as yet been attained. 



4-3. ELEMENTARY PROCESSES FOLLOWING IONIZATION 

 IN GASEOUS SYSTEMS 



4-3a. Collisions of the Second Kind: Charge Exchange. The most 

 important type of collision of the second kind which an ion may undergo 

 is one in which it captures an electron from the colliding partner. Thus 



A+ -{- B -^ A -j- B+ 



Such processes have been observed, using beams of ions passing through a 

 gas, in an impressive number of cases (the experimental data have been 

 collected by Massey and Burhop, 1952). Most of these involve atomic 

 ions, but a few studies have been made using H^ and N^ ; the recipient of 

 the charge has also usually been an atom, but some instances in which it is 

 a simple molecule have been recorded. It would, of course, be difficult 

 to produce a beam of polyatomic ions of appreciable intensity. 



Some examples of this process in which A is a multiply charged ion 

 have also been investigated. (Only a single electron is exchanged in a 

 collision.) 



Theoretical treatment of charge exchange (also called electron transfer) 

 is very difficult and can be accomplished only if A and B are both atomic. 

 The dominant feature of the theory, which is corroborated by experiment, 

 is the importance of the "resonance rule" (Sect. 3-lc) : the closer are the 

 ionization potentials of A and B, the greater is the probability of charge 

 exchange. In the case of exact resonance, for instance a beam of 5+ ions 

 passing through B gas, the cross section can be of order of magnitude 

 10~^* cm^, i.e., about ten times the geometrical cross section. ^^ If the 

 ionization potentials are much different, the cross section is very much 

 smaller. This behavior is well illustrated by the (at first sight) para- 



1* This cross section is not nearly as great as it is in the case of exact resonance in 

 energy transfer (sensitized fluorescence), for which it can reach 10"^' cm^. The differ- 

 ence between these two cases can be understood in terms of the wave-mechanical 

 result that the maximum distance through which the transfer can take place is of the 

 order of magnitude of one wave length — wave length of the electron for charge 

 exchange, wave length of the photon for energy exchange. 



