70 



likely that the Jaffe theory can give a true picture of the phenomena in a 

 region only one or two orders of magnitude larger than molecular dimen- 

 sions. 



KAMEN: Was his error in the choice of the region over which it acted? 



BOAG: Read's paper was mainly aimed at pointing out the difficulties 

 and inconsistencies of the Jaffe theory when applied to liquids. Having shown 

 that the calculated field strengths were so high, he concluded that the theory 

 was badly in need of revision. 



ONSAGER: Ions produced by charged particles, either alphas or elec- 

 trons, have three chances to recombine before they get to the walls. The 

 first possibility is that an electron recombines with its parent positive ion, a 

 process which is much more probable if the electron can attach itself to a 

 molecule first and form a negative ion. This type is known as "preferential" 

 recombination. Secondly, the passage of a fast particle leaves a string of 

 ionized atoms and molecules in its track; an electron can recombine with any 

 positive ion in the same track and it is liberated in a favorable position to do 

 so. This is known as columnar or "initial" recombination. Finally, the 

 electron may recombine with a positive ion formed in any track. This is 

 called "general" recombination. These three we have to deal with. I think 

 most of you know these concepts, but maybe the terminology is variable and 

 I am not taking any chances. 



The theory of general recombination has been known for a long time, 

 more or less. At low pressures it seems to depend on three-body collisions; 

 the binary rate constant increases with the pressure. On the other hand, at 

 very high pressures the rate constant decreases again because the ions have 

 to find each other first, and the speed of that process is inversely proportion- 

 al to the pressure (20). The optimum pressure depends on the ions and on 

 the gas. 



For the columnar recombination we have an old theory due to G. Jaffe 

 (3). It is not an exact theory , but it ought to give the right orders of mag- 

 nitude. In the absence of an external electric field, the recombination com- 

 petes with diffusion in such a manner that the total number of ions surviving 

 is inversely proportional to the logarithm of the time. An electric field helps 

 to separate the ions in such a manner that a finite proportion of the ions will 

 escape recombination forever, even from a track of infinite length, and those 

 will be collected at the electrodes if they escape general recombination on the 

 way. If we measure the current as a function of the field we can use Jaffe's 

 theory to estimate the initial distance of separation of the ions. When the 

 gas is dry air at high pressure, the electrons seem to get attached to the 

 oxygen molecules fairly soon, and the initial distance in Jaffe's theory would 

 be the distance at the time of attachment. From the fact that there is hardly 

 any columnar recombination in beta tracks in argon, hydrogen, or nitrogen, 

 we may infer that a free electron is not likely to enter into this kind of re- 

 combination. Electrons exchange their energy much less readily by collisions 

 than ions do, and this difference affects all types of recombination. 



As regards preferential recombination, I worked out a theory (21) fifteen 

 years ago for Brownian motion kinetics, which is valid at high pressures, 

 where the Langevin theory (20) applies. In the absence of an external electric 

 field, the chance that a pair of ions created at a certain distance will escape 

 from each other is simply the Boltzmann factor for the Coulomb energy. 

 Even here, a strong collection field can increase the chance of escape quite 



