342 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS Chap. 11 



The operating voltage for a proportional counter is determined largely 

 by the size pulse required for the particular radiation to be measured. Before 

 the counter can be used, however, it is necessary to determine the proportional 

 region by plotting the counting rate against anode voltage. As shown in Fig. 

 77, the region for proportional pulse size lies between the starting voltage 

 at which the first counts are detected and the beginning of the transition to 

 the Geiger-Miiller region. 



11.2. Theory of Operation. When certain simplifying assumptions are 

 made which appear to be valid for most proportional counters, the formation 

 of a voltage pulse proportional to the initial number of ion pairs is adequately 

 explained in terms of a Townsend avalanche [3,4,5]. It is assumed that 

 (1) the probability of electron photoemission is negligibly small; (2) the 

 probability for secondary electron emission by positive ions collected at the 

 cathode is negligibly small; (3) negative ions such as O - , F~, and Cl~ are not 

 sufficiently numerous to produce an appreciable lag in the counter action; 

 (4) recombination of positive ions and electrons within the gas is negligible. 

 From the N initial ion pairs produced by an incident charged particle, the 

 electrons are collected at the anode in a time of the order of a few micro- 

 seconds while the positive ions formed remain essentially stationary during 

 this time. Within a distance of several mean free paths from the anode, 

 electrons acquire sufficient energy between collisions in the strong electric 

 field to produce additional ion pairs and hence a Townsend avalanche. The 

 avalanche at this point differs from the Geiger-Miiller counter discharge in 

 that the descendants of a single electron multiply to a smaller and, on the 

 average, constant number which is a function of the operating voltage. The 

 factor by which an electron multiplies itself in the avalanche, called the 

 amplification A , may have a value up to a maximum of 10 4 , although generally 

 it is of the order of 10 3 or less. Within the range from 1 to 10 4 , its value can 

 be chosen arbitrarily by the proper choice of operating voltage, a factor 

 that permits some control over the pulse size which may be desired. When 

 the amplification factor increases beyond 10 3 or 10 4 owing to a high operating 

 voltage, the pulse size is no longer strictly proportional and some of the 

 characteristics associated with the Geiger-Miiller discharge make their 

 appearance. Following the completion of the Townsend avalanche the 

 residual positive ion cloud drifts slowly to the cathode. However, during 

 the dead time of roughly 10 -4 sec, it still exists as a space charge sufficiently 

 near the anode to reduce the effective electric field and thus prevent a second 

 avalanche which might be initiated by a charged particle arriving within this 

 time. 



The total charge collected by the anode is approximately Q = eAN, 

 where e is the electronic charge. With a total capacitance of C for the 



