Sec. 10.17] GEIGER-MULLER COUNTERS 323 



horizontal sweep is triggered by incoming pulses which are then traced at a 

 fixed position on the screen and allow more careful measurement. This 

 provides a better opportunity to observe closely spaced pulses and hence to 

 verify the resolving time. 



10.17. Coincidence Corrections for High Counting Rates. Pulse-counting 

 devices such as counter tubes, ionization chambers, and electrical circuits 

 are never linear in their recording rate when the events registered occur in 

 random intervals. As the average counting rate increases, a greater propor- 

 tion of the events producing the counts occurs in intervals shorter than the 

 resolving time of the device, and therefore pairs and triplets of events are 

 more often registered as a single count. This increase in coincidence rate of 

 multiple events causes the response of a counter to deviate markedly from a 

 linear relation to source activity. Unless a coincidence correction is made, 

 the observed counting rates at high levels (> 10,000 cpm) have little signifi- 

 cance and even at levels greater than 1 ,000 cpm may be in serious error. The 

 coincidence correction therefore must determine from the observed counting 

 rate the true rate of events or that rate which would be observed if the 

 resolving time were zero. 



It is apparent that the true counting rate should be a function of the 

 resolving time and the registered rate, but it also depends on the mechanism 

 of recovery since two distinct alternatives present themselves. The first 

 mechanism leads to a correction formula [35] in the form 



N = n + thN cpm 



where N = true counting rate 



it = recorded counting rate 



r = counter resolving time 

 At low counting rates where N ~ n, the more convenient approximation 



N = n + rn 2 cpm 



can be used. This formula and the preceding one are derived on the assump- 

 tion that the insensitive time is more or less independent of events that occur 

 immediately before or after a count is recorded and, in particular, the occur- 

 rence of an unrecorded event during recovery of the device does not extend 

 the insensitive interval. Although this is not strictly true for counters, 

 the influence of this factor is small and the formulas above are the most 

 nearly valid in this case. It is seen from the formula that as the true activity 

 increases to very high levels the recorded counting rate approaches asymp- 

 totically the limiting value 1/r as N — » <=o ; counts are recorded only as fast 

 as the tube can recover. 



The second correction formula applies less to counters but represents 

 more accurately the counting loss in electronic and mechanical devices. It 



