194 Chapter 3. Gas Filled Detectors
3.6.B DeadTime
The physical process of a Geiger breakdown takes some time to subside in a GM
counter. The output pulse therefore is not only large but also fairly long. The
problem is that from the initiation of the breakdown until it has died and the pulse
has been recorded, the counter remains dead for the subsequent ionization events.
The time is called the dead time of the GM counter. Since it is not possible to
eliminate the dead time therefore one must make corrections in the recorded count
rate to account for the missed events. IfNcandNtare the recorded and true count
rates then, for a GM counter, they are related by
Nc=ηNt, (3.6.1)whereηcan be thought to represent theeffiiencyof the counter. The efficiency
depends on many factors, for example the dead time due to the discharge process,
the dead time due to electronics, and efficiency to discriminate the good events
from noise etc. Let us now see if we can derive a simple relation for the efficiency
using intuitive arguments. Suppose there is an average dead timeτduring which the
detector becomes unable to record any new ionizing event. We can assume this since
under constant operating conditions the time it will take the avalanche to spread
throughout the detector, cause breakdown, and then subside should not vary from
pulse to pulse. Now, ifCis the total number of counts recorded by the detector in
atimet, then the recorded count rate will be
Nc=C
t. (3.6.2)
Sinceτis the dead time of the detector therefore the rateNlostat which the true
events arenotrecorded is given by
Nlost=τNcNt, (3.6.3)whereNtis the true count rate or the rate at which the detector will record pulses
if it had no dead time. It is simply the sum of the recorded count rate and the lost
count rate.
Nt=Nc+Nlost (3.6.4)
Using the above two equations we can write
Nt = Nc+τNcNt⇒Nt =Nc
1 −τNc. (3.6.5)
Hence the efficiency of a GM tube can be written as
η=1−τNc. (3.6.6)Typical GM tubes have a dead time of the order of 100μs.Itisobviousfromthe
above relation that such a detector will have an efficiency of 50% if operated in a
radiation field of 10kHz. In other words, on the average, it will detect one particle
out of two incident particles.