Physics and Engineering of Radiation Detection

196 Chapter 3. Gas Filled Detectors

Note that, in order to determine the dead time using this method, one does not
require the knowledge of the true count rates of either of the two sources. Hence
any source with arbitrary strength can be chosen for the purpose. However one must
make certain that the decay rate is neither very low nor very high to ensure that
the efficiency of the detector does not fall too low.

Example:

In an attempt to find the dead time of a GM counter, three measurements

are taken. The first two with separate radiation sources give average count

rates of 124s−^1 and 78s−^1. With both the sources in front of the detector,

the count rate is found to be 197s−^1. Estimate the dead time of the counter.

Solution:

We can use equation 3.6.8 to estimate the dead time as follows.

τ ≈

Nc, 1 +Nc, 2 −Nc, 12

2 Nc, 1 Nc, 2

=

124 + 78− 197

2(124)(78)

=2. 6 × 10 −^4 s.

3.6.C ChoiceofGas...........................

As with proportional counters, the basic design criteria for the GM counters is
that the filling gas should have low avalanche multiplication threshold. All inert
gases fulfill this requirement and therefore can be used in GM counters. There is,
however, an additional condition for the detector to operate in GM region, that is,
it should allow the process of avalanche multiplication to cause breakdown in the
gas. We discussed the process of breakdown earlier and noted that the condition for
breakdown is governed by the so called Paschen’s law, equation 3.3.12

Vbreak=

BPd

ln [AP d/ln (1 + 1/γ)]

,

whereAandBare experimentally determined constants,Pis the gas pressure and
dis the separation of electrodes. Using this equation we arrived at the expression
for the value ofPdat which the minimumVbreakwas possible.

(Pd)min=

e

A

ln

[

1+

1

γ

]

This is a very useful relation as it can be used to determine the threshold value
of the product of gas pressure and electrode gap for Geiger breakdown. Generally
the physical dimensions of the detector are fixed by the engineering considerations.
This means that the type of gas and its appropriate pressure can then be determined
from the above relation.
Apart from the above condition, another thing to note is that sometimes due to
safety considerations it is desired that the operating voltage is kept as low as possible.