Physics and Engineering of Radiation Detection

3.6. Geiger-Mueller Counters 195

Example:

A GM detector having an efficiency of 67% is placed in a radiation field. On

the average, it reads a count rate of 1. 53 × 104 per second. Find the true rate

of incident radiation and the dead time of the detector.

Solution:

The rate of incident radiation is the true count rate of equation 3.6.5. Hence

we have

Nt =

Nc

η

=

1. 53 × 104

0. 67

=2. 83 × 104 s−^1.

For the dead time we use equation 3.6.6 as follows.

η =1−τNc

⇒τ =

1 −η

Nc

=

1 − 0. 67

1. 53 × 104

=2. 15 × 10 −^5 s =21. 5 μs

Dead time for GM tubes is generally determined experimentally in laboratories
by using the so called two-source method. This involves recording the count rates
from two sources independently and then combined.
According to equation 3.6.5, the true count ratesNt, 1 ,Nt, 2 ,andNt, 12 of the two
sources independently and combined are given by

Nt, 1 =

Nc, 1

1 −τNc, 1

Nt, 2 =

Nc, 2

1 −τNc, 2

Nt, 12 =

Nc, 12

1 −τNc, 12

WhereNc,xwithx=1, 2 ,12 represent the recorded count rates in the three respec-
tive configurations. Now, since the atoms in the two sources decay independent of
each other therefore their true rates should add up, that is

Nt, 12 =Nt, 1 +Nt, 2. (3.6.7)

Substituting the true count rate expressions in this equations gives

Nc, 12

1 −τNc, 12

=

Nc, 1

1 −τNc, 1

+

Nc, 2

1 −τNc, 2

⇒τ ≈

Nc, 1 +Nc, 2 −Nc, 12

2 Nc, 1 Nc, 2

. (3.6.8)