Determination of Activity by the Coincident method
By: David Long 03457885
Partner: Matthew Slack
Abstract:
In this experiment, the activity of a sample of radioactive Co60 was measured
using the coincidence method. It was measured in two different independent ways to be:
A = 6.3  104  2.5  104 Bq, using the γ-γ coincidences, and A = 3.75  104  3.5  103 Bq,
using the βγ-γ coincidences. The overall efficiencies of the detectors for the different
types of radiation were also measured: εβγ1 = 2.5  104  2  105 ;
εγ1 = 2.25  104  1.5  105 ; εγ2 = 1.13  104  8  106 . These results were then used to
calculate the intrinsic efficiencies of the detectors for the various types of radiation:
εβγ1 = 3.33  102  2.7  103 ; εγ1 = 3.0  102  2  103 ; εγ2 = 1.5  102  1  103 . This
was done by taking into account the fraction of emitted particles detected by the detector
with respect to the total number of emitted particles.
Introduction:
The aim of this experiment was to measure the absolute activity of a radioactive
source using the coincident method. This involves using two detectors at the same time to
measure the rate of coincident detection of the same disintegration event in both
detectors. Effectively what happens is that a source is used that emits two γ-rays with
roughly the same energy per disintegration. These two –rays are detected by two different
Geiger counter detectors, which are connected using a circuit which can be set to count
the rate of coincident events, as well as their own individual rates. The overall activity of
N 1 N 2
the source, therefore, is: A 
, where N  1 is the counting rate of detector 1, N  2 is
2 N 1, 2
the counting rate of detector 2, and N  1, 2 is the rate of coincident events between the two
detectors. N  1 can be obtained using the formula N 1  2 A  1 , where A is the absolute
activity of the source, while   1 is the overall efficiency of the detector. Similarly for
N  2 , while N  1, 2 is obtained using the formula N 1, 2  2 A  1  2 .
In this experiment, the activity of a Co60 source was determined using the outlined
method. Due to the nature of the Co60 source, this also involved accidental coincidences.
An accidental coincidence is one that occurs when two particles from separate decay
events trigger the separate detectors within the response time of the detector, τ. If this
occurs, an accidental coincidence is registered. In this experiment, the response time of
the detectors was measured, and used to calculate the contribution to the overall detection
of accidental coincidences, N 1, 2,a . This was done using a Cs source, as outlined below,
along with the equation: N 1, 2,a  2 N 1 N 2 . This was possible as due to the fact that Cs
is a single γ-ray emitter, any coincidences measured will be the result of accidental
coincidences.
There were 5 parts to this experiment. In this write-up, these parts will be
separated only within the overall headings, as each part was too small to be treated
separately.
Experimental Details:
The apparatus involved in this experiment consisted of 2 Geiger Counters set-up
facing each other, one with an aluminium cap, the other without. Between the counters
was a small platform where the radioactive sources and aluminium shields could be
placed. Both Geiger counters were connected to a coincidence unit containing two pulse
shapers and a coincidence circuit, the output of which was connected to a scalar. The
coincidence unit had a selection dial which could be set to take readings from counter1,
counter 2 or coincidence events from both counters.
In the first part of the experiment, a Cs source was used to measure the response
time, τ, of the detectors. This was done by placing it between the two Geiger Counters,
and setting the coincidence unit to measure coincidence events only. In this case, as the
Cs source only emits 1 γ-ray, the coincidence rate may be taken as the accidental
coincidence rate. The response time was then calculated using the methods outlined
below.
The second part of the experiment involved measuring the count-rate on the βdetector with thickness of Aluminium plates. This is necessary for measuring the γ-γ
coincidences in the next part of the experiment. Plates of Aluminium of varying thickness
were placed in front of the Co60 source, and the count rate on the β-detector was
measured. These measurements were then graphed and used to determine the β-particle
range, and compare with the expected range of β-particles emitted by Co60.
The third part of the experiment involved placing an Aluminium sheet of the
required thickness in front of detector 1. This allowed the γ-γ coincidences of the Co60
source to be measured. From this, using the formulae and methods outlined below, the
activity A of the source was determined.
In the fourth part of the experiment, the Aluminium sheet was removed, and the
βγ-γ coincidences were measured for the Co60 source. This allowed a second independent
determination of the Activity A of the source.
Finally, the gathered data was used to determine the overall β-, and γ-efficiency of
detector 1, along with the overall γ-efficiency of detector 2. The intrinsic efficiency of
both detectors was also measured. This was done by measuring the solid angle subtended
by the detector aperture at the source, assuming that the source is a point source. This is
compared to the total solid angle, giving the fraction of emitted particles that enter the
detector. The actual efficiency of the detector is equal to the intrinsic efficiency
multiplied by the fraction of emitted particles entering the detector.
Results and analysis:
(i):
Using the Cs source from the Gamma ray spectroscopy experiment, the
coincidence resolving time of the equipment used was measured. This was done by
setting the equipment to measure coincident events over a period of 4000s. This then
gave a result of: Nγ1,γ2,a = 0.0005 ± 0.00025 s-1. Using the formula given in the
experimental handout; Nγ1,γ2,a = 2τNγ1Nγ2, the coincidence resolving time τ was measured
to be: τ = 1.65  106  5  108 s. This was then used to calculate the accidental
coincidence rate for the measurements made in (iii) and (iv).
(ii):
For the second part of the experiment, sheets of Al metal were placed between the
Co60 source and detector 1. The count rate vs. the thickness of the Al sheets was then
measured and graphed, as outlined here:
Count Count Error Count (max) Count (min) Time Rate (max) Rate (min) Rate
Rate Error Density
1677
40.95
1717.95
1636.04 300
5.72
5.45
5.59
0.13
0.27
1519
38.97
1557.97
1480.02 300
5.19
4.93 5.0633
0.1299
0.54
1447
38.03
1485.03
1408.96 300
4.95
4.69 4.8233
0.1267
1.01
1354
36.79
1390.79
1317.20 300
4.63
4.39 4.5133
0.1226
1.67
1308
36.16
1344.16
1271.83 300
4.48
4.23
4.36
0.12
3.15
1272
35.66
1307.66
1236.33 300
4.35
4.12
4.24
0.11
5.28
1223
34.97
1257.97
1188.02 300
4.19
3.96 4.0767
0.1165
7.99
This resulted in the graph:
Figure 1
5.8
5.6
Count Rate (counts-1)
5.4
5.2
5
4.8
4.6
4.4
4.2
4
0
1
2
3
4
5
-3
Density (kgm )
(iii):
Sheet used: 1.678 kgm-3
7 counts in 4000s. Therefore count => 7 ± 2.6 counts
6
7
8
9
9.6
4.4
 0.0024;
 0.0011
4000
4000
0.0024  0.0011
 0.0018  0.0006countss 1 = Count Rate for γ-γ coincidences.
2
However, the accidental coincidences must be subtracted from this to give the actual
count rate. This is done by using the equation: Nγ1,γ2,a = 2τNγ1Nγ2, where τ was found as
shown above. This gives Nγ1,γ2,a = 4.6  104  3  105 s-1. From this the actual count rate
is: Nγ1,γ2 = 1.34  103  5.7  104 s-1.
N 1, 2 
Then, using the actual count rate measured above, the activity of the sample can be
N N
measured using the formula given in the experiment sheet: A   1  2 . This then gave
2 N 1, 2
the result: A = 6.3  104  2.5  104 Bq.
(iv):
20 counts in 4000s. Therefore count => 20 ± 4.5 counts
24.5
15.5
 0.006;
 0.004
4000
4000
0.006  0.004
 0.005  0.001countss 1 =Count Rate for βγ-γ coincidences.
2
Again, the accidental coincidence rate must be subtracted from this to give the actual
count rate. Nβγ1,γ2,a was found using the equation: Nβγ1,γ2,a = 2τNβγ1Nγ2. This gave
Nβγ1,γ2,a = 2.05  104  1.5  105 s-1.
N  1, 2 
Again the activity for the sample was found using the formula given in the experiment
( N  0.5 N 1 ) N 2
handout: A   1
. Nβγ1 was found by measuring the count rate of the Co60
N  1, 2
sample for detector 1, measuring both γ-rays and β-radiation. This was found to be:
Nβγ1 = 0.0018 ± 0.0006 counts s-1. Using all this data, the activity of the sample using this
method of measurement was found to be: A = 3.75  104  3.5  103 Bq.
(v): Using the existing data, and the formulae;
( N  N 1 )
  1   1
;
A
N
 1   1
2A
N
 2   2
2A
the efficiencies of the detectors were measured. The efficiency of detector 1 for βradiation, and γ-radiation was calculated, along with the γ-efficiency of detector 2. The
results were: εβγ1 = 2.5  104  2  105 ; εγ1 = 2.25  104  1.5  105 ;
εγ2 = 1.13  104  8  106 .
Using the above results, the intrinsic efficiency of each detector for the various types of
radiation was measured. This was done by calculating the solid angle subtended by the
detector aperture at the source, and comparing it to the total solid angle. This gave the
fraction of emitted particles entering the detector. The actual efficiency of a detector is
equal to the intrinsic efficiency of the detector multiplied by the fraction of emitted
particles entering the detector. The solid angle was found to be: θ = 0.094 steradians.
0.094
 0.0075 .
Therefore the fraction of emitted particles entering the detector is:
4
This therefore gave an intrinsic efficiency of: εβγ1 = 3.33  102  2.7  103 ;
εγ1 = 3.0  102  2  103 ; εγ2 = 1.5  102  1  103 .
Conclusion:
The aim of this experiment was to measure the absolute activity of a radioactive
source using the coincident method. This was done using a Co60 source, and was
measured for βγ-γ coincidences; (A = 3.75  104  3.5  103 Bq), and also for the γ-γ
coincidences; (A = 6.3  104  2.5  104 Bq). The efficiencies of the detectors were also
measured; both actual and intrinsic, along with the density of Aluminium needed to block
β-radiation. This experiment showed that the coincidence method is a very effective way
of measuring the activity of a sample, but that it is liable to be susceptible to errors.