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In this experiment, the field of timing measurement was introduced and the strength of the gamma source
was measured using the gamma-gamma coincidence technique, which is an application of timing
measurement and is based on measuring two events occurring in short intervals of time. For this purpose,
crossover timing based electronic equipment was used. The resolving time of the coincidence circuit was
calculated using pulser as well as detectors and Co 60
source. The delay time between the pulses was set
for maximum coincidence and chance coincidence count rate and then strength of the gamma source was
calculated after taking all required count rates including coincidence and background count rates.
Finally, the actual source strength was also calculated analytically.
In many applications, information on the precise arrival time of a radiation in the detector is the prime
interest. When this is the case, the detector pulses are handled quite differently than when accurate pulse
height measurement is the objective. What is done is that a logical pulse is produced at some suitable pint
of the linear pulse which than indicates the arrival time of the radiation in the detector. The selection of
the point at which this logic pulse is produced is dependent on the dynamic range of the signal pulses and
the specific detector being used.
There are different methods used for the generation of the logic pulses from the linear pulses. These are:
1. Leading edge triggering
2. Crossover timing
3. Constant fraction timing
4. Amplitude and rise time compensated (ARC) timing
5. Extrapolated leading edge timing (ELET)
6. First photoelectric timing (FPET)
All these techniques have different applications and their own advantages and disadvantages. The type of
technique must be selected for a specific application after due consideration of the type of detector
In this experiment the purpose was to introduce the field of timing measurement and the strength of Co 60
source was to be determined. This experiment made use of crossover timing which is although not the
ideal choice but it illustrates some of the problems associated with timing measurements.
The strength of a radioactive source can be measured by different techniques. One of these is time
coincidence method. This method is based on measuring two events occurring in short intervals of time.
Apart from being used for determining the unknown source strength, the time coincidence has manifold
applications like determination of decay schemes, angular correlation of radiations and measurement of
short half-life etc.
Many nuclear processes, such as the decay of an excited state by gamma emission after an alpha or a beta
decay occur in very short time, so that the sequence of events is essentially simultaneous. Similarly a
nucleus may emit gamma rays in cascade. These gamma rays are effectively at the same time because the
time lag between their emissions is very short, perhaps as small as 10 -15
The determination that two nuclear events occur at same time is made electronically with a coincidence
circuit. A coincidence circuit, in general is one in which an output is produced only when suitable input
signals appear in a preset time (τ) at each of the several inputs. The condition for time coincidence
requires that the time lag between the arrivals of the input pulses be less than τ, the resolving time of the
In case of a Co 60
source the time difference between the emission of two gamma rays or between beta and
any gamma ray is less than 10 -12
seconds, which is much less than the resolving time of a slow
If the pulses produced by the two gamma rays emitted from the same Co 60
nucleus reach the coincidence
unit during the resolving time an output pulse is registered and true coincidence is then said to have
occurred. Apart from such true coincidence there will be random or chance coincidence due to the pulses
which are accidentally in coincidence. The effect of such chance coincidence is to be omitted since the
source strength is obtained from the knowledge of true coincidence only. The rate at which chance,
random or accidental coincidence occur is given by:
NCC = 2 τ N10 N20
NCC = rate of chance coincidence and
N10 N20 = counting rates obtained from detector No.1 and 2 respectively.
τ = resolving time of the coincidence circuit.
Let S (disintegrations / sec) be the source strength of Co 60
source. The number of gamma rays emitted per
second is then 2S because two gamma rays are emitted in each decay. If η1 and η2 are detection
efficiencies of detectors 1 and 2 respectively, then count rates on detectors 1 and 2 will be:
N1 = 2Sη1
N2 = 2Sη2
NC = 2Sη1η2
Where NC = coincidence count rate. If all the counts along with the background counts from the two
detectors are taken then:
N1 = N10 – N1B
N2 = N20 – N2B
NC = NC0 - NCC
Thus we can write:
N1N2 / NC = (2Sη1) (2Sη2) / (2Sη1η2)
S = N1N2 / 2NC (disintegrations / sec)
Experimental setup, procedure and results
Operating voltage determination and amplifier adjustments:
1. Before switching on the equipment, make sure that the high voltage switches are at their
2. Connect the correct polarity high voltages to the photomultiplier tubes, and the preamplifier
outputs to the amplifier inputs. Make sure that the preamplifier power is supplied from the
3. Use bipolar outputs of the amplifier and determine the operating voltages of detectors. It is
recommended not to exceed the voltage limit beyond 1200 volts.
4. Adjust the voltage gain of the amplifier in such a way that the pulses are of the reasonable height
of 3 to 5 volts.
Detection and removal of walk:
In case of Leading edge timing a logic pulse is produced by the TSCA when input pulses reach a certain
percentage of the maximum value. This output of the TSCA varies in time as a function of amplitude and
rise time of the input pulse and may cause an error in the timing measurements.
When a bipolar pulse is fed to the TSCA working in the cross over mode then the logic pulse is produced
when the input pulse crosses the zero axis. If this cross over point is different for pulses of different
amplitude having different rise times then bipolar pulses of different amplitudes will produce logic pulses
at different times. This is known as Walk.
Walk can be adjusted by feeding constant height pulses from the pulser to the preamplifier test inputs,
varying the gain and adjusting the walk from the walk adjustment potentiometer from the TSCA.
Following procedure should be followed:
1. Remove the source; lower the high voltages to around 300 volts. And switch on the pulser. The
pulser outputs are fed to the test inputs of the preamplifier.
2. Adjust amplitudes of pulses from the pulser so that the heights of the pulses obtained from the
amplifier outputs are roughly the same as those of pulses from the source. If the amplitude of the
pulses is too high or too low change their amplitude from the pulses.
3. Connect the bipolar amplifier outputs to the TSCA operating in the cross over mode and the
outputs of the TSCA to the two channels of a dual trace oscilloscope. Trigger the oscilloscope
internally in the vertical mode. Two logic pulses will be visible on the oscilloscope. Now trigger
the oscilloscope from any one of the channels. The two logic pulses will still be visible but with a
certain amount of delay. Now when the gain of one of the amplifiers is changed the delayed logic
pulses should not move on the time axis. If It does this, this shows the presence of walk which
can now be removed by adjusting the potentiometer on the TSCA. Remove walk from both the
Determination of resolving time:
1. Connect the counter and the timer. Make sure that they are operating properly, that is all of them
can be switched on and off from the timer.
2. Connect outputs from the TSCAs to the coincidence unit inputs and its output to the rate meter
and a counter. Also connect the TSCA outputs to separate counters.
3. Now connect the TSCA outputs to the separate channels of the oscilloscope. Delay on both the
TSCAs should be around 5 microseconds. Trigger the oscilloscope from one of the channels and
coincide the two logic pulses by varying the delay of the TSCAs.
4. When the pulses are in coincidence, check count rate. It should be equal on all the three
5. Switch off the pulser. Place a Co60 source between the detectors and apply the high voltages.
Observer the coincidence count rate on the rate meter while increasing or decreasing the delay in
one of the TSCAs. The count rate will decrease in both the directions.
6. Remove the delay from one of the TSCAs. This will decrease the count rate as observed earlier.
Now start increasing the delay in small steps, say of 0.1 microseconds and note down the
coincidence count rate (NC). It will first increase and then decrease.
7. Plot the counts versus time. A curve will be obtained. Full width at half maximum of this curve
is twice the resolving time i.e. FWHM = 2τ.
1. Set delay time at the central value of this curve. Since the data will be collected at these two
settings of the delay times, note them down.
2. Record N10, N20 and NC0 for a suitable interval of time and then record N1B and N2B after the
source has been removed.
3. Calculate the source strength using the relations given in the theoretical portion of this
Resolving time determination:
Resolving Time Determination Using Pulser
From the graph
2τ = 1.45 – 0.45 = 1
τ = ½ = 0.5µs
Resolving Time Determination Using Source and Detectors
2.6 57 1.6 85 1 4725 0.45 987
2.5 45 1.5 3419 0.9 4758 0.4 542
2.4 50 1.4 4337 0.8 4725 0.3 318
2.2 41 1.3 4482 0.7 4761 0.2 223
2 53 1.2 4636 0.6 4849 0.1 205
1.8 68 1.1 4700 0.5 2487 0 150
From the graph
2τ = 1.53 – 0.51 = 1.02
τ = 1.02/2 = 0.51µs
Calculation of source strength (S) of Co 60
After setting the delay time at the value corresponding to the maximum coincidence counts, following
data was collected:
N10 N20 N1B N2B
13565 14407 1586 2486
13842 14027 1577 2554
13562 13931 1564 2362
Avg. = 13656 Avg. = 14121 Avg. = 1576 Avg. = 2467
NCC = (1.02μs)*(13656/10s)*(14121/10s)
N1 = N10 – N1B = (13656/10s) - (1576/10s) = 1208cps
N2 = N20 – N2B = (14121/10s) - (2467/10s) = 1165cps
NC = NC0 - NCC = (4849/10s) - 1.967cps = 482.9cps
S = N1 N2 / 2NC
= (1208)*(1165) / (2*482.9) = 1457.15cps
The actual strength of the Co 60
source was determined as follows:
A = Ao e -λt
= 0.223µCi On 07/07/2011
% error = (0.223-0.039)*100 / 0.223 = 82.5%
The resolving time the coincidence circuit was calculated using electronic pulser which was found to be
0.5µs. This was done due to the fact that this was the actual resolving time of the coincidence unit. The
resolving time was also calculated using source and detectors to testify the experimental setup by
comparing the new calculated value of resolving time with the previous one calculated using pulser. By
this technique the resolving time was found to be 0.51µs which was very close to that calculated by using
pulser. Thus the setup was proved to be correct.
The chance coincidence count rate was calculated in order to omit the effect of accidentally coincident
events which occurred instead the emission of two gammas in a single decay of Co 60
sample. Thus it was
tried to obtain the actual coincident events occurrence rate relating to the emission of two gammas.
The strength of the Co 60
source, thus calculated, was found to be 0.039µCi, whereas, the actual strength,
calculated analytically, was found to be 0.223µCi. There was an error of 82.5%. The reasons for such a
large error may be:
The source was placed between only two detectors and there was a lack of 4π geometry.
Therefore, only those gammas were detected which were emitted towards the detectors and all
other events were lost.
Since, the coincidence counts relate to only those decay events in which one of the two gammas
is detected on one detector and the other one on the second detector, therefore all the remaining
decays were lost.
Ao = 11.29µCi On 01/09/1981
t = 29.85 years
T1/2= 5.27 years
λ = 0.693/5.27 = 0.1315 y -1
It has been concluded that the resolving time of the coincidence circuit can be measured accurately using
pulser technique. The strength of the Co 60
source was found to be 0.039µCi, whereas, the actual strength,
calculated analytically, was found to be 0.223µCi. There was an error of 82.5%. Due to such a large error,
it has been concluded that the coincidence method is not a very accurate and reliable method for source
1. Knoll, G.F. ; Radiation Detection and Measurement, John Wiley & Sons (1999)
2. Nasir Ahmad ; Experimental Radiation Detection, CNS-20, (1987)