Gamma Gamma Coincidence-Basics of Physics-Lab Report, Exercises for Advanced Physics. Alliance University
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sankaraa16 July 2012

Gamma Gamma Coincidence-Basics of Physics-Lab Report, Exercises for Advanced Physics. Alliance University

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This is lab report for Advanced Physics Course. It was submitted to Prof. Dhirendra Kapoor at Alliance University. Its main points are: Gamma, Coincidence, Theory, Experiment, Radioactive, Decay, Scheme, Circuit, Emissio...
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1

Abstract

In this experiment, the field of timing measurement was introduced and the strength of the gamma source

Co 60

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.

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Introduction

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

involved.

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.

Theory

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

seconds.

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

circuit.

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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

coincidence circuit.

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

Where

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)

Therefore,

S = N1N2 / 2NC (disintegrations / sec)

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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

minimum.

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

amplifier.

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.

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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

sides.

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

counters.

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.

Data collection:

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

experiment.

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Resolving time determination:

Resolving Time Determination Using Pulser

From the graph

2τ = 1.45 – 0.45 = 1

Then

τ = ½ = 0.5µs

Resolving Time Determination Using Source and Detectors

Delay

time(µs)

Coincidence

counts/10sec

Delay

time(µs)

Coincidence

counts/10sec

Delay

time(µs)

Coincidence

counts/10sec

Delay

time(µs)

Coincidence

counts/10sec

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

Delay

time (µs)

Coincidence

counts/10 sec

0.4 0

0.5 500

0.6 500

0.7 500

0.8 500

0.9 500

1 500

1.1 500

1.2 500

1.3 500

1.4 500

1.5 0

1.6 0

1.7 0

1.8 0

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From the graph

2τ = 1.53 – 0.51 = 1.02

Then

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)

= 1.967cps

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

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S = N1 N2 / 2NC

= (1208)*(1165) / (2*482.9) = 1457.15cps

= 0.039µCi

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%

Discussion

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

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Conclusion

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

strength determination.

References

1. Knoll, G.F. ; Radiation Detection and Measurement, John Wiley & Sons (1999)

2. Nasir Ahmad ; Experimental Radiation Detection, CNS-20, (1987)

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