Gamma Spectroscopy using NaI(Tl) detector

Spectroscopy of any kind, deals with analysis of spectrum, i.e. a variation of intensity with eitherwavelength or frequency or energy. A γ radiation carries no charge and therefore detection of suchradiation depends on how it interacts with the detector material to deposits its total energy. The γray interacts with any material through three processes :

(a) Photo electric effect: Gamma radiation transfers entire energy to the medium and thereforegenerates a discrete peak. The process dominates in lower energy region up to a few keV. The crosssection for the effect varies as Z4.5

(hν)3where Z is the atomic number of the medium and hν is the energy

of the radiation.(b) Compton Effect: Gamma radiation deposits partial energy according to the angle through

which the radiation gets scattered. For large number of events the scattering can occur at variousangles ranging from zero to 180◦ and therefore we observed a continuous spectrum. The energy of thescattered photon is :

hν ′ =hν

1 + hνmec2

(1− cosθ)(1)

And the energy of the scattered electron is :

hν − hν ′ = hνhν

mec2(1− cosθ)

1 + hνmec2

(1− cosθ)(2)

The above two equations reveal two extreme conditions :1) When the scattered angle is the grazing angle or θ = 0◦ then almost entire energy is carried by

the scattered photon whereas the electron receives almost zero energy. 2)When θ = 180◦ or when therehappens a head on collision the incident radiation is backscattered. Therefore, this is the conditionwhen maximum energy can be transferred to an electron. The expression for energy of scattered photonand electron would be :

hν ′ =hν

1 + 2 hνmec2

[BackscatteredPeak] (3)

hν − hν ′ =2hν/mec

2

1 + 2 hνmec2

[ComptonEdge] (4)

Here is a small exercise for you. Say, we have two photons, one with 0.511 keV ofenergy whereas the other one carries 0.511 MeV energy. Now calculate the minimumscattered energy for both the cases and draw suitable inference.

The cross section for the process varies linearly with Z of the medium.

(c) Pair Production : This process takes place for radiation with energy at least equal to ormore than 1.02 MeV. Here, the radiation creates an electron hole pair. Electron’s rest mass energy ismec

2 = 0.511MeV , and therefore, so to observed this phenomenon we need an incident energy which

1

is twice that of electron’s rest mass energy. So if the energy of incident radiation is sufficiently high,it results in pair production which ultimately deposits the kinetic energies of electron and positronwhereas the annihilation radiation may deposit the full or partial energy.

hν = 2mec2 + e− + e+ + E(nuclear) (5)

E(nuclear) is the kinetic energy of the nucleus, however small, it is necessary for the conservation oflinear momentum. The positron is unstable and it immediately annihilates with the nearest availableelectron and produces two oppositely directed γ photon with a total energy of 1.02 MeV. Both ofthese photons might get absorbed within the detector medium by Photoelectric absorption. Then weshould get a peak at hν which is same as if the incident radiation deposits all of its energy throughphotoelectric effect (ν is the frequency of incident radiation). Sometimes both the annihilation photoscan escape without detection and we get a peak at 2mec

2 below the photopeak whereas in case a singlephoton escapes it generates a peak at mec

2 below the photopeak. The first one is called Double EscapePeak and the latter one is known as Single Escape Peak.In this case the cross section of the event is proportional to Z2 of the medium.

(d) Sometimes, if a source emits more than one γ radiation, there will also be probability, thoughsmall, that at some instances, both the energies will get deposited simultaneously in the detector andwe will observe a photopeak worth the summation of both the energies.

• NaI Crystal : Having understood the interaction process of radiation with the material, we cannow think of designing a solid state detector which would ensure the above mentioned processesto take place within it and helps in generating signal against incident photon energy. Here willdeal with scintillator detector NaI(Tl). It consists of single crystal ( here the dimension is 1.5” ×

1.5”) of thallium activated sodium iodide which is optically coupled to the photocathode. When-ever radiation is incident on the crystal it creates ionization within sodium iodide. This createsexcited states in the crystal which decay through emission of photons. In early days these photonswere bombarded on any scintillating layer where the impact of bombardment was perceived asvisible dots. The dots were counted and intensity of radiation was determined. Thus the nameis given to be scintillation detector. Nowadays, the purpose is being served by photomultipliertube. The thallium doping is done to ensure shifting of wavelength of photons which is sensitiveto the photocathode material. Photocathode is generally made with a layer of photosensitivematerial like Cs3Sb.

We know, NaCl (sodium chloride, table salt) is hygroscopic in nature. What aboutNaI ? Do we ensure that NaI does not get affected by moisture?

• Photomultiplier Tube: As a γ radiation comes in, it interacts with the material medium ofthe crystal in above said possible ways. These release the scintillation photons through excitationof NaI which in turn incidents on to the photocathode thereby releasing photoelectrons. Photo-cathode is followed by a series of plates called dynodes. Dynodes are biased through potentialdivider arrangement in such a way that the emitted electrons from photocathode sees a positive

2

Figure 1: Experimental set up for NaI detector system for gamma spectroscopy.Taken from the companymanual http://www.spectrumtechniques.com/resources/instrument-manuals/

voltage at first dynode, then higher positive voltage at the second one and so on. Therefore,photoelectrons get accelerated towards dynode. As they strike the surface of dynode they knockout more number of electrons from dynode and therefore the amplification of electronics currenttakes place. This process of multiplication continues up to the anode where the number of elec-trons would get multiplied by a factor of around 104 to 106. It should be remembered that thetotal charge getting accumulated at anode is proportional to the energy deposited by the incidentradiation in the detector.

A figure of experimental set up of NaI detector is shown in Fig.1 and a schematic diagram of thesame is shown in Fig.2.

• Preamplifier : The detector set up is followed by preamplifier which collects the charge fromanode and converts it into voltage pulse. Remember it acts as a buffer between detector andthe amplifier with unity gain. One can even calculate the relation between output voltage andenergy of photon. It comes out to be around 50mV/MeV. It is placed as much as close to thePMT as capacitive reactance of long distance connecting cables would deteriorate the signal tonoise ratio. The requirement of low noise and stable sensitive preamplifier is prepared with FETinput stage. Noise in preamplifiers is generally taken care of by input FET and leakage currentsfrom it, input capacitance including contribution from detector, resistances of entire circuitry. Aspreamplifier is placed just next to the PMT, the voltage bias of the detector is supplied throughthe preamplifier.

Exercise : Calculate the voltage energy relation for charge sensitive preamplifier.Given that the capacitance is 1 × 10−12 f, electronic charge is 1.6 × 10−19 and theenergy to create electron hole pair in the detector is 3.62 eV at 300 K.

Exercise : We have talked about FET as input stage to reduce noise to signal ratio.Can we also use bipolar transistor instead of FET ? If we decide to continue with

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Esc

ape

Rad

iatio

n

Photocathode

Source

PreAmp

Detector

Bias Voltage

R

Lead Shield

Compton Scattered Radiation

NaI(Tl)

Annihilation

ReflectorUV Photons

Anode

Photoelectrons

Tube

multiplier

Photo−Set of Dynodes

RL

R

R

C

Figure 2: Schematic diagram of NaI detector system.

4

FET what other measures can reduce the noise ?

• Detector Bias: For the entire operation we need to provide a high stable voltage. Designingdetector bias also depends on the fact that whether detector draws a small current or highcurrent. For example, for gas based detectors the current drawn is very low while the appliedvoltage is high. The supplied bias should be properly filtered and regulated otherwise high-voltagefluctuations might interfere with the signal output.

• Amplifier: As the name suggests it amplifies the signal which is fed from preamplifier. But theamplifier has another major task to perform, that is, pulse shaping. The output from preamplifiergenerally consists of steep rising step with a slow exponential decay. Amplitude of the step rep-resents the energy of the radiation. The exponential decay part is due to the feedback resistanceand capacitance shown in the Fig.2. In NaI detectors the steep rise time is around 500 ns. Now,as the nuclear radiation is random, so the steeply rising step of next pulse generally overlapswith the decaying part of the previous pulse. When the number of pulses become very large, thisresults in Pile Up. Now overlap of consecutive pulses would result in meaningful data. These pileup events can be statistically studied with the Paralyzable and Non-Paralyzable models (Referto Radiation Detection by G. F. Knoll).

Therefore, amplifier pulse shaping should convert the long decaying part of preamplifier signalto a short decay waveform to avoid restriction of meaningful count rate. To implement pulseshaping, one can use CR-RC network where CR represents high pass filter followed by a low passfilter. The first part cuts of the low frequency jitters and improves the signal to noise ratio. Iteven acts as CR differentiator which shortens the decay time appreciably. The latter preventsthe high frequency noise to propagate thereby further increasing the signal to noise ratio. So, theoutput is received as a nicely shaped pulse.

The same objective can be persued using delay-line pulse shaping. The delay can be combined toproduce rectangular pulse against each step function from preamplifier. But, again using a delayline worsen the signal to noise ratio.

• Single Channel Analyzer: Once we get the meaningful pulse, now it is important to count thepulses along with the energy and timing information to extract the details of incident radiation.Once a radiation source is placed, it randomly emits entire range of γ energy and simultaneouslyeach of them deposit their energy in to the detector. So, we need an electronic method todiscriminate between these energies. The purpose is solved by using single channel analyzer.This module generates a logic pulse only when the input voltage height lies in between a certainlimit. As we know, the height of voltage pulse is proportional to the energy, so by selecting Lowerand Upper Limits we can chop out entire voltage input into bins of voltages. These limits areknown as Lower Level Discrimination (LLD) and Upper Level Discrimination (ULD).

• Scalers and Counters: Now the logic pulses are gradually sent to simple electronic Register,where the count gets enhanced by unity as a logic pulse arrives. This is also called scalers orcounters.

5

Figure 3: Multichannel analyzer and inbuilt electronics set up for gamma spectroscopy.Taken from thecompany manual http://www.spectrumtechniques.com/resources/instrument-manuals/

• Multichannel Analyser: As the name suggests, the module can perform the operation of singlechannel analyzer spanned over entire voltage range at a single time. Here, we will be using MCAwhose output can directly be visualized on PC in form of spectrum. Fig.3 shows the set up forthe experiment which incorporates power supply, amplifier and MCA.

The figure4 shows the flowchart of different modules connected to each other for single channelanalyzer as well as multichannel analyzer based detection system.We have discussed so many parameters for the gamma spectroscopy. Figure5 highlights the parame-

ters which need to be set during the experiment.

• The first parameter is the High Voltage bias. Set it at 800V. Polarity of the voltageis positive.

• Then comes the Coarse Gain, that is the gain of amplifier. Keeping in mind thathow much large energy we are going to observe, we need to set the gain of amplifier.Otherwise amplification would be so large that high energy peaks would lie outsidethe given range. For most of the experiments this can be set at 8. Fine gainparameter can be set at 1.24. Of course for sum spectrum experiment you need toalter these values.

• Thereafter, drop down option for conversion gain is given. If you see closely, thesenumbers represent the number of bites. The maximum is 1K byte for this setup. In practice, the voltages are recorded bit by bit and are in general knownas channels. Here we should also understand another important feature, that thespectrum directly does not reproduce the energy of radiation. So, we need to doCalibration of these channel numbers with respect to energy.

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Detector

Detector PreAmp

PreAmp

Amplifier

Amplifier

Single Channel

Analyzer

Counter /

Timer

Analog to Digital

Converter

Display on board

Analysis

Memory

High Voltage Bias Supply

High Voltage Bias Supply

Multi Channel Pulse Height Analysis

(a)

(b)

Figure 4: (a) Shows the hierarchy of electronics for SCA set up. (b) Shows the circuit diagram ofdetection system with MCA.

• The we have LLD and ULD. For MCA there is no need to define these parametersexplicitly. But sometimes, high level noise is found at very low energy range. Bysetting proper LLD values we can cut off those noisy regions.

• Figure6 shows the demo spectrum output on screen. On top, one can see lot of menu options arethere. We will briefly discuss the most important ones.

Mode It should be set at PreAmp In mode.

Settings The option Amp/HV/ADC can be set for High Voltage Bias.

Coarse gain and fine gain can be adjusted.

Through the option Preset time, a time period can be set for data acquisition.

ROI (Region of Interest) : Using this option two bounds of a region, especially a peak, can beset whose area can be calculated.

Energy Calibrate : Calibration can be done. 3 Point calibration is preferable.

• Caution : High Voltage must be turned on after loading set up

7

Figure 5: Parameters for gamma spectroscopy experiment.Taken from the company manualhttp://www.spectrumtechniques.com/resources/instrument-manuals/

8

Figure 6: Screen display of data acquisition through software for gamma spectroscopy.Taken from thecompany manual http://www.spectrumtechniques.com/resources/instrument-manuals/

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EXPERIMENT : Energy Calibration with 137Cs and 60Co

Purpose As we have discussed in detail that the voltages are recorded as per channel number. Soto retrieve energy information we need to calibrate the channels in terms of energies.

Underlying Theory Already discussed in introduction.

Procedure

1. Set the gain and fine gain parameters and high voltage bias. Start a run without any radio activesource nearby. Check the dead time displayed is around 1% else adjust the LLD till it attainsthe 1% of dead time.

2. Place the source with the labeling down side. Place the source at third groove preferably. Acquirethe spectra for both the sources for preset time of say, 500 s.

3. Now read the channel numbers corresponding to the respective photopeaks and read their energyfrom NNDC website. Register your result in the following table :

Table 1: Table for Study of Gamma SpectraS. No. Item Channel Number Energy (keV)

1. 137Cs photopeak 6622. 60Co photopeak1 11733. 60Co photopeak2 1173

4. Fit a straight line curve through points drawn with channels as x axis and Energy on y axis. Getthe slope and intercept. Now one can use the equation to correlate channel number to energy forany source. A demo plot is shown in Fig.7.

5. The plot also shows the error bar plots. We have rounded off the value of γ energy, so an error of1 keV can be considered. Similarly, for the channels, 1 unit of channel can be taken as error forx axis. Then after plotting the error bars and determine the error slope, we can expect an errorof 3 or 4 keV in the values of γ energy.

InferenceThe voltage to energy bears a linear relation for NaI detectors.

10

350 400 450 500 550 600 650 700 750 800600

700

800

900

1000

1100

1200

1300

1400

Energy(keV) Line Fit of Energy(keV)

Energy

(keV

)

Channel

Equation y = A + B*xAdj. R-Square 0.99936

Value Standard ErrorEnergy(keV) A 0 0Energy(keV) B 1.71854 0.00801

Figure 7: Calibration of γ energy w.r.t. channel number.

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EXPERIMENT : Analysis of spectra for sources : 137Cs, 60Co, 22Na

Purpose To study the spectrum for each of the given sources and determine various characteristicsparameters of sources as well as the detector.Underlying Theory Already discussed in introduction.Procedure

1. Set the gain and fine gain parameters and high voltage bias. Start a run without any radio activesource nearby. Check the dead time displayed is around 1% else adjust the LLD till it attainsthe 1% of dead time.

2. Place the source with the labeling down side. Place the source at third groove preferably. Acquirethe spectra for both the sources for preset time of say, 500 s.

3. Once the spectra are acquired, try to determine various parameters as per the following table.

4. Demo spectra for 137Cs and 60Co with all the detailed parameters are shown in Fig.8 and Fig.9.

5. A separate plot for spectrum of 22Na has been shown in Fig.10. In the plot the y-axis has been taken as loge of counts. This method is applied when there are certainpeaks whose intensity is so small that due to linear scaling of the vertical ordinatewith respect to the strong peaks, these low intensity peaks are not traceable. If thecounts are represented in log scale, all the peaks are clearly visible. One can observethe sum peak at the end.

Inference

• Spectral analysis reveals characteristics of γ radiation sources. The calibration parameters havebeen used to find out energies of unknown source.

• Compare the observed values for Compton edge and Backscattered peak with the theoreticalvalues :

• Once the resolution is calculated for all the photopeaks, correlate Resolution with γ energythrough a plot.

Post Lab Questions and Take Home Messages

1. Does the calibration plot intersect the energy axis at zero energy ? If not, what might be theprobable reasons?

2. What is the reason behind annihilation peak in 22Na.

3. In NNDC web page we find that the intensity percentage of 1332 keV is slightly higher than thatof 1173 keV. But in the spectrum the former shows less area count. Why ? We will try to findthe answer in subsequent experiments.

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100 200 300 400 500 600 700 800 9000

200

400

600

800

1000

1200

1400

Back

scat

ter p

eak

184k

eV

Com

pton

Edg

e 47

8keV

Counts Gauss Fit of Counts

Cou

nts

Energy(keV)

Phot

opea

k 66

2keV

52keV

Resolution =

Figure 8: Spectrum of 137Cs.

2 4 6 8 10 12 14 16 180

200

400

600

800

1000

1200

1400

1600

1800

Phot

opea

k 13

32ke

V

Phot

opea

k 11

73ke

V

Counts

Cou

nts

Energy(keV)*100

Back

scat

ter p

eak

240k

eV

Com

pton

edg

e 92

5keV

R1332 = 62/1332% = 5%R1173 = 80/1173% = 6%

Figure 9: Spectrum of 60Co.

13

0 500 1000 1500 2000 2500 3000 3500

0

1

2

3

4

5

Com

pton

edg

e

C

C

Energy (keV)

511k

eVAn

nihi

latio

n pe

ak

1275

keV

Sum

Peak

=178

6keVBa

cksc

atte

red

Com

pton

edg

e

Figure 10: Spectrum of 22Na in semi log plot.

4. If you have derived the approximate difference between the Photopeak and the Compton edge,you can apply the same here for the real sources and check what values you obtain and do yousee correlation with certain known parameter?

5. Think of a small adjustment in the give experimental set up, which can enhance the intensity ofbackscattered peak.

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Table 2: Table for Study of Gamma SpectraS. No. Item Channel Number Energy (keV)

1. 137Cs photopeak 6622. 60Co photopeak1 11733. 60Co photopeak2 13324. Compton edge in 137Cs5. Compton edge in 60Co6. Backscatter peak in 137Cs7. Backscatter peak in 60Co8. Escape peak (if any)9. 22Na photopeak10. Annihilation peak22Na11. Sum peak 22Na and 60Co(if any)12. Compton edge in 22Na13. Backscatter peak in 22Na14. Energy resolution 137Cs15. Energy resolution 60Co16. Energy resolution 60Co17. Energy resolution 22Na18. 65Zn photopeak19. 65Zn Compton edge20. 65Zn Unknown peak21. 54Mn photopeak22. 54Mn Compton edge23. 54Mn Backscatter24. 65Zn Resolution25. 54Mn Resolution26. 137Cs photofraction27. 60Co photofraction28. 54Mn photofraction

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Table 3: Table for Theoretical CalculationsS. No. Item Energy (keV)

1. Compton edge in 137Cs2. Compton edge in 60Co3. Backscatter peak in 137Cs4. Backscatter peak in 60Co5. Compton edge in 22Na6. Backscatter peak in 22Na7. 65Zn Compton edge8. Backscatter peak in 65Zn9. 54Mn Compton edge10. 54Mn Backscatter

16

EXPERIMENT : Measurement of Efficiency

Purpose In GM counter experiment, we have already understood that any detecting system shouldhave an efficiency parameter which depends on geometrical as well as internal factors. But, as GMcounter does not differentiate between individual energy values of radiation, we measured the efficiencyfactor for whatever radiation was emitted by the source. Now, with the help of scintillator detectorwe can measure individual energies of radiation, therefore, it will be interesting to look for variation ofefficiency factor with individual γ-ray energies.Underlying principle We have already seen that β and γ radiation have different penetrating capa-

bility when these are bombarded on to a material medium. Similarly, if only γ radiation is considered,the low energy rays would not be able to penetrate much into the detector crystal and in process mightnot get detected. Similarly, if the γ energy is too high then it might escape through the detectormedium without interaction and hence, no signal will be registered. But the energies which are in midregion might well interact with the medium and hence the chances of their detection would be more.Thus, efficiency wise the radiations can be categorized in three regions.

Procedure

1. Set the gain and fine gain parameters and high voltage bias. Start a run without any radio activesource nearby. Check the dead time displayed is around 1% else adjust the LLD till it attainsthe 1% of dead time.

2. Place the 133Ba source with the labeling down side. Place the source at third groove preferably.Acquire the spectrum for preset time of say, 500 s.

3. Once the spectrum is acquired, try to look for photopeaks. 133Ba has four prominent peaks whichyou can trace from general information.

4. A demo spectrum of the nucleus is shown in Fig.11 with Gaussian fitting for four peaks.

5. Here we will learn a new method. First of all, if we see our data file, it writes into two columns.First column is the channel number which runs from zeroth row to 1023rd whereas the secondcolumn shows the count at each corresponding channel. There is a software package called RAD-WARE which was developed by David Radford of the Physics Division at Oak Ridge NationalLaboratory. The package is dedicated to spectral analysis of various nuclear experiments. Refer-ence for the same ishttps://radware.phy.ornl.gov/

Here one can plot the corresponding data file and generate the spectrum.

Question comes, why do we need special package when we can plot the spectra withany plotting software ?

17

Here we would have to recall a bit of our computational classes. Then we would realize thatwhenever a computer coding is done each of the defined parameters either integer or float ordouble, all have a certain limit of accuracy. It depends upon the user and his/her purpose thatwhat limit of accuracy should we impose.

In the very first experiment we have carried out calibration of detecting system byfitting the data points with a linear fit. In actual experiments, the demand of accu-racy is much more and fitting is done with Quadratic equations. Similarly for the arealfitting we need a level of accuracy which Radware can support.But the program does not read the two column data file. It reads a different format of input data

file. The data file tells us that the channels are nothing but available bit of computer memory.

Each voltage is registered as channel in each of the bit. That means from the spectrum itself one

can tell how much memory one need to spare for storing a spectrum file.

We can convert the data file in the desired format by writing a small code. The 133Ba sourceis considered as a standard source in which standard total emitted counts across each of the γenergies are known.

Now the process is straight forward. If we know the counts under each of the transitions by fittingthe peaks and then compare the same with the standard ones, one can get the efficiency valuesvery easily. The RADWARE package performs the entire calculation. A demo result is shown inFig.13. The fitting is done with the following relation :

eff = EXP [(A +B ∗ x+ C ∗ x ∗ x) ∗ ∗(−G) + (D + E ∗ y + F ∗ y ∗ y) ∗ ∗(−G)] ∗ ∗(−1/G),(6)

where x = log(EG/E1) and y = log(EG/E2). Here EG is the gamma-ray energy, and the constantsE1 and E2 have the values 100 keV and 1 MeV, respectively.

Inference

• From the efficiency vs energy plot, it is revealed that the efficiency peaks at around 80 keV andthereafter gradually decreases.

Post Lab Questions and Take Home Messages

1. During actual experiment, 152Eu is also used in addition to 133Ba and the efficiency is calculatedover a large range of γ energies.

2. If the activity of a source is known then can you calculate the standard activity across each ofthe γ rays emitted by the source?

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Figure 11: Spectrum of 133Ba with Gaussian fitted photopeaks.

19

0 500 1000 1500 2000 2500 3000E (keV)

0

20

40

60

80

Effi

cien

cy

Figure 12: Variation of efficiency of detection for different transitions in 133Ba.

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EXPERIMENT : Activity of Gamma-ray emitter (Absolute and RelativeMethods)

Purpose To measure the activity of the source using absolute method. In absolute method theefficiency of detector system is taken into consideration. Once the activity of a source is known, onecan determine the activity of another source with respect to the known one.Can we use two separate sources for the relative method ? What about the γ-ray energy,

should it be same for both the sources ? Will the pattern of decay scheme of two differentsources affect the results ?

Underlying PrinciplesAbsolute activity of a source is given by :

Activityofthesource =Counts−Background

livetime

1detectorarea(cm2)

4πr2εpf

(7)

Where, r is the distance of source from the detector, εp is the intrinsic efficiency for given detector(see Fig.13) and f is the fraction of total disintegration in which the measured gamma ray. Gammadecay fraction for a few known energies is given in the table4.

Table 4: Table for Gamma decay fractionIsotopes Energy (keV) Decay fraction (f))

137Cs 662 0.85160Co 1173 0.998660Co 1332 0.998622Na 511 1.7822Na 1275 0.999465Zn 1116 0.50654Mn 835 0.9998

Now, if the same source (S1) is to be used for relative measurement method to determine activity ofanother source, say, S2. Then,

Activity of Source (S2) = (CountsS2 −BackgroundS2CountsS1 −BackgroundS1

)(ActivityofSource(S1)) (8)

Procedure

1. Place the source approximately 6 - 10 cm away from the detector.

2. Acquire the counts under photopeak for a sufficient period of time so that at least 10,000 countsare accumulated under photopeak.

21

Figure 13: NaI(Tl)detection efficiency for 3.8cm × 2.5 cm cylindrical crystal with a source on eighthshelf. Taken from the company manual http://www.spectrumtechniques.com/resources/instrument-manuals/

22

3. Remove the source and again repeat the above steps for the background measurement within thebounds of given photopeak.

4. Get another source whose activity is to be determined.

5. Place the source in the same slot as that of the former one.

6. Acquire the counts under the photopeak for the same amount of time as that of the known source.

7. Repeat the steps for background measurement withing the limits of the photopeak of unknownsource.

8. Use appropriate relations and determined the activity through absolute and relative methods.

Observations : The Sources are placed at a distance of ............................cm from the detector.Dimension of the Detector face .....................................

Table 5: Table for Measurement of Activity of Sources through Absolute and Relative Methods

Source Counts under Photopeak Background Count under Photopeak Time

Know SourceUnknown Source

One should also try to calculate the standard deviation in the activity due to the counting statisticsunder photopeak.

Inference1. Activity of the source through absolute method .....................±....................2. Activity of the source through relative method ......................±....................For every source, the activity is mentioned on top of it. How close is your result to these values ?

Post Lab Questions and Take Home Messages

1. What is the importance of intrinsic photopeak efficiency ?

2. Placing the source closer to the detector should increase the counting rate but does it affect theaccuracy of measurement ?

23

EXPERIMENT : Sum Peak analysis in 60Co and 22Na

Purpose To confirm the existence of sum peak for 60Co and 22Na and analyze the same.

Underlying theoryWe have already recorded the spectra of 60Co and 22Na. For 22Na, we have shown the spectrum on

semi log plot which clearly shows sum peak at 1786 keV. Similarly, if the spectrum of 60Co is drawnin semi log plot we will observe a sum peak at 2507 keV. Let us discuss the case of 60Co which decaysto 2.507 MeV state of 60Ni through β decay. 60Ni decays to the ground state through emission of γenergies 1.17 and 1.33 MeV. It is to be mentioned here that both of these transitions are in coincidenceor they are emitted instantaneously one after the other. We also assume that each of these events areisotropically distributed,i.e; if one of the γ radiation goes in a particular direction then the other cango in any of the direction spanned over entire 4π. Even though for 60Co, there is a deviation of 16%from the isotropic distribution. There lies a finite though small probability that both of theme γ rayswould go in the same direction and hence would get detected simultaneously given that both of thesearrive within the resolving time of the detector. The number of counts under first photopeak, say, γ1is given by :

C1 = ε1Gf1tA (9)

where, all the terms have same meaning as discussed in the experiment of ”Activity measurement”.A is the activity of the sample and t is the time of acquisition. Similarly for γ2 :

C2 = ε2Gf2tA (10)

Therefore, the sum peak would comprise of :

Cs = ε1ε2G2f1f2A[W (0◦)] (11)

where, W (0◦) accounts for angular correlation function (in general it forms a Legendre PolynomialSeries) and in this case it can taken to be unity. Therefore,

Cs = ε1ε2G2f1f2A (12)

ProcedureSpectrum is already acquired for both the nuclei ensuring that at least 1000 counts are accumulated

under sum peak. Plot the corresponding semi log spectrum and perform the above analysis for boththe nuclei.Inference

• The sum peak of 60Co is ...................±............keV

• Experimental intensity of sum peak ..............±.............

• Calculated intensity of sum peak ............................

• The sum peak of 22Na is ...................±............keV

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• Experimental intensity of sum peak ..............±.............

• Calculated intensity of sum peak ............................

25

EXPERIMENT : Absorption of γ rays by Materials

Purpose To study the absorption of γ radiation by different media like Lead, Aluminium, and Plastic.

Underlying Theory As gamma ray passes through any material, it interacts with the mediumthrough Photoelectric, Compton Scattering and Pair Production. This can cause loss in intensity of γray owing to either deflection or absorption. If I is the intensity of radiation after passing through thematerial, then this can be correlated to the actual intensity I0 through following relation :

ln(I) = ln(I0) + (−µx) (13)

where, parameter µ is called the coefficient of linear absorption. If the interaction is predominantly,photoelectric in nature then the absorption coefficient can be approximately written as :

µ ∼ Z4.5/E3γ , ln(µ) ∼ −3ln(Eγ) + 4.5ln(Z) (14)

So, by determining the coefficient of absorption either by varying Z of different material or with Eγ ,we can very what fraction of radiation interacts with the medium through photoelectric effect.Procedure

1. Place the source in either of third or fourth groove and record the counts under photopeaks (sothe process is photoelectric) ensuring that around 10,000 counts are accumulated.

2. Now place the absorber (say, aluminum but do not use the foils) on the shelf just above the shelfwhere source is placed.

3. Vary the thickness of absorber gradually and record the counts subsequently.

4. Choose another absorber (say, lead) and repeat the steps 1 - 3.

5. Replace the source with another.

6. Repeat the steps from 1 to 4.

7. Plot ln(I) vs thickness and deduce value of µ from the slope.

8. Plot ln(µ) vs ln(Eγ) as well as ln(µ) vs ln(Z) and deduce the corresponding slopes. Match thesame with the expected values.

9. Draw the error bars and try to find out the estimate of deviation.

InferenceFrom the slopes of the graphs drawn between ln(µ) vs ln(Eγ) as well as ln(µ) vs ln(Z) the deduced

values of :

Linear Absorption Coefficient in Al = .............................

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Linear Absorption Coefficient in Pb = .............................

Linear Absorption Coefficient in Plastic = .............................

Power of Z = ............................

Power of Eγ = ....................

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Table 6: Table for Gamma decay fractionThickness (mg/cm2)

Isotopes Energy (keV) Aluminium Lead Absorber137Cs 662

60Co 1173

60Co 1332

54Mn 835

65Zn 1116

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