Gamma Ray Spectroscopy

Lizelle Niit; Partners: Kevin Murray, Daniel Adamiak

April 28, 2014

Contents

1 Introduction and Aim 2

2 Theoretical background 22.1 The photoelectric effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Compton scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.3 Pair production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.4 Backscatter peaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.5 Electron capture peaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.6 Decay schemes for nuclei involved in this experiment . . . . . . . . . . . . . . . . 4

3 Equipment and Methods 5

4 Results 74.1 Calibration function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.2 Histogram plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.3 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5 Analysis 115.1 Energy resolution function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

6 Discussion 136.1 Discussion of histogram features . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

6.1.1 137Cs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136.1.2 60Co . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136.1.3 22Na . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136.1.4 Unknown source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

6.2 Background when no source is present . . . . . . . . . . . . . . . . . . . . . . . . 146.3 Resolution function of NaI detector . . . . . . . . . . . . . . . . . . . . . . . . . . 146.4 Relative usefulness of parts of the spectrum . . . . . . . . . . . . . . . . . . . . . 15

7 References 15

Abstract

This experiment involved measuring the decay spectra of six different radioactive sourcesand examining the energy resolution function of the detector. It was found that the energyresolution function depended on the energy of the incoming gamma rays, so that the linewidth was inversely proportional to the energy. An unknown source was identified.

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1 Introduction and Aim

Our aim was to study the modes of decay of four different radioactive sources. We aimed to iden-tify one unknown source. We also studied the energy resolution function of the detector.

2 Theoretical background

When gamma rays enter a NaI crystal they interact with the electrons in the crystal in variousways which will be detailed below.

In the case of the photoelectric effect a gamma ray ionises a single electron. This electron thenimparts energy to many other electrons. For example, if a gamma ray has an energy of 1 MeVand imparts all its energy to a single electron, that electron can raise on the order of 100000other electrons to higher energy levels. (This is assuming it takes on the order of 10 eV to excitean electron to a higher energy level.

Photoelectrons, Compton electrons and/or electron-positron pairs are produced, all of whichhave energies less than or equal to the incident gamma ray energy. These electrons causeionization in the sodium iodide, and a fraction of their energy is converted into a burst ofvisible or ultraviolet photons - a scintillation.

A proportion of these photons enter the photomultiplier, causing a voltage pulse. The amplitudeof the pulse is proportional to the gamma ray energy.

There are three ways that gamma rays (which are high-energy photons) interact with mat-ter:

Photoelectric effect

Compton scattering

Pair production

We will discuss each of these in turn.

2.1 The photoelectric effect

All of a protons energy gets transferred to a single electron. The incident photon disappearsand the bound electron is freed from its shell.

The energy of the freed electron is Ee = E Eb, where E is the gamma ray energy and Eb isthe energy binding the electron to its shell [2].

Photopeaks are generated through the transfer of energy from gamma rays to electrons. Theseprimary electrons are freed from their shells and pass on energy to other electrons. Theseelectrons give off photons in the visible to ultraviolet range, and those photons enter the photo-multiplier tube. The photomultiplier tube then generates a voltage pulse, which is proportionalto the energy deposited by the incoming gamma ray. In the case of the photoelectric effect thegamma rays deposit all their energy, so the voltage pulse is proportional to the energy of thegamma rays.

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This is why the photopeak forms a relatively distinct peak compared to the Compton edge:each gamma ray has the same energy, and because this energy is proportional to the voltagepulse generated we have a scenario where multiple pulses fall into the same channel bin.

2.2 Compton scattering

During Compton scattering, a gamma ray transfers only part of its energy to an electron. Agamma ray hits an electron at an angle and is scattered away at an angle . The energytransferred to the electron is given by Ee = E E , where E = E 11+E (1cos()

m0c2

.

Hence, at = 0, Ee = E [1 1] = 0, so the gamma ray and electron do not interact.At = pi the maximum amount of energy is transferred. However, even then Ee = E

[1

11+E

2m0c

2

]< E , so not all of the gamma rays energy is transferred to the electron.

Because there is a range of possible scattering angles (0 to pi), the amount of energy transferredto electrons is inconsistent. This means that the voltage pulse generated in the photomultipliertube is inconsistent and is not proportional to the energy of the incoming gamma rays. Thereforethe pulses generated due to the Compton effect fall into a range of bins that extends from thebin corresponding to zero energy to the bin corresponding to the energy that is transferredwhen the scattering angle is pi.

2.3 Pair production

A gamma ray is converted to an electron-positron pair close to the nucleus [2]. The gamma raymust have an energy of at least 1022keV for pair production to take place.

...............................

The above processes result in energetic electrons moving around the detector. They ionise otherelectrons; each primary electron can ionise N = Ee/ other electrons, where is the energyneeded to ionise a single electron.

2.4 Backscatter peaks

Gilmore and Hemingway [2] point out that most gamma rays are scattered through a largeangle by the [detectors] shielding. This is called backscattering. It turns out that the energiesof backscattered gamma rays fall within the range 0.200 to 0.300 MeV, leading to a broadpeak.

2.5 Electron capture peaks

Certain nuclides undergo + decay according to this formula: p n+e++e. The free positroncomes into contact with an electron and annihilates before reaching the detector. Two gammarays of energy 0.511 MeV each are given off. They travel in opposite directions to conservemomentum and so the detector detects at most one of them.

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2.6 Decay schemes for nuclei involved in this experiment

Decay scheme for 22Na [3]

Figure 1: Decay scheme for 22Na

Decay scheme for 137Cs [4]

Figure 2: Decay scheme for 137Cs

Decay scheme for 60Co [5]

Figure 3: Decay scheme for 60Co

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3 Equipment and Methods

Figure 4: Equipment used in the experiment

The detector consisted of a NaI crystal and a photomultiplier tube. The 5 cm diameter by 5cm long crystal was mounted on the photomultiplier tube. A high voltage source with positivepolarity powered the photomultiplier.

Signals from the photomultiplier were sent to a pre-amplifier, then to a linear amplifier and

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then to a delay amplifier. The purpose of the delay amplifier was to synchronise signals fromthe linear amplifier with signals coming from the gate and delay generator (GDD). Signals weresent from the delay amplifier to an analogue to digital converter (ADC).

Pulses from the linear amplifier were also sent through a timing single channel analyser (TSCA).The TSCA outputted a 5V logic pulse when the input pulse from the linear amplifier fell withina set range. The purpose of this gate was to filter out noise: since background radiation occursmainly at low energies, we could simply set the lower bound high enough that most noise waseliminated but low enough that we did not lose essential data.

The logic pulses from the TSCA were reshaped by the gate and delay generator (GDG) andthen used to determine whether the MCA would process signals from the ADC.

The ADC was connected to a multi-channel analyser (MCA). The MCA only processed signalsfrom the ADC which were accompanied by logic pulses from the GDG.

The MCA sorted the digital pulses to form a spectrum, and was connected to a computer whichwas running software to acquire the data.

An oscilloscope was used to view pulses travelling through various parts of the circuit.

To take the measurements, we placed the radioactive sources close to the detector in turn,and manipulated the lower bound for the gate until we had eliminated most noise withouteliminating significant data.

Since the histograms were of counts versus channel number instead of counts versus energy, wehad to come up with a calibration function to convert channel number to energy. We plottedchannel numbers versus previously known energies for 60Co and 137Cs. We guessed that thefunction was linear and fitted a straight line to the data. The parameters of this line then gaveus a way of converting channel numbers to energies.

Analysis:

We used Origin to plot histograms of counts versus channel number. We fit gaussians to thephotopeaks and recorded the means, sigmas and their errors. I used Python for the rest of myanalysis.

We also recorded the approximate positions of the Compton edges.

We plotted E/E versus E in order to examine the energy resolution function of the detec-tor.

Uncertainty analysis:

For peaks that were not photopeaks, I estimated the range in which the true value of the peakdefinitely lay. Then I calculated the uncertainty from that range by the formula |maxmin|/(2

6).

To get uncertainties for photopeaks, I used two methods:

Method 1: I calculated uncertainties for the energies (on the x axis of the calibrationgraph) using the formula yerror =

x2var a+ var b+ 2xcov ab. I used this method in the

rest of my analysis.

Method 2: I calculated the differences between the energies of the two Na peaks and theinverse of the calibration function f1(ADC) and used those differences to get percentageuncertainties. This method was only used for comparison with Method 1.

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4 Results

4.1 Calibration function

Peaks used for calibration:

Co60 peak 1

Co60 peak 2

Cs137 peak 1

Figure 5: Calibration line

y = ax+ b = 342.83307364x+ 1.14335137 (1)

where x is the ADC value and y is the energy.

(u(a))2 = 1.73668 u(m) = 21.95161862(u(b))2 = 1.89857 u(k) = 33.3489816However, the uncertainties are correlated so one cannot simply use the above uncertainties toget the uncertainty of a specific y value.

Covariance matrix:

21.95161862 -26.89940113-26.89940113 33.3489816

The uncertainty on y values of the calibration graph:

yerror =x2var a+ var b+ 2xcov ab

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4.2 Histogram plots

Figure 6: Histogram for 137Cs

Figure 7: Histogram for 60Co

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Figure 8: Histogram for 22Na

Figure 9: Histogram for unknown source

4.3 Tables

Table 2 shows the percentage errors arrived at by comparing Na22 peak 1 and peak 2 withcalibration line.

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Energy (MeV) Energy error (MeV)

Cs-137 0.6564 0.0030Co-60 peak 1 1.1746 0.0019Co-60 peak 2 1.3316 0.0025Na-22 peak 1 0.5105 0.0038Na-22 peak 2 1.2727 0.0022Unknown 1 0.6648 0.0030

Table 1: Experimentally determined energies and their errors

Energies

0.66201.17301.33300.51201.2700

Table 2: Theoretical energies (MeV)

Method 1 Method 2

Na peak 1 0.75 0.29Na peak 2 0.18 0.21

Table 3: Error comparison (percentage error)

Compton edge energy

Cs-137 0.411Co-60 0.904Na-22 0.288Unknown 0.437

Table 4: Compton edge energies (MeV)

Calculated energy

Cs-137 0.4777Co-60 1.173 MeV decay 0.9632Co-60 1.333 MeV decay 1.1186Na-22 annihilation peak 0.3416Na-22 1.27 MeV decay 1.0573

Table 5: Compton edge theoretical energies (MeV)

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Min value Max value

Cs-137 0.3588 0.4492Co-60 0.8114 0.9434Na-22 0.2736 0.3214Unknown 0.3091 0.4649

Table 6: Compton edge min and max energies (MeV)

Uncertainty (MeV)

Cs-137 0.018Co-60 0.027Na-22 0.0098Unknown 0.032

Table 7: Compton edge uncertainties

Peak Energy value (MeV)

Cs137 backscatter 0.2069+/-0.0079Co60 other 1 0.2417+/-0.0071Co60 other 2 0.895+/-0.016Na22 other 0.2000+/-0.0071

Unknown other 1 0.207+/-0.013Unknown other 2 1.173+/-0.062

Table 8: Other peaks

5 Analysis

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5.1 Energy resolution function

Figure 10: Energy resolution function for the NaI detector

Figure 11: Energy resolution function for the NaI detector (str line)

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6 Discussion

6.1 Discussion of histogram features

6.1.1 137Cs

Photopeaks

The photopeak of 137Cs had a mean value of 0.6564 0.0030 MeV.Compton edge

The compton edge for 137Cs is at 0.411 0.018.The predicted value is at 0.4777. This does not agree with the measured value within the aboveuncertainty.

Backscatter peak

The backscatter peak for 137Cs is at 0.2069 0.0079 This makes sense, because accordingto Gilmore and Hemingway the backscattered gamma rays have an energy of 0.200 to 0.300MeV.

6.1.2 60Co

The first and second photopeaks of Co60 are at 1.1746 0.0019 MeV and 1.3316 0.0025 MeVrespectively.

The Compton edge is at 0.904 0.027. The predicted value is at 0.9632 or 1.1186 MeV,depending on which decay mode we look at. Hence the values do not agree.

6.1.3 22Na

The second and third peaks of 22Na are at 0.5105 0.0038 MeV and 1.2727 0.0022 MeVrespectively. The second peak is an electron capture peak and agrees with the expected valueof 0.511 MeV. The third peak is a photopeak and agrees with the expected value of 1.274MeV.

The first peak is a backscatter peak and falls within the broad range of 0.200 to 0.300 MeV.

The Compton edge is at 0.2884 0.0098. The predicted value for the Compton edge is at1.0573 MeV and hence the values are far from agreeing.

6.1.4 Unknown source

The only clearly visible photopeak of the unknown source is at 0.6648 0.0030 MeV.The Compton edge is at 0.437 0.032Sources that match this within uncertainty:

Cs-137 gives off photons of energy 0.6617 MeV which falls outside the uncertainty range for theunknown source. However, there is only a 2/3 chance of the true value lying with the uncertainty

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range so it is still possible that Cs137 was contained in the unknown source (especially sincethe values are close to agreeing).

Zn-65 decays by electron capture and the average energy of the photons it it releases is 1.115MeV [1]. There is a very faint peak on the histogram at 1.173 0.062 which suggests that theunknown source may have contained Zn-65.

The other nuclides with decay energies that fall within the above ranges have half-lives that aretoo short for their use in this experiment to be practical.

6.2 Background when no source is present

Gamma rays are still detected even when no obvious source is present. This backgroundradiation can come from various sources:

High energy natural background [6]: high-energy gamma rays, cosmic ray muons

According to Wikipedia [7] the biggest source of natural background radiation is radon inair, where the radon is released from the ground.

6.3 Resolution function of NaI detector

Source: ORTEC manual [8].

We were asked to devise a scheme to measure the width E in a reproducible way. Thiswas done for us by the software Origin, which determined the values of for our Gaussian fits,where is a measure of the spread of the Gaussian distribution.

FWHM= 2

2 log 2 = 2.35.

Therefore since sigma is linearly dependent on the FWHM and the values of sigma were readilyavailable, I plotted /energy versus energy to determine the resolution function of the equip-ment. I could do this since we were only looking at the way the parameters depended on eachother and not their absolute values.

One can see from the graph that as the energy increases, the spread of the gaussians (relativeto the energies of their means) decreases. This suggests that the resolution of the detectorimproves with increased energies of gamma rays.

A possible reason for this is that the effect of background radiation becomes comparatively lessat higher energies, since background radiation mostly occurs at low energies.

According to [10] the average energy to produce a photon in NaI due to 0.662 MeV gamma raysis on the order of 10 eV. Since a single gamma ray has an energy of the order of 1 MeV, onegamma ray can produce on the order of 100 000 photons. This number fluctuates and leadsto inconsistencies in the amplitudes of the voltage pulses generated by the photomultiplier andhence leads to a non-zero peak width.

Sources of uncertainty in the calibration

The uncertainty in individual mean values was small and hence contributed little to the uncer-tainty in the slope and intercept of the best fit line. The main source of uncertainty was the

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spread of the different values. This spread could be due to a number of things:

Different energies of gamma rays may have interacted with the detector in different ways,causing more or less of a gamma rays energy to be absorbed.

There could have been fluctuations in background radiation.

6.4 Relative usefulness of parts of the spectrum

The photopeaks were most useful for calibration because their means were clearly defined andthose means corresponded to the full decay energies of the incoming gamma rays. It would havebeen difficult to pin down a value for the position of a Compton edge, and we would have hadto carry out additional calculations to determine the full energy of the incoming gamma raysfrom that.

7 References

[1] Radionuclide safety data sheet. Stanford University. Accessed 22 April 2014, http://www.stanford.edu/dept/EHS/prod/researchlab/radlaser/RSDS_sheets/Zn-65.pdf

[2] Gilmore, G. and Hemmingway, J. Practical Gamma Ray Spectroscopy, 2nd edition. Wiley(2007).

[3] Na22 decay scheme image modelled on image at http://flippedclassroom.net/fsi/summer/projects/2009/DaltonAlex/.

[4] Decay scheme for Cs-137. Wikipedia. http://en.wikipedia.org/wiki/File:Cs-137-decay.svg.Accessed April 2014.

[5] Decay scheme for Co-60. Wikipedia. http://en.wikipedia.org/wiki/File:Cobalt-60m-decay.svg

[6] http://www.physics.rutgers.edu/grad/506/detectors-00326398.pdf

[7] en.wikipedia.org/wiki/Background_radiation

[8] ORTEC. Experiment 3: Gamma-Ray Spectroscopy Using NaI.

[9] http://www.physics.uoguelph.ca/~detong/phys3510_4500/outlines/highres.pdf

[10] http://jjap.jsap.jp/link?JJAP/45/6420/

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Introduction and AimTheoretical backgroundThe photoelectric effectCompton scatteringPair productionBackscatter peaksElectron capture peaksDecay schemes for nuclei involved in this experiment

Equipment and MethodsResultsCalibration functionHistogram plotsTables

AnalysisEnergy resolution function

DiscussionDiscussion of histogram features137Cs60Co22NaUnknown source

Background when no source is presentResolution function of NaI detectorRelative usefulness of parts of the spectrum

References