Physics 334

Advanced Experimental Physics

Angular Correlation of GammaRays

Author:

Mohamed Abdelhafez

April 28, 2015

Abstract

We study the angular correlation of gamma rays produced by 22Naand 60Co using two NaI photomultiplier tubes and a coincidence cir-cuit. The decay of both include the emission of two gamma rays thatare correlated in angles. Theoretical analysis predicts that two gammarays of the same energy are simultaneously produced back to back (atan angle of 180◦ of each other) in the case of 22Na. As for 60Co, thetwo gamma rays have different energies but they are almost simul-taneous, and the angular correlation between them is dominated bythe 4-2-0 quadropole-quadropole transitions of Ni60 which 60Co decaysprominently to. Our measurements confirm the back to back emissionof Na gamma rays while the experimental fit for the Cobalt sourcegives the expected correlation function within the fit errors.

1 Introduction

Decay of radioactive sources often include the emission of gamma rays byseveral mechanisms. The directions and energies of emitted photons dependon the energy, momentum and spin of the source atoms and hence can beanalyzed to extract information about the source. Here we investigate thedecay processes of both 22Na and 60Co and the angular correlation of theiremitted gamma rays.

1.1 22Na decay and angular correlation

Our first source is 22Na which has the decay scheme shown in Figure 1 [1]. Itmainly decays through either positron emission (90% of the time) or electroncapture (10% of the time) to the 2+ excited state of Ne22 which eventu-ally decays to the ground state of Ne through the emission of a 1.27 MeVgamma ray. There is also a small chance (around 0.05%) of a direct decayfrom Na to the ground state of Ne. The positron emitted 90% of the timecombines with an electron in the source to form a positronuim atom that hasa binding energy of 6.8 eV and a lifetime that is dependent on the spins ofits constituents. If the positron is captured by an electron having the samespin of it, the resulting positronium has a total spin of 1 and is called theortho-positronium, the triplet state denoted by 3S1. This state has a meanlifetime of about 10−7 s and its decay is a pair annihilation process thatproduces an odd number of photons to conserve spin. It can not decay to a

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single photon since that will never conserve momentum, which we assume tobe close to zero since the positronium is almost at rest. So, the major decayof the ortho-positronium is into 3 photons.On the other hand, if the spin of the positron is anti-paralel to the spin of theelectron, the atom has a total spin of zero and is called the para-positronium,the singlet state denoted by 1S0. The singlet state is much more short livedthan the triplet state, with a mean life time of 10−12 s. To conserve spin, itonly decays to an even number of photons, and it mainly does decay to twoback to back photons assuming the positronium is at rest.

Figure 1: The nuclear decay scheme for 22Na

The singlet state has a total spin angular momentum of 0. So the photonsmust have a total spin of 0 to conserve spin angular momentum. This canonly happen if an even number of photons is produced since each carries aspin of 1. However, the triplet state has S=1, so only odd number of photonscan match that condition. It can not decay to a single photon because ofmomentum conservation.It is not possible for any of the two states to produce just one photon. Onephoton can not have a linear momentum of zero while both para and orthopositronium is almost at rest so the momentum should be zero. Even if itweren’t at rest, a single photon can not conserve both energy and momentumconservation of a two particle atom. So, there must be more than one photonto conserve both momentum and energy.

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Although the creation of para and ortho positronium states should have thesame probability, the process of spin flipping ensures that we only observethe decay of the para positronium. Spin flipping happens because one photoncan invert the spin of the electron in the positronium and this process hasa lifetime of around 10−9 s. This means that spin flipping can rarely turna singlet into a triplet since the singlet has a shorter lifetime, so it decaysbefore it flips. However, the lifetime of the triplet state is long enough forspin flipping to occur and hence we can only see the para positronium decay.So, the main observation coming from a 22Na should be a simultaneous emis-sion of two photons which have to produced back to back to conserve mo-mentum. Each photon has an energy of almost 511 keV to conserve energy.

2Ephoton = 2mec2 + Ebinding (1)

Ephoton = 511keV − 6.8/2eV (2)

Ephoton ≈ 511keV (3)

The two photons must be back to back so that their momenta cancel eachother because the positronium is almost at rest. The angle between themmust be 180◦.

To sum up, the angles of gamma rays of a 22Na decay are correlated. Ifwe define w(θ) to be the angular correlation function of a photon emitted atan angle θ, then for a 22Na source, it is given by

w(θ) = δ(θ − π) (4)

Of course, in reality, due to finite detector widths and accidental simultaneousemission of gamma rays at angles other than pi, the behavior will not beexactly a delta function. Hence, this model should be modified to accountfor these effects.

1.2 60Co decay and angular correlation60Co decays mainly to a 2.507 MeV 4+ excited state of Ni60 through β− de-cay with a lifetime of 5.26 years. It has been observed that the quadropole-quadropole or 4-2-0 mode is the most dominant mode of decay where theNi60 4+ emits a 1.173 MeV photon to reach an intermediate state 2+. Thisintermediate state decays quickly to the ground state emitting another 1.333

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MeV photon. Hence the decay diagram of 60Co should look like Fig 2 [1].

Figure 2: The nuclear decay scheme for 60Co

The intermediate 2+ state is extremely short lived (lifetime around 8x10−13

s), hence both gamma rays can be considered to be simultaneous for mostdetectors within their resolving time (usually longer than 1 ns). Figure 2shows that we expect to see two peaks in the spectrum around 1.17 and 1.33MeV.

Since the decay includes a cascade of photons between different spinstates, we must carefully account for their spins to study the angular corre-lation. A general formula for w(θ) is given by

w(θ) = 1 +l∑

i=1

aicos2i(θ) (5)

where 2l is the order of the lowest multipole in the photons cascade [2]. Hence,the quadropole-quadropole 4-2-0 transition will be having 2 terms in thesummation. The coefficients for the 4-2-0 mode are theoretically calculated[2]. They are given by

w(θ) = 1 +1

8cos2(θ) +

1

24cos4(θ) (6)

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Our task is to experimentally probe both 22Na and 60Co decays and com-pare their experimental angular correlation functions to equations (4) and(6) respectively, within the limitation of having finite detector size. To doso, we are using the coincidence experimental setup discussed in Sec 2.

2 Experimental Setup

Our experimental setup can be divided into three parts: the source, thedetector and the signal processing (coincidence) modules.

2.1 The radioactive source

1. 22Na:The 22Na source used has an activity of 300 µCi. The active sodiummaterial is sealed in the tip of a rod and is centered between the twodetectors. The diameter of the rod is 12.75 mm and the distance be-tween it and each detector is 19.5± 0.5 cm.To get a rough idea of how much total counts will happen at a detectorusing that source, let’s assume each sodium decay results in the emis-sion of two photons, so we have 300 × 3.7 ×104 photon pairs emittedper second. Since the diameter is much smaller than the distance tothe source, we can approximate the source as a point source. This to-tal number of photon pairs are emitted each second and the portionof them hitting the detector is the area intersection of the detectorarea and the sphere centered at the source with radius at the detectordivided by the total area of the sphere. So, if we approximate the in-tersection area to be the circular area of the detector, which we haveto be 24.63 ×10−4m2, then we expect to see number two photons atthe detector after time t given by

t =surface area of sphere of photons

Activity× detector area= 17.5µs. (7)

This translates into a rate of 57215 counts/sec. However, our source isdated May 2002, so it has been decaying for 13 years. With a lifetime of2.6 years, we see that the activity actually drops to 1

25of its value, which

gives an expected rate of 1787.97 counts/sec. This is actually close tothe experimental rate we got at one detector which had an average of

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1386.82 counts/sec. Of course, the experimental rate is smaller sincenot each decay corresponds to a pair of photons and the detectors donot have 100% efficiency.

2. 60Co:

We used a source of 60Co with activity of 250µCi, lifetime of 5.26 yearsand dated May 2003. It has a similar shape but its rod diameter is15.9 mm. The source is placed at the same position centered betweenthe detectors. Repeating the same calculation for the expected countrate, we get an expected count rate of 9807.72 counts/s compared tothe experimental value of 6434.73 counts/s.

2.2 The Detectors, NaI-PMT:

We use a NaI scintillator as our main detector followed by a photomultipliertube (PMT) which amplifies the signal to be ready for processing. We usetwo of this NaI-PMT detectors, one of them is fixed at some angle, and theother is movable in a carriage around a circular track as shown in Fig 3.

2.2.1 NaI(Tl)

NaI(Tl), doped with Thallium, is the most commonly used scintillator mate-rial in gamma ray sepctroscopy. Its job is to convert incident photons on itto a larger light signal. Gamma rays incident on it interact with the atoms inthe NaI crystal and produce more photons. The intensity of produced lightmust go linearly with the incident gamma ray energy to reflect it for lateranalysis. NaI(Tl) is preferred mainly because it gives a larger light yield thanthe other scintilators for gamma rays at room temperature [3].The detectors have a circular area with a diameter of 5.6 ± 0.1 cm.

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Figure 3: The source mounted between two NaI-PMT detectors, one fixedand one movable.

2.2.2 PMT

The PMT is used to turn light produced by the NaI(Tl) detector into anamplified electric signal. The basic PMT components are shown in Fig 4 [3].

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Figure 4: Photomultiplier Tube (PMT)

First a photocathode interacts with the photons and produces electronsof a proportional energy. These electrons can be emitted by three main dif-ferent mechanisms: the photoelectric effect, which is dominant in low gammaenergies up to several hundereds KeVs, Compton scattering and pair produc-tion which requires energies in the range of few MeVs.

The photoelectric effect is usually the one with the best reflection of theincident peak since in the photoelectric effect, the total energy of the incidentphoton transfers to the ejected electron. Meanwhile, Compton scattering willcause the ejected electron to have a wide range of energies based on the angle

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of the incident photon and its energy. That’s why the typical spectra of PMTsshow a wide plateau at lower energies corresponding to Compton scattering[4]. The Compton scattering for a gamma ray with a certain energy has toend at a certain maximum energy delivered to the electron, known as theCompton edge which is less than the energy of the incident photon Eγ [4].

Compton Edge =2E2

γ

mec2 + 2Eγ(8)

Also, some of the gamma rays will backscatter with any material aroundthe detector, and hence will be detected with much less energy. Therefore, atypical gamma ray spectrum will first have a backscattering peak, followedby a Compton plateau that ends at the Compton edge, then the photopeakproduced by the photoelectric effect, which is usually a gaussian centered atthe energy of the photon, as shown in Fig 5 [4].

Figure 5: A typical gamma ray spectrum

After the photocathode emits electrons, they get amplified through a se-ries of dynodes in an electron multiplier module. A final amplified electricsignal is generated in both the final dynode (positive signal) and anode (neg-ative signal) as in Fig 4. The output gets spread as a gaussian because ofstatistical path differences between electrons and the FWHM of the pulserepresents the resolution time of the device [3].

The detector is powered by a high voltage supply that provides negativevoltage in the range of -2 to -2.5 KV.

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2.3 Coincidence Circuit

It is a series of modules designed to count events happening in the two de-tector only if they are simultaneous. The anode signal from each detector isconnected to a separate CF discriminator which filters the events from thePMT to only events within a specified range of energies. This is how we canlimit the counts to the events around the relevant peaks in our radioactivesources spectra.The output of the CF discriminator, which is pulses with uniform shape, isconnected to a scaler, to count the total number of events within the specifiedrange without the coincidence limitation. More importantly, the output ofthe CF discriminator is also connected to the rest of the coincidence circuit.A Time to Amplitude Converter (TAC) is used to make sure the two signalshappen at the same time. This is done by delaying one of the CF discrimi-nator outputs using an analog delay module (up to 63 ns of delay) and theother is not delayed. The delayed signal goes into the stop input of the TACwhile the other CF signal goes into the start input. The TAC then producesa signal at an amplitude proportional to the specified delay only if the twosignals arrive simultaneously. Note that adding a delay is necessary sinceotherwise with time difference of 0, simultaneous events will appear as a zeroamplitude TAC output signal.The output of the TAC is then integrated using a Pulse Height Analyzer(PHA) and displayed on a computer.An oscilloscope is also used to have a look at the different signals at inter-mediate stages.

The coincidence circuit schematic is shown in Fig 6.

Figure 6: A schematic of the coincidence circuit

More information about the models of equipment used is presented in

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Appendix A.

3 Procedure

3.1 The dynode and anode signals

Using first the 22Na source, we adjust the high voltages applied to each PMTto generate almost equal amplitude anode signals. The values used were 2 and2.08 KV. Analyzing using the scope, the anodes produce a negative signalwhenever a photon is detected. The dynode signal is similar but positiveand with lower amplitude since it is the signal before the final acceleration toreach the final anode. The dynode signal had a peak of 0.96 V and a widthof 282.3 ns while the anode signal had a peak of 1.66 V and a time width of325.6 ns as shown in Figs 7 and 8. Both peaks of the two anodes have beenmade equal by adjusting the power supply.

Figure 7: The anode signal capturing one event

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Figure 8: The dynode signal capturing one event

3.2 Generating the spectrum

Using the PHA unit, we get the following experimental spectrum of 22Nausing the amplified dynode signal of one of the detectors. The spectrumwith elapsed time of 20 minutes is shown in Fig 9.

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Figure 9: The spectrum of the Na source

The curve shows the Compton plateau followed by the two expected pho-topeaks at 511 keV and 1275 keV. Calibrating the values of the curve onthe 511 keV gives that the 2nd peak is at 1195 KeV which is close to theexpected value, so we are sure that the first peak is the peak we are afterproducing the two simultaneous gamma rays.

3.3 Selecting the relevant peak

The next step is to use the CF discriminator to limit our signals to the oneswhich are around the 511 keV peak. This is done by using the SCA (SingleChannel Analyzer) output of the CF discriminator as an indicator of having asignal that is within the limits set by the two knobs in the CF discriminator.The SCA output looked like a rectangle pulse of width 2 µs and height of6 V which happen simultaneous to the detection of a filtered event by theCF. We used the fact that we have two simultaneous signals from the samedetector, the anode and dynode signals to use one of them as a timing clockcontrolling the other one. The SCA output of one CF discriminator whoseinput is the anode signal of a PMT is connected as the gate input to thePHA. The gate input controls which events are counted by the PHA, onlyinputs within the signal of the gate input will be counted in the PHA. Thedynode signal of the same PMT is amplified and then connected to the directinput of the PHA so that we can select the relevant peak of it by adjusting

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the min and max knobs of the CF. This process is shown in block diagramin Fig 10.

Figure 10: Block diagram of the circuit used to bracket the relevant photo-peak using the CF discriminator

The SCA output is approximated as a square wave as shown in Fig 11.As the figure shows, the dynode signal indeed occurs within the time of theSCA pulse.

Figure 11: The SCA output of and the associated dynode signal (with noamplification)

Then this section is completed by performing the process in Fig 10 forthe two PMTS for the 22Na source with adjusting the low and high thresholdof the two CF discriminators to only accept the relevant peak events.

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3.4 Time calibration of the TAC

After selecting events of the wanted peaks, the outputs of the two CF dis-criminators need to be correlated using the TAC as highlighted by Fig 6. Todo so, the TAC needs to be time calibrated with the PHA on the computer.So, we connect one CF output signal directly to the start of the TAC, andconnect a delayed version of some known delay time to the stop signal asillustrated in Fig 12.

Figure 12: A block diagram of the circuit used to calibrate the TAC output

Then we can calibrate the TAC output using the known delay. We useddelay times of 16, 32 and 40 ns to calibrate the output.

We also note that the CF outputs used to operate the TAC have stan-dardized shape for all events. Any event captured within the CF thresholdshas the same width and height, which increases the timing precision for theTAC. The uniform CF output shape observed is shown in Fig 13. They havea width of around 10 ns and an amplitude of 0.75 V.

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Figure 13: The uniform output of the CF discriminator for any countedevent

After the calibration, the TAC becomes ready to collect coincidence data.

The same procedure is used with the 60Co source. The spectrum of itis found to be as shown in Fig 14. The two photopeaks occurring after theCompton plateau have calibrated energies of 1.17 and 1.3 MeV, matchingthe theoretical decay scheme in Fig 2.

Figure 14: The obtained spectrum for 60Co

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4 Data and analysis

4.1 Na source

A delay of 63 ns is used for the coincidence circuit and coincidence countsare collected for angles around 180◦. Since the data will follow a Poissondistribution, the error of N counts is

√N . So, to obtain 1% statistics, we

need to collect at least 10000 counts for each angle. The counts for anglesbetween 165◦ and 180◦ along with our accidental data at 90◦ using a 63 nsdelay and counting for 200s is shown in Fig 15. Each graph is fitted to aGaussian and then the FWHM is calculated for each. The net counts andFWHM of each angle is tabulated in Table 1.

Angle(◦) Delay (ns) Net counts Time (s) ± 1s FWHM (ns)180 63 66091 ± 257.08 200 2.6959 ± 0.01049

177.5 63 62255 ± 249.51 200 2.7834 ± 0.01116175 63 45842 ± 214.11 200 2.7269 ± 0.01274

172.5 63 29231 ± 170.97 200 2.8358 ± 0.01659170 63 13992 ± 118.29 200 2.8211 ± 0.02385

167.5 63 3701 ± 60.84 200 3.2474 ± 0.05338165 63 814 ± 28.53 200 5.2355 ± 0.18350

162.5 63 686 ± 26.19 200 5.4246 ± 0.2071190 63 397 ± 19.92 200 7.62 ± 0.38244

Table 1: Counts and FWHM for different angles for the Na source

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(a) 180◦ (b) 177.5◦

(c) 175◦ (d) 172.5◦

(e) 170◦ (f) 167.5◦

(g) 165◦ (h) 90◦, accidental coincidence

Figure 15: Counts vs delay time for different angles for the Na source using63 ns delay

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Using the values we got for the width of each peak, the weighted averagevalue for the FWHM is 2.995 ns with a standard deviation of 0.105 ns. Thisis our approximate value for the resolving time of the experiment. Any twoevents within that time are considered simultaneous. This of course causesaccidental events to be counted as simultaneous. To get a theoretical estimateof that accidental rate, we use the equation

Naccidental = 2τN1N2 (9)

where τ = 2.995 ± 0.105 ns is the resolving time and N1 and N2 are thesingles rates for the two PMTS [5]. Using our data for the singles rates,N1=1184.92 ± 10.31 Hz and N2=1386.82 ± 12.21 Hz, we get an accidentalrate of 0.0098 ± 0.0004 Hz.However, the measured accidental rate is 1.985 ± 0.1 Hz. This big discrep-ancy might be caused by other processes than the 511 keV emission whichwe limit our scaler counts to.So, we take the experimental data at the 90◦ angle to be our accidental data.Subtracting them from each data point gives us the corrected counts.

To compare our results to the theoretical result of equation (4), we mustmodify it to account for the fact that our detectors have finite dimensions.We will account for that first by making a 2D analysis of our detectors. Givenour measurements of the detector sizes and approximating the source to beof negligible thickness, our analysis in Fig 16 shows that we should expectto get no coincidence counts after an angle deviation of 16.34◦ ± 0.46◦. Thisagrees with our data since our count rate significantly drops at angles furtherthan 163.66◦.

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Figure 16: 2D analysis of our detectors to predict the limiting angles of theactual correlation function

In order to predict the actual angular behavior with the finite detectorsize, we performed a Monte Carlo simulation with the dimensions of theapparatus. The experimental angular correlation function is compared tothe Monte Carlo predictions in Fig 17. The errors have been propagatedusing the standard formula.

Figure 17: The corrected experimental angular correlation function ofsodium-22 vs Monte Carlo simulation results to account for detector sizes

we see that our data is consistent with the Monte Carlo simulation andhence the theoretical prediction of equation (4) within our modifications.

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The Monte Carlo prediction is higher at lower angles because the efficiencyof our detectors decreases for photons reaching at an angle to the detector.

4.2 Co Source

Since the correlation function is expected to have significant values at allangles, we took data for angles between 90 and 180 degrees with 10 degreesresolution with delay time 63 ns for 750s. The cobalt data are shown in Table2. The graphs are shown in Fig 18 with their Poisson error bars.

Angle(◦) Delay (ns) Net counts Time (s) FWHM (ns)180 63 12274 ± 110.79 750 1.8354 ± 0.01657170 63 11972 ± 109.42 750 1.7865 ± 0.01633160 63 11846 ± 108.84 750 1.8167 ± 0.01669150 63 11540 ± 107.42 750 1.8120 ± 0.01687140 63 11508 ± 107.28 750 1.8424 ± 0.01717130 63 11367 ± 106.62 750 1.8123 ± 0.01700120 63 11073 ± 105.23 750 1.8261 ± 0.01735110 63 11073 ± 105.23 750 1.8348 ± 0.01744100 63 10894 ± 104.37 750 1.8575 ± 0.0178090 63 10428 ± 102.12 750 1.842 ± 0.01804

Table 2: Counts and FWHM for different angles for the Co source

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(a) 180◦ (b) 170◦

(c) 160◦ (d) 150◦

(e) 140◦ (f) 130◦

(g) 120◦ (h) 110◦

(i) 100◦ (j) 90◦

Figure 18: Counts vs delay time for different angles for the Co source using63 ns delay

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The resolution time is then calculated to be 1.8266 ± 0.02 ns.So, the accidental rate is calculated using equation (9) to be 0.14 ±

0.0016 Hz. Using that we correct our counts. In addition, a fit was made tofit the corrected experimental data to a function 1 + a1cos

2(θ) + a2cos4(θ).

The fit gives values for a1 to be 0.2431 ± 0.0548 and a2 to be -0.0884 ±0.0689 with χ2=0.0041 and an adjusted R squared value of 0.9996. But tobetter compare theses results to the theoretical model, we have to accountfor the smearing of the correlation function caused by the detector size. A2D numerical integration convolving the theoretical w(θ) with the effect ofrotating the finite detector was performed to calculate the effect of smearingon the angular correlation function. The result of integration was fitted againto the same function. The result of the fit is close the original theoreticalfunction, so we see that the detector sizes did not significantly affect thecorrelation function. The fit gives a1 of 0.1247 compared to the original0.125 and a2 of 0.0396 compared to the original 0.0833.To conclude our comparison, the corrected data are drawn with its fit andwith the integrated correlation function in Fig 19.

Figure 19: W(θ) for the cobalt source as corrected experimental data vs itsfit and the theoretical model

Although our measurements are not perfectly matching the prediction,we see that most of the theoretical points lie within our error bars of thefit. We also still get the predicted shape and the value for the measuredanisotropy A = w(180◦)−w(90◦)

w(90◦)of 0.1788 ± 0.0016 is within 7.26% error of the

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theoretical value of 0.1667.

The noticeable difference between the fit parameters and the theoreti-cal parameters may have occurred because of taking the data over differentdays and the conditions for the apparatus may have changed. Noticing thatreadings of angles from 120◦ to 180◦ were taken on a separate day than theremaining data , we do a check by fitting the data from a single day only.The fit gives a1 of 0.1796 ± 0.055 and a2 of -0.0324 ± 0.063 with an adjustedR squared value of 0.9999. We see now that the parameters a1 and a2 arecloser to the theoretical values. The new curves are shown in Fig 20.

Figure 20: W(θ) for the cobalt source for data taken in a single day ascorrected experimental data vs its fit and the theoretical model

Therefore, we confirm that the Na source matches the expected deltaangular distribution function and the cobalt data is consistent with the 4-2-0decay scheme withing our error estimates.

5 Possible Sources of Error

Although our data matches theory within our estimates of error, there weremore sources of error that can be worked on for future work.

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For both sodium and cobalt sources, a 3D solid angle approach to modelthe detectors will help in decreasing the errors.Especially for the sodiumsource, using smaller detectors and sources will enhance the accuracy of mea-suring the correlation function. Also, increasing the time of collection for eachangle to make each channel in the gaussian peak reach 1% error instead offocusing on the net counts in the peak will decrease the statistical error.

For the cobalt source, we did not have a concrete way to measure theexperimental accidental rate since we have non-trivial counts at all angles.One way to measure that will be by delaying one of the two PMT outputsignals such that the two simultaneous signals are not counted as coincidentand then measuring the remaining counts.

One of the reasons why accidental counts happen in the Na source is thatthe decaying positronium might not be at rest. It can have some kinetic en-ergy in the range of the binding energy of it which causes the angle betweentwo gamma rays to be different from 180◦.

In addition, one main source of error is taking data for the same sourceon different days to make sure the setup did not change. Also, to increasethe precision of our data, data points can be taken with small spacing be-tween each other. Taking data with a step of 1◦ will decrease the statisticaluncertainty which causes the fit to have statistical fluctuations.

6 Conclusion

Our measurements show that the gamma rays emitted from each of the 22Naand 60Co sources are correlated in angles. Their correlation function canbe theoretically predicted as in equations (4) and (6), respectively. Ourexperiment results agree to the predictions within our windows of error. Toget more accurate experimental results, more careful data collection measuresshould be applied. For example, data can be taken for longer periods andwith smaller size detectors.

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Appendix A: Coincidence Circuit Equipment

• ORTEC 583B Constant Fraction Differential Discriminator, Fig 21

Figure 21: The CF discriminators

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• 720 Mech-Tronics 20 MHz Scaler, Fig 22

Figure 22: The Scaler

• Fluke 415B High Voltage Power Supply, Fig 23

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Figure 23: The High voltage power supply

• 500 Mech-Tronics Amplifier, Fig 24

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Figure 24: The amplifier

• Delay unit, Fig 25

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Figure 25: The delay unit

• ORTEC 467 Time to Pulse Height Converter/SCA, Fig 26

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Figure 26: The TAC

• Tektronix TDS210 Digital Oscilloscope, Fig 27

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Figure 27: The oscilloscope

References

[1] Curran D. Muhlberger. Experiment ix: Angular correlation of gammarays. University of Maryland, College Park, 2008.

[2] E. L. Brady and M. Deutsch. Angular correlation of successive gamma-rays. Phys. Rev., 78:558–566, Jun 1950.

[3] Glenn F Knoll. Radiation detection and measurement. John Wiley &Sons, 2010.

[4] Gamma-ray spectra. Department of Physics University of Toronto, 2008.

[5] Jr Fort A. Veser. Gamma-gamma angular correlation in the decay ofcobalt 60. Master’s thesis, United States Naval Postgraduate School,1960.

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