Gamma-Ray Spectroscopy - Trinity College Dublinsheridev/labs/gammar.pdf · Gamma-Ray Spectroscopy...

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Gamma-Ray Spectroscopy Evan Sheridan with Niall Robertson 11367741 November 25th 2013 Abstract γ -ray spectroscopy is investigated using a Cs 137 , Co 60 and Na 22 coupled with a scintillator, photocathode, photmultiplier and the Maestro software. Using Cs 137 , the dependence of H 0 , the γ -ray energy, on V is theoretically deduced as H 0 V n . This dependence is verified theroet- ically with n, the dynode number, being found as 7.78477 ± 0.02261. The dependence of FWHM on V is also investigated and verified. The averagre resolution of the the detector with a varying PM using Cs 137 voltage is found to be ¯ R =0.070525 ± 0.004765908. The energy spetra of Cs 137 , Co 60 and Na 22 are obtained and analysed, illustrating the various ways γ -rays intereact with matter. Using the Na 22 and Co 60 spectra the efficiency of the detector is found to be 18% at 511 keV and 4% (using Na 22 )in the interval 1.17 MeV and 1.32 MeV. Finally the abundance ratio, half life and branch ratio is are found for K 40 and compared against the theoretical values given . 1

Transcript of Gamma-Ray Spectroscopy - Trinity College Dublinsheridev/labs/gammar.pdf · Gamma-Ray Spectroscopy...

Page 1: Gamma-Ray Spectroscopy - Trinity College Dublinsheridev/labs/gammar.pdf · Gamma-Ray Spectroscopy Evan Sheridan with Niall Robertson 11367741 November 25th 2013 Abstract 137-ray spectroscopy

Gamma-Ray Spectroscopy

Evan Sheridan with Niall Robertson11367741

November 25th 2013

Abstract

γ-ray spectroscopy is investigated using a Cs137 , Co60 and Na22 coupled with a scintillator,photocathode, photmultiplier and the Maestro software. Using Cs137 , the dependence of H0 ,the γ-ray energy, on V is theoretically deduced as H0 ∝ V n. This dependence is verified theroet-ically with n, the dynode number, being found as 7.78477±0.02261. The dependence of FWHMon V is also investigated and verified. The averagre resolution of the the detector with a varyingPM using Cs137 voltage is found to be R = 0.070525±0.004765908. The energy spetra of Cs137

, Co60 and Na22 are obtained and analysed, illustrating the various ways γ-rays intereact withmatter. Using the Na22 and Co60 spectra the efficiency of the detector is found to be 18% at 511keV and 4% (using Na22 )in the interval 1.17 MeV and 1.32 MeV. Finally the abundance ratio,half life and branch ratio is are found for K40 and compared against the theoretical values given .

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Introduction and Theory

In this experiment we primarily deal with how γ-rays interact with matter and how their inter-action can reveal the properties of radioactive elements. When radioactive atoms decay by betaemission γ-rays are emitted. In this experiment we deal with Cs137 , Co60 and Na22 , where intheir energy spectrum well defined peaks can be found at the corresponding γ-ray energy. Theγ-ray spectrometer enables us to record these energy spectra appropraitely and consists of 3 mainparts: the scintillator, photomultiplier and multichannel analyser.The γ-ray undergoes a number of transitions. After beta emission it can undergo Compton Scatter-ing on the Lead Shield and in the scintillator giving the γ-ray photon a defined energy. Interactionsin the scintillator(the production of electron hole pairs and the subsequent recombination of these)induce Photoelectric Absorption and subsequently lead to photons incident on a photocathode.These photons may then excite electrons which are accelerated towards the photmultiplier whereat each dynode the number of electrons will be multiplied by the time they reach the anode. Theseadditional electrons then produce extra charge on the anode that give rise to a voltage pulse thatcan be interpreted by the multichannel analyser.The spectra can then be produced using the Maestro software and the decay series of the radioac-tive elements can be interpedted. Instead of well defined peaks as should be expected there arebroad peaks which are a result of statistical fluctuations at each stage of the process before thevoltage pulse is induced.

Interaction of γ-rays with matter

Primariliy γ-rays can interact with matter, much the same way as light does, and we consider 2ways in whcih it does so in this experiment :

•Photoelectric Absorption

•Compton Scattering

Photoelectric Absorption

We consider the γ-rays incident on the scintillator. The γ-ray photon ejects an electron from oneof the shells of the thallium atoms in the scintillator with energy :

Ee = Eγ − EbNow the emission of this electron leaves a vacacny in the thallium atom that can be filled by afree electron. This free electron in turn emits a photon of energy Eb and this photon undergoesphotelectric absorption in another thallium atom exciting another electron with energy Eb . Thecombined energy of these two electrons is Eγ , giving rise to the “total energy peak” in the energyspectrum.

Compton Scattering

Now when we talk about Compton Scattering we are talking about the γ-ray photons being scat-tered on the lead shield by electrons there. So, the source emits γ-rays and then it collides withelectrons on the shield. Only γ-rays along a straight line to the scintillator will reach the scintil-lator so we only consider γ-ray photons that have been scattered through 00 or 1800. Intuitevlythe γ-rays that are scattered through 1800 will have less energy because it actually scatters andimparts some of it’s energy to an electron in the shield.

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The γ-ray photons that are scattered through 1800 give rise to a phenomena called the “Backscat-tering peak” in in the energy spectrum (which is given by a lesser enegy because the excitedelectrons due to these γ-ray photons in the scintillator will have a less energy) while the otherγ-ray photons give rise to the “Compton edge”, whereby electrons in the scintillator will acquiremaximum energy from the incident unscattered γ-ray such that there will be a sudden dip justbefore the “total energy peak” due to photoelectric absorption in the scintillator.

We have the following argument :

λ′ − λ =

h

c2me(1− cos(θ))

using the conservation of momentum and energy for an incident photon on a rest electron. Havingλ = 1

hf we get the following for the energy of the scattere photon:

hf =hf

1 + hf(1−(

cos θm0c2

))

and thus gives rise to the inequality :(hf

1 + 2hfm0c2

)≤ Eγ ≤ hf

where the minimum value corresponds to the “Backscattering peak” and the maximum the “Comp-ton edge”.

Operation of the Photomultiplier

The Photomultipler setup is given by :

Incident photons on the photcathode will excite electrons from it and then are accelerated througha potential difference towards the first dynode in the electron multiplier.

Now these electrons in turn excite more electrons from the dynode. Each incident electron on thedynode will excite a mean m number of electrons. Thus for n dynodes there will be an excitation

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of mn electrons.

Therefore the total charge Q at the anode is given by Q = (e−m)n and the voltage pulse inducedis V = Q

C with C the anode capacitance, but this is H0 , the γ-ray energy and thus :

H0 =(e−m)n

C

⇒ H0 ∝ V n

showing the proportionalality relation we will use.

R dependence on H0 at constant PM Voltage

Since :

R =H2 −H1

H0

at constant PM voltage we expect that since H0 ∝ V n then FWHM ∝ V n also as the resolutionwill remain constant at a constant PM voltage, we expect.

Nuclear Physics Terms

We have :

−dNdt

= λN

the negative sign indicates that N decreases as t increases with dNdt being the number of particles

decaying per unit time.

λ is the decay constant of a radioactive substance, with λ = 1.76x10−17s−1 for K40 which will beused in the experiment.

The Half Life of a radioative substance is the time it will take for exactly half of the number ofparticles in the substance to decay, it is denoted by τ 1

2and τ 1

2= 1.26x109 years for K40.

The Abundance Ratio is the amount of a radioactive substance that is present in an element, forinstance, the abundance ratio of K40 in potassium is 0.011%.

The Branching Ratio of a radioactive substance is the percentage of a particular type of decay ifa radioactive substance has more than one channel of decay. For K40 the branching ratio for theemission of a γ-ray is 11%.

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The Experiment

Preliminaries

The Maestro software must be initialised so that the data from the spectrometer can be interper-ated. The software was started up on the computer.

Firstly, we got the laboratory technician to administer the installation of the Cs137 source that willbe used for the first part of the experiment.

We modified the settings in the Maestro software so that the photomultiplier(PM) voltage is set to600V . The calibration of the energy scale was necessary for the correct results so at channel zerothe energy is calibrated to 0 keV and at the peak position set the channel to 662 keV.

Part 1

•To record and analyse the effect on a spectrum of changing the photomultiplier voltage

Using the Maestro software we found the total energy peak for Cs137 . As well as this we foundboth the position H0 and its full width at half height (FWHM ).

We found the limit of detection at low voltage by varying the PM voltage until the the Maestrosoftware no longer detects the γ-ray peaks.

Now the the varitaion in H0 , FWHM and R as a function of PM voltage can be measured. Weused this data to verify that H0 ∝ V n and furthermore deduce how FWHM and R will depend onV.

Part 2

With the help of the lab technician to install the radioactive sources,we recorded the spectra forCs137 , Co60 and Na22 .

The calibration of each element was considered, the first peak for Cs137 being at 1.17 meV and thestrongest peak in Na22 being at 511 keV.

By using the decay chains for the respective elements we predicted what values one should find forthe energy of the γ-rays peaks.

For all the single peaks record R and we deduced how R should vary with the peak energy at afixed PM voltage.

Part 3

By using the spectra obtaned in Part 2 and the equations for the detector efficiency the detectionefficiency of the γ-ray spectrometer was found using first Na22 and then Co60 .

Using 3.625 g of KCl and its energy energy spectrum the abundance ratio, half life and branchingratio of K40 was found.

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Results and Analysis

Part 1

The following table illustrates the effect of varying the PM voltage for a Cs137 sample :

V (Volts) H0 (keV) H1 (keV) H2 (keV) FWHM (keV) R

500± 1 157.36± 2.7 159.54± 2.7 163.1± 2.7 3.567± 3.81 0.02264± 0.02418

550± 1 333.71± 2.7 320.38± 2.7 344.26± 2.7 23.88± 3.81 0.07155± 0.01143

600± 1 662± 2.7 638.72± 2.7 685.69± 2.7 46.97± 3.81 0.07095± 0.00576

625± 1 914.32± 2.7 881.98± 2.7 946.08± 2.7 64.11± 3.81 0.07011± 0.00417

650± 1 1239.89± 2.7 1196.72± 2.7 1283.94± 2.7 87.22± 3.81 0.07034± 0.00307

675± 1 1676.7± 2.7 1613.3± 2.7 1730.08± 2.7 117.08± 3.81 0.06982± 0.00227

700± 1 2224.75± 2.7 2146.89± 2.7 2303.47± 2.7 156.58± 3.81 0.07038± 0.00171

the resolution, given by : 0.063684286±0.00754013. Now excluding the first value we get an averageof R = 0.070525± 0.004765908 . With the uncertainty in R given by:

R = R

√((∆H2)2 + (∆H1)2

(H2 −H1)2

)+

(∆H0

H0

)2

A log plot illustrating the proportionality relation, H0 ∝ V n, is given below. The dynode number,n, is given by n = 7.87446±0.006297 with ln(H0) = 7.87556(±0.006297) ln(V )−44.8755(±0.0404),the linear fit employed.

The quoted, integer value, for the dynode number is 8, and we are almost within accuracy.

Plotting FWHM against Voltage to investigate how FWHM should depend on it we get the following:

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So the slope is given by 10.5275± 1.103 and the equation ln(FWHM) = 10.5275(±1.103) ln(V )−63.7091(±7.074).Now omiting the first point, since it does not fit the data and may be due to statstical fluctuations,we get the following:

So the slope is given by 7.78477±0.02261 and the equation ln(FWHM) = 7.87477(±0.02261) ln(V )−−45.9507(±0.1458). This illustrates that FWHM ∝ V n also as theoretically predicted, giving usthe same expected value of the dynode number.

Now plotting the Resolution as a function of voltage we get :

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where the average resolution is given by the average with the first point omitted, which we see asthe volatge increases it settles onto the average resolution. This illustrates that the resolution iseffectively constant for high voltages, though when we go to lower voltages it begins to vary. Thismay perhaps be due to the fact that at lower PM voltages the incident electron may not knockout as many electrons as it would with higher energies, it does not multiply as it would at higherenegies so to say. Therefore, the number of electrons that induce the voltage at the anode will beless and since there are less the effect of missing one is greater than the effect of missing one at agreater voltage, so we get a sharper resolution instead.

Part 2

Cs137

The energy spectrum for Cs137 looks like :

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The Backscattering Peak, the peak furthest to the left, is observed to occur at an energy of 231.67±2.7 keV while the total energy peak occurs at 662±2.7 keV. The Compton Edge can cleary be seenas the count rate “dips” just before it reaches the total energy peak as it should be expected. Thesefeatures illustrate the effect of both Photoelectric Absorption that happens in the scintillator andthe Compton Scattering that can hapen in both the lead shield (corresponding to the backscatteringpeak) and the scintillator (corresponding to the Compton Edge).

Co60

The data collected for Co60 is as follows :

H0 (MeV) H1 (MeV) H2 (MeV) FWHM (MeV) R

1.17± 0.0005 1.13075± 0.0005 1.2022± 0.0005 0.07145± 0.0007 0.0610± 0.0006

1.32± 0.0003 1.2815± 0.0003 1.3600± 0.0003 0.0785± 0.0004 0.0595± 0.0003

The total energy peak values are within error of the theoretical predictions.

It’s energy spectrum looks like:

In this instance, the backscattering peak is observed to occur at the energy of 0.280 ± 0.01 MeV.The two total energy peaks are given in the table above, with the sum peak being observed at anenergy of 2.69± 0.0005 MeV. In essence, this illustrates that in the decay of Co60 it will emit twoγ-rays of distinct energies. Given that Co60 is expected to decay onto Ni60 which in an excitedstate emits two γ-rays the energy spectra is correct in this sense.

The sum peak corresponds to when the two γ-rays that are emitted in the decay of Co60 bothundergo photoelectric absorption in the scintillator. The “Compton Edge” and this sum peak areidentifable in the spectrum. Though it is noted that the sum peak does not occur as theoreticallypredicted, that is twice the energies of the indiidual γ-rays . It is still within 8% of the expectedvalue, however.

Na22

The data collected for Na22 is as follows :

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H0 (keV) H1 (keV) H2 (keV) FWHM (keV) R

511± 2.7 491.169± 2.7 533.136± 2.7 41.9671± 3.81 0.0821± 0.0074

Sum Peak

1024± 2.7 961.88± 2.7 1054.286± 2.7 92.406± 3.81 0.0902± 0.0037

1240.61± 2.7 1208.479± 2.7 1278.950± 2.7 70.471± 3.81 0.0568± 0.0030

It’s energy spectrum looks like :

The backscattering peak occurs at an energy of 175 ± 2.7 keV and the Compton Edge occurs at475.5± 2.7 keV while the total energy peaks and sum peak are in the table above.

Part 3

Efficiency of the Detector

Using the Na22 spectrum found in part 2 and using the formulae :

∆c1∆t

= 2Aε

and

∆c2∆t

= Aε2

the efficiency is found to be

ε =2∆c2∆c1

which is the efficiency of the detector. With ∆c1 being the counts for the total energy peak andDeltac2 being the counts for the sum peak. Considering this we get an efficiency of the detector tobe :

ε = 2.152

1610≈ 0.18

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giving the efficiency to be about 18% at 511 keV.

Using similar arguments for Co60 we have that :

∆c1 + ∆c2∆t

= 2Aε

giving the efficiency to be :

ε =2∆c3

∆c1 + ∆c2

Where when looking at the Co60 spectrum the ∆c1, ∆c2, ∆c3 can be identified giving :

ε = 2.10168 + 7712

400≈ 0.04

giving the efficiency to be about 4% between 1.17 MeV and 1.32 MeV.

Sample of K40

The energy spectrum (over a day) for K40 is given by :

The Count Rate

Our goal here is to calculate the count rate for under the total energy peak. It can be observedthat the peak spans a total of 85 channel numbers with channel 514 being where the peak occurs.Ideally, to get the total number of counts would require counting the counts at each channel numberand summing them up. Instead, we take the number of counts at channel number 472 and channelnumber 556 (corresponding to H1 and H2) and taking the average and multiplying by 85 to giveus the total count number C. We get:

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C = (3.5± 1)× 105

The backround radiation must now be taken into account. Taking both count numbers at the endsof both peaks, averaging over these two and taking them away from C we get C such that :

C = (2.5± 1)× 105

Now the count rate C is found by dividing C by the time t = 93336.72 s. It gives:

C = 0.26± 0.1s

Remembering this is actually the number of counts that are detected and not emitted, C mustbe divided by the detectors efficiency at 1446 keV, which was approximately calculated as 0.04 byusing Co60 . Now we get:

Ctot =dN

dt= 6.5± 1s−1

the total count rate.

The Abundance Ratio

Since :

−dNdt

= λN

and λ has been quoted. However the we must take into account that the branching ratio of theγ-rays is 11% so we divide the N above by 0.11 to get the total number of particles given by:

N = (3.36± 1)× 1018

considering that the abundance ratio of K40 in potassium is 0.011% the theoretical value of N isgiven by 1.6 × 1018. Though the experimental value is not strictly within error, it is of the sameorder of magnitude.

The Half Life

In order to calculate the half life we must first calculate N2 . This is given by :

N

2= 1.68× 1018 = D

This is the number of particles that decay in the half life time. The number of particles that decayin t = 93336 seconds is given by P such that P = 2272727. The half life is thus given by :

τ 12

=Dt

P≈ (7.97± 100)× 1016s

which is equivalent to:

τ 12≈ (2.4± 1)× 109y

where y is years. Since the quoted value of the half life is given by 1.26 × 109 years we are againnot strictly within experimental error but are on the correct order of magnitude.

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The Branching Ratio

We let :

f =t

τ 12

be the fraction that will decay in the half life.

Let g = 2.5× 105 the amount that decay by γ-ray emission . Thus if we let:

f × N

2= l

then the abundance ratio is given by:

A =g

l≈ 0.10± 0.1

Since the actual abunace ratio is given by 0.11 we see that our result is quite good, for the procedurewe applied.

Discussion

The first part of the experiment, where we investigated the dependence of the γ-ray energy on thePM voltage could have been improved by taking more values than the ones we took. Especiallyin the case when we plotted resolution against voltage. The discontinuty effected both this graphand the FWHM graph. Perhaps a larger data set would illustrate what is going on a little clearerand then might give some of the arguments in the analysis a bit more clarity and weight. In sayingthis, even though the dynode number was not within the experimental error it was very close, andplotting FWHM as a function voltage and getting the same result is interesing. Given that n shouldtake on an integer value, we are certainly close. Also, on another note the way in which H1 andH2 were calculated in each case could improve on accuracy.

In the second part of the experiment much of what was discussed in the theory appeared, suchas the various backscattering peaks and Compton Edges for each of the radioactive substances.It is unfortunate that these peaks were not theoretically predicted using the Compton inequal-ity derived in the theory so we could compare theory against result. Nevertheless, in the case ofCo60 the total energy peaks were as expected by theory and within experimental error. Thoughthe sum peak did not correspond to this perhaps letting a longer run time could have improved this.

The first part of the the last part of the experiment in calculating the efficiency had no gauge untilwe did the last part and actually used the efficiency at ≈ 1.4 to calculate the counting rate. Sincethe results for the half life ( (2.4± 1)× 109y ) and branching ratio ( ≈ 0.10± 0.1) are of the sameorder of magnitude it can be said that the aforementioned efficiencies must also be at least in someway correct if they lead to the correct results in the various properties of K40 .

Finally, instead of approximating the count rate with averages like we did, maybe a more formalapproach would be appropraite, that being actually count all the counts on the channel numbers oreven approximate the peak by a function and integrate over it would give us more accurate results.Though the average taking is hand-wavy it’s a start and gives quite close results.

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