gamma ray spectroscopy

12
GAMMA RAY SPECTROSCOPY TREVOR DOLINAJEC PARTNER: YOUNG PYO HOUNG Abstract: In this experiment gamma rays are produced from four radioactive isotopes, 22 Na, 137 Cs, 60 Co, 54 Mn. The spectra of these isotopes are investigated. Characteristics of these spectra are explained through decay types and interactions of the gamma rays in matter. The detection method is a sodium iodide scintillator, a photomultiplier tube and a pulse height analyzer. The inverse square law is confirmed for these radioactive sources and the absolute intensity of 137 Cs is calculated using its measured intensity. Also, a number of mass attenuation coefficients for different metals were experimentally calculated using 22 Na and 137 Cs, and compared to accepted values. Introduction: Gamma ray spectroscopy is the study of energy spectra created by radionuclides (radioactive isotopes). It is not a counting method as with a Geiger counter but a acquisition of data pertaining to the actual energies of individual gamma rays. The procedure results in two- dimensional graphs that plot energy versus number of counts, although the values on the energy axis require certain calibration that will be discussed later. Number of counts is simply the num- ber of times that a particular energy is recorded during the time period of data acquisition. These graphs are particular to a given radioactive isotope (see Data section for graphs of the four ra- dioactive isotopes used in this experiment). In the simplest sense these graphs should consist of tall narrow peaks that correspond to the energy or energies of the gamma rays produced by a radioactive isotope. The reality is that this graphs consist of peaks with substantial widths and entire areas of continuum that are not even near the peaks of interest (more on this widths and continuums in the Theory and Discussion sections). Nevertheless, gamma ray spectroscopy re- mains the appreciable precise measurement of energies from specific gamma rays. Gamma ray spectroscopy has been carried out for the last fifty years it is a very well docu- mented and repeated. To understand the success of gamma ray spectroscopy it is important to understand the nature of gamma rays and the equipment used for the procedure. Gamma rays carry the highest energy of the electromagnetic waves (on the order of MeV). Gamma rays are produced in a number of ways but the ones of most interest to us are those of de-excitation of daughter radionuclides following beta-negative decay, positron emission or electron capture and electron-positron annihilation (which in our case is a direct result of the positron emission de- cay route). The four radioactive isotopes used in this experiment produce gamma rays via the above mentioned processes (more on specifics in Theory, Data and Discussion). Outside of be- ing interested in how gamma rays are produced we are also interested in how they interact with matter because not only will we discuss absorption and mass attenuation coefficients of different thicknesses of different materials (see Data) but it is matter interaction that forms the backbone of Date: 11/16/09. 1

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Page 1: Gamma Ray Spectroscopy

GAMMA RAY SPECTROSCOPY

TREVOR DOLINAJEC

PARTNER: YOUNG PYO HOUNG

Abstract: In this experiment gamma rays are produced from four radioactive isotopes, 22Na,137Cs, 60Co, 54Mn. The spectra of these isotopes are investigated. Characteristics of these spectraare explained through decay types and interactions of the gamma rays in matter. The detectionmethod is a sodium iodide scintillator, a photomultiplier tube and a pulse height analyzer. Theinverse square law is confirmed for these radioactive sources and the absolute intensity of 137Csis calculated using its measured intensity. Also, a number of mass attenuation coefficients fordifferent metals were experimentally calculated using 22Na and 137Cs, and compared to acceptedvalues.

Introduction: Gamma ray spectroscopy is the study of energy spectra created by radionuclides(radioactive isotopes). It is not a counting method as with a Geiger counter but a acquisition ofdata pertaining to the actual energies of individual gamma rays. The procedure results in two-dimensional graphs that plot energy versus number of counts, although the values on the energyaxis require certain calibration that will be discussed later. Number of counts is simply the num-ber of times that a particular energy is recorded during the time period of data acquisition. Thesegraphs are particular to a given radioactive isotope (see Data section for graphs of the four ra-dioactive isotopes used in this experiment). In the simplest sense these graphs should consist oftall narrow peaks that correspond to the energy or energies of the gamma rays produced by aradioactive isotope. The reality is that this graphs consist of peaks with substantial widths andentire areas of continuum that are not even near the peaks of interest (more on this widths andcontinuums in the Theory and Discussion sections). Nevertheless, gamma ray spectroscopy re-mains the appreciable precise measurement of energies from specific gamma rays.

Gamma ray spectroscopy has been carried out for the last fifty years it is a very well docu-mented and repeated. To understand the success of gamma ray spectroscopy it is important tounderstand the nature of gamma rays and the equipment used for the procedure. Gamma rayscarry the highest energy of the electromagnetic waves (on the order of MeV). Gamma rays areproduced in a number of ways but the ones of most interest to us are those of de-excitation ofdaughter radionuclides following beta-negative decay, positron emission or electron capture andelectron-positron annihilation (which in our case is a direct result of the positron emission de-cay route). The four radioactive isotopes used in this experiment produce gamma rays via theabove mentioned processes (more on specifics in Theory, Data and Discussion). Outside of be-ing interested in how gamma rays are produced we are also interested in how they interact withmatter because not only will we discuss absorption and mass attenuation coefficients of differentthicknesses of different materials (see Data) but it is matter interaction that forms the backbone of

Date: 11/16/09.1

Page 2: Gamma Ray Spectroscopy

2 TREVOR DOLINAJEC PARTNER: YOUNG PYO HOUNG

gamma ray spectroscopy. It is scintillators that make gamma ray spectroscopy possible. This isbecause a ”gamma ray is uncharged and creates no direct ionization or excitation of the materialthrough which it passes” (Knoll 306) and thus they can not be detected directly. A scintillatorsuch as the one used in this experiment (thallium-doped sodium iodide crystal) emit photons inthe visible light range that can be directly detected. Therefore it is the interactions of the gammarays within the crystal in which they transfer all or a portion of their photon energy to electronsthat is crucial to interpreting gamma ray spectrums. These in-matter processes are photoelectricabsorption, Compton scattering, and pair production these processes will be discussed in greaterdepth throughout this report. In is not the scintillator alone, of course, that allows for applicablegamma ray spectroscopy. The remainder of the equipment, including the photomultiplier tube,the preamp and pulse height analyzer are outlined in the following Equipment section.

Gamma ray spectroscopy is a mature science and the use of thallium-doped sodium iodidecrystals is a tested and proven method. Interestingly, despite NaI(Tl) being the first widely usedscintillators for gamma ray spectroscopy over fifty years ago they retain their position as the mostwidely used and relied upon scintillators even today due to their ride range of linear response,their output of relatively large burst of light and their ability to be produced in large crystals.Gamma ray spectra for hundreds of radioactive isotopes have been measured and recorded in theliterature. Through accepted values such as the annihilation energy or the gamma ray producedby Cesium-137 one can calibrate spectra from unknown sources and identify the composition ofa sample. This would require a good deal of precision and unknown samples were not identifiedin this particular experiment. This experiment does, however, investigate characteristic shapesof gamma ray spectra including the width of the photopeak, the Compton scattering region andlocation of Compton edge. It is important to understand what causes such shapes in the spectra ifone ever hopes to use gamma ray spectroscopy for investigative research.

Equipment and Procedure: The equipment for this experiment essentially consisted of a Harshawmounted Scintillator NaI(Tl), an RCA Photomultiplier tube, an amplifier and a Tracor NorthernPulse Height Analyzer (PHA). The Photomultiplier was powered by a high voltage power sourcewhich was used in conjunction with a voltage divider. The small signal from the photomultipliertube (PMT) was amplified by a Canberra Amplifier built into our instrument rack. This amplifi-cation was necessary to place the signal in the middle of the range of the PHA which was 0 to 8V.We found 271x an advantageous amplification setting with regards to the applied voltage to thePMT from our high voltage power source. This amplification was obtained by setting the coarseknob on the amplifier to 16 and the fine to 5. This amplification setting was used for all parts ofthe experiment. As will be discussed briefly a pulse generator was also used in order to ascertainsome behaviors of the PMT but overall the experiment consisted of the following in order:

1. Source placed some distance (15cm) from scintillator with lead collimator in between.2. Scintillator crystal NaI(Tl) taped onto photomultiplier with back electric tape.3. Photomultiplier tube powered by -1532.9V from high voltage.4. Amplifier set at 271x amplification.5. Pulse height analyzer set to 2048 channels and connected to PC.

To determine the most appropriate setting of the high voltage applied to the PMT the volt-age was varied using the voltage divider and the relative gain of the photomultiplier tube wasgraphed as a function of high voltage using the photopeak of the 137Cs source.

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GAMMA RAY SPECTROSCOPY 3

The curve on this graph shows good agreement with a twelfth order polynomial or at least ahigh order polynomial and this is what we would expect from the number of dynodes in the pho-

tomultiplier. We expect the gain of the photomultiplier to be GPMT =(VHV − VOUT

12V0

)12

ε. Where

VHV is the applied high voltage to the PMT, VOUT is the output voltage that goes into the amplifierbefore the PHA, V0 is the work function from the photoelectric effect and ε is the efficiency of thePMT. We would like this function not to be a function of the incoming energy, i.e. we would likethe voltage sent to the PHA to be V (E) = GE 6= G(E)E. This is the sought after linear rangeof operation and according to what we know about the PMT as laid out in the above equationand supported by the data his will occur when VOUT << VHV . Choosing ≈-1530V from the highvoltage power source allowed operation within this linear range.

It was also necessary before taking data from our radioactive isotopes to confirm that the PHAwas indeed on a linear scale with regards to its two axes linearity on voltage to channel and fromrepetition rate to photopeak height. This proved to be a simple check using a pulse generator thatsimulated the type of pulses one would receive from a radioactive isotope. The following twographs confirm this linearity nicely.

Theorey: The theory behind gamma ray spectroscopy falls into two primary categories the theorybehind their genesis and the theory behind their interactions in matter. The only other significantpiece of theory behind gamma ray spectroscopy is the statistical resolution of the photopeaks (atleast within the scope of this experiment).

Two of the four radioactive isotopes used in this experiment undergo beta-negative decay, theseare 60Co and 137Cs (in fact 54Mn also undergoes beta-negative decay but it is not that decay routethat leads to gamma rays). Below are the decay routes for 60Co and 137Cs:

Page 4: Gamma Ray Spectroscopy

4 TREVOR DOLINAJEC PARTNER: YOUNG PYO HOUNG

These two decay schemes are exceptionally easy to read because we see all the gamma rays onthe schemes themselves. 60Co releases two gamma rays, one with an energy of 1.17MeV and theother with 1.33MeV, this happens as the excited nuclear sate of the daughter nucleotide 60Ni cas-cades downward to an unexcited state. Likewise 137Cs releases one gamma ray at 0.662eV as itsdaughter nucleotide 137Ba goes from an excited nuclear state to an unexcited one. Of course, it isnot actually 137Cs and 60Co that directly release the gamma rays, it is the excited nuclei of theirdaughter nucleotides, but by convention and convenience we refer to the spectra as belonging tothe parent radioactive isotope. Next are the decay schemes for 22Na and 54Mn:

The 54Mn scheme is in many ways comparable to that of Cesium except that it is electron capturethat leads to the daughter nucleotide with the excited nucleus not beta-negative decay. Again wecan clearly see the gamma ray energy on the schematic with its energy of 0.834MeV as 54Cr trans-fer to an unexcited nuclear state. Our last isotope, 22Na, is different, however, the decay schemeonly shows one of the two detectable gamma ray energies. The 1.28MeV gamma ray is similar toall the other gamma rays previously mentioned in that it is created when a daughter nucleotidehas an excited nucleus that releases energy on the order of MeV to reach an unexcited state (inthis case 22Ne). Our other gamma ray of energy 0.511Mev is not displayed on the diagram of thedisplay scheme because that gamma ray is produced by electron-positron annihilation which isnot a separate event but a direct result of the positron emission that began the decay from 22Na to22Ne in the first place. The original isotope, 22Na, decays via positron emission 90% of the time(the other 10% of the time the decay via electron capture would not lead to annihilation gammarays) and the positron created finds an electron in the container surrounding the isotope withwhich to annihilate. This event of annihilation occurs almost simultaneously with the release ofthe 1.28MeV gamma ray owing to the speed at which the positron travels and the short distancerequired to find an electron. In actuality two gamma ray photons are created by this process (eachwith energy equal to the rest energy of the positron or electron) but these gamma rays are directed180 from each other and thus only half of them will be detected in this experiment.

Due to the precision of measurement with regards to this annihilation energy as well as its

Page 5: Gamma Ray Spectroscopy

GAMMA RAY SPECTROSCOPY 5

prevalence in the spectrum of 22Na it is a natural choice for calibration of our spectrum. All ofthe spectra presented in this paper will have been calibrated using the annihilation energy peakfrom 22Na, which is to say that the bin corresponding to 0.511MeV was changed as such and aone-to-one conversion of all other channel numbers to energy values followed. This was based onour demonstration of linearity in the scintillator, PMT and PHA.

While on the subject of gamma ray production it is an appropriate time to mention half-livesand consequently natural widths (also called decay widths). The half-lives of 22Na, 137Cs, 60Coand 54Mn are 2.6 years, 30 years, 5.2 years and 312 days respectively. This directly relates to the

notion of natural width in that Γ =~τ

where γ is the natural width, τ is the half-life. Thus 137Cs

would for example have a natural width of ≈ 7 × 10−24eV while 54Mn would have the largestnatural width at ≈ 2× 10−22eV. These values represent infinitesimally narrow lines as one wouldexpect from energy spectra (their only width coming from the Heisenberg uncertainty principle)and the purpose of mentioning them here is to conclude in the Data section that the width of ourphotopeaks are not a result of natural width but entirely of other factors such as statistical spread.

When gamma rays pass through matter they will interact with it in one of three ways (other in-teractions are possible but not significant to this experiment). These three possible interactions arePhotoelectric Absorption, Compton Scattering and Pair Production. The predominate interactionof gamma rays in matter is photoelectric absorption (at least those gamma rays of low energy, <5MeV) and in may ways photoelectric absorption is the most desirable because it produces pho-topeaks that actually correspond to the energies of the incoming gamma rays. An approximationof the probability of photoelectric absorption per atom over all ranges of gamma ray energies is

τ ' Const. × Zn

E3γ

, E3γ is the gamma ray energy in question and Z is the atomic number of the

absorber with n usually around 4 or 5 (Knoll 63). Thus large value of Z have a very strong effecton chance of absorption which is why lead with Z=82 is used for shielding and why NaI(Tl) withZ=53 is used for gamma ray spectroscopy where absorption is preferable over other interactions.This value of τ is called the cross section for photoelectric absorption and it can be seen along withthe cross section for pair production (represented by κ) on the following graph that relates gammaray energies, Z of absorbers and dominant reactions by region:

Photoelectric absorption occurs when the gamma ray completely disappears when it comes incontact with an atom of the absorber. Compton scattering, on the other hand, is when the gamma

Page 6: Gamma Ray Spectroscopy

6 TREVOR DOLINAJEC PARTNER: YOUNG PYO HOUNG

ray is deflected, only loosing some of it’s energy, and a subsequent recoil electron is scattered. Theway in which the original energy of the gamma ray is divided between the deflected gamma rayand the recoil electron is dependent on the scattering angle. This angular dependence is given by

the formula hv′ =hv

1 +hv

m0c2(1− cosθ)

where m0c2 is the rest energy of the electron at 0.511MeV

and hv′ is the energy of the deflected gamma ray as compared to the original energy of the gammaray at hv. Thus the maximum amount of energy of the deflected gamma ray occurs when θ=0 andthe maximum amount of energy of the recoil electron is when θ=180. This 180 degree arrange-

ment will result in a recoil electron with energy Ee = hv

[2hv/m0c

2

1 + 2hv/m0c2

]the max energy of the

recoil electron. This energy value is called the Compton edge and its distance from the center of

the photopeak can simple be calculated as hv − Ee,θ=180 =hv

1 + 2hv/m0c2(Knoll 310-312). Thus

Compton scattering should be a continuous distribution that falls off sharply some time before thephotopeak. The spectra for the radioactive isotopes used in this experiment all show Comptonscattering that matches this theoretical description, including the presence of the Compton edge.The spectra also show another dominant feature a large mound near 0.25MeV. This is called thebackscatter peak and can be explained by the energies of the scattered gamma ray photons in asimilar way that the Compton edge was explained by the energies of the recoil electrons. Againwe look at values of θ near 180 (near because values greater than 120 result in nearly identicalenergies as according to the above formula, see diagram) but this time look at hv′ and conclude

that for hv >> m0c2/2, hv′θ=180 '

m0c2

2≈0.25MeV. Thus a pile up of energies for gamma rays

that scattered between 120 and 180 degrees.Pair production, the third significant gamma ray interaction in matter, can occur when the in-

coming gamma ray energy exceeds twice the rest mass of an electron (1.02MeV). This energy isrequired because an electron-poistron pair houses such energy. The energy equation that exlainsthe process is hv − 2m0c

2 = Ee− + Ee+ (Knoll 312). Thus on a gamma ray spectrum this processwould result in a peak a distance 2m0c

2 from the center of the photopeak. Only two of the fourradioactive isotopes used in this experiment had gamma rays with enough energy to possible cre-ate this interaction in the scintillator. According to the table above and considering the atomicnumber of NaI(Tl) is 53 we would need gamma rays with energy 7MeV to approach the pair pro-duction dominant region. Thus is it is very unlikely that we will see any pair production in matteras a result of passing gamma rays and our only exposure to annihilation energy will be the decaysequence of 22Na.

A concept that combines these three interaction in matter is the attenuation coefficient. It isdefined as µ = τ(photoelectric) + σ(compton) + κ(pair). The attenuation coefficient is inversely

related to the mean free path λ =1µ

. The attenuation coefficient allows for the number of transmit-

ted photons to be compared to the number without an absorber I0 asI

I0= eµt. A more common

expression than the attenuation coefficient is the mass attenuation coefficient which is simpleµ

ρ, ρ

being the density of the material (Knoll 68).The last major theoretical topic of this experiment is the observed width of the photopeaks on

the PHA and statistical explanation behind that width. Photopeaks, as will be shown in Data andDiscussion are not narrow sharp lines but have a finite width. This is because scintillators have apoor energy resolution this is simple an inconvenience one must live with when using scintillatorsthat is largely balanced by the crystal’s many advantages as mentioned in the Introduction. This

Page 7: Gamma Ray Spectroscopy

GAMMA RAY SPECTROSCOPY 7

resolution can be calculated by R =FWHM

H0where FWHM is the full width at half maximum

of the energy photopeak (our absorption peak) and H0 is the mean pulse height correspondingto that peak which is just the channel that the center of the peak falls into. The are a number ofphenomenon that contribute to this resolution loss; charge collection statistics, electronic noise,variations in the detector response over its volume and drifts in operating parameters. Statisticalspread, however, are the single most important spread of peak spreading in the scintillator. It canbe shown that the FWHM of a peak is proportional to the square of the energy of the gamma ray.Combine that with the fact that average pulse height is by definition directly proportional to the

energy of the gamma ray and resolution can be rewritten as R =FWHM

H0= k

√E

E=

k√E

(Knoll

344-345). Thus the energy resolution should be beinversely proportional to the square root of thegamma ray energy, lnR = ln(k) − 1

2 lnE. We will attempt to confirm this relationship in the Dataand Discussion section.

Data and Discussion: At the core of this experiment are the spectra of the four radioactive iso-topes. We will look at this spectra one by one and indicate how the observed structures in thespectra match up with theoretical concepts mentioned in the Theory section. For all the spectraof the isotopes we used the precise set up described in Equipment and Procedure (including the15cm distance from source to scintillator). The only thing that will vary is included in this report isa a 50s spectra of 54Mn rather than a 10s spectra as for the other three isotopes. Data was taken fora longer time with 54Mn because of the short half-life of 312 days and the relatively old specimenlife (around 4 years) of this sample and the precious few data points acquired after only 10s. Allof the spectra will be shown calibrated with the horizontal axis in MeV rather than channels; thecalibration used was that of the annihilation peak as described above. First, is the spectrum for22Na:

The photopeak at the annihilation energy of 0.511MeV is clearly visible. The much smaller pho-topeak of the 1.28MeV gamma ray can also be seen to the far right of the spectrum. This peak,however, located at 1.13MeV, within 10% of its accepted value. The resolution on the annihilationpeak is 10.9% and the resolution of the second peak is 7.1%. The width of these peaks is on the or-der of keV so is in no way comparable to the natural widths of these gamma rays. Our resolutionloss is due to statistical spreading as mentioned above. What appears to be a backscatter peak islocated at 0.23MeV, very close to where we would expect to see a backscatter peak (≈0.25MeV).

Page 8: Gamma Ray Spectroscopy

8 TREVOR DOLINAJEC PARTNER: YOUNG PYO HOUNG

Another small peak is visible to the left of the backscatter peak and this may be a characteristicx-ray peak by secondary radiation caused by gamma rays interacting with the surrounding ma-terial. Lastly, the Compton edge is calculated at 0.34MeV which is in good agreement with thelocation of the Compton edge in this spectrum. Compton edges, however, like resolutions shouldexist for each photopeak and thus the 1.28MeV gamma ray should have a Comton edge of its own.Perhaps that is the small lump of counts around 0.9MeV. Second, is the spectrum for 137Cs:

In this spectrum we see our only photopeak at 0.627MeV which is within 6% of the accpetedvalue of 0.6616MeV. The Compton continuum is evident and houses the backscatter peak near theexpected value of 0.25MeV. The Compton edge is calculated at 0.48MeV which, as was the casewith 22Na, is in good agreement with the fall of point of the Compton continuum on this spectrum.The large peak at around 50keV is due to internal conversion of the gamma ray, a process we onlysee with 137Cs. The resolution of the photopeak is 10.2%. Third, is the spectrum of 60Co:

Although this spectrum is not as well endowed with data points as our previous two spectrawe can still clearly see two small peaks to the far right of the spectrum. These are actually ourphotopeaks and the larger peak is the backscatter peak, as evidenced by its location. There are also

Page 9: Gamma Ray Spectroscopy

GAMMA RAY SPECTROSCOPY 9

two other small peaks present one just to the left of the larger of the two photopeaks and anotheraround 70keV. It is likely that the one with lower resolution is an x-ray peak caused by secondaryradiation. The other odd peak with energy approximately of 0.85MeV may just be an exaggeratedCompton edge. The 1.17MeV photopeak should have a Compton edge around 0.96MeV whichmatches nicely with the spectrum. There is no evidence for another Compton edge correspondingto the other gamma ray energy but due to the proximity of these two peaks any such subtitleswould be lost when one considers the meager amount of data taken. The peaks are located at1.06MeV and 1.16MeV, this is significantly off from the accepted values but still within 12%. Theresolution of the two peaks where 7.25% and 6.9%. Last but not least, is the spectrum of 54Mn:

We used a longer data acquisition time for this isotope and the result was quite pleasing. We seea well defined photopeak at 0.74MeV which is within 12% of the document value. The Comptoncontinuum is typical with the backscatter peak close to 0.25MeV and the experimental Comptonedge at about 0.55MeV as compared to the theoretical value of 0.64MeV. The resolution of thephotopeak is 10.3%.

As mentioned above the relationship between resolution and energy of the gamma ray is givenby lnR = ln(k) − 1

2 lnE. The following graph shows a plot illustrating whether our experimentalresults coincided with this theoretical relationship.

This graph does not show a conclusive agreement with the theoretical supposition, namely thatstatistical spreading is the only significant cause of photopeak width. This is probably due, how-ever, more to the lack of precision with which the FWHMs were calculated and less to do withother significant contributions to resolution loss. If the graph was conclusive the data points

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10 TREVOR DOLINAJEC PARTNER: YOUNG PYO HOUNG

would be much closer to the line and the slope would be much closer to −12 (Knoll 336). The

graph does show that as a general trend the resolution decreases as the energy increases.To confirm that Compton scattering is a significant interaction in matter of gamma rays with

energies on the scale of this experiment a aluminum block was placed behind the 137Cs sourceand another spectrum was taken with all other parameters unchanged. The 0.6616MeV gammarays of 137Cs and aluminum’s atomic number of 13 put their interaction firmly in the Comptonscattering dominated range. Thus their should be a significant amount of gamma rays that scatteroff the aluminum at approximately 180 and still make their way to the scintillator where theywill add to the hight of the backscatter peak.

This graph of experimental data confirms our assumption. Indeed the backscatter peak has growon average about 50 counts while the rest of the spectrum, most notable the photopeak has re-mained the same. This is because the backscattered gamma rays off the aluminum that reach thescintillator do not have the same energy as the gamma rays that add to the height of the absorp-tion peak. In fact, it is the backscattered gamma rays’ absorption that contributed to the height ofthe backscatter peak, not further scattering.

Choosing the appropriate distance from the source to the detector is important. We choose15cm as a convenient distance for many of our data runs but that distance was not mandated.Closer distances can be useful because more counts are acquired in a shorter amount of time atsuch distances. For weaker sources such as the aging 54Mn this can save a lot of time. One doesnot want to place the source two close however or the incoming counts will overwhelm the PHAwhich becomes evident when the ”dead time” on the device exceeds 10%. As one might expectthis distnce from the detector and the resulting hight of the photopeaks obeys the inverse squarelaw. The follwing data confirms this:

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GAMMA RAY SPECTROSCOPY 11

We have been talking extensively about spectra, their characteristics, limitations and how to iden-tify the spectrum of one radioactive isotope from another. Sometimes, however, it is useful andrelevant to consider not the just the spectrum of energies that a detector like a scintillator wouldreceive but the overall intensity of a radioactive source. This can be necessary if someone wantsto determine the health risks of a certain source for example. Our measured intensity was 3526counts/second. If we consider that Imeasured = Iabsolute(n(E)∆Ω

4π ) then we can use the value inthe brackets as supplied in the documentation for the NaI(Tl) (at 15cm distance and a gamma rayenergy of approximately 0.5MeV with a scintillator thickness of 1in our efficiency should be 0.2%)Thus our absolute intensity was calculated as 1.76× 106.

The mass attenuation coefficients of aluminum, copper and lead were calculated for the 137Csand 22Na isotopes. This was done by setting up two collimators and placing the radioactive source25cm from the detector. Two runs were made without any absorber present to determine the ini-tial intensity through the lead collimators. Then three thicknesses of each material was used foreach of the two radioactive isotopes, a total of eighteen runs. A data collection time of 350s wasused for 137Cs and 400s for 22Na. These times were much longer than for our other data runs be-cause significant less gamma rays were making their way to the detector due to a combination ofthe collimators and obviously the absorbers. As explained in the Theory section mass attenuationcoefficients are calculated by

µ

ρ−x−1ln(I0/I) with x = ρt being the mass thickness of the material.

The thicknesses of aluminum used were 3.23, 19 and 25.4mm; the thicknesses of the copper usedwere 0.81, 12.85, 16.18mm; the thicknesses of the lead used were 1.98, 6.29, 13.72mm. The densitiesof aluminum, copper and lead are 2.7, 8.9, 11.34 g/cm3. Using our initial intensities and each ofour absorber intensities we calculated mass attenuation coefficients.

Values for 137Cs through Al: 9.18× 10−2, 5.51× 10−2, 7.45× 10−2

Values for 137CS through Copper: 13.4× 10−2, 5.9× 10−2, 7.8× 10−2

Values for 137Cs through Lead: 1.08× 10−1, 1.28× 10−1, 0.83× 10−1

Values for 22Na through Al: 19.8× 10−2, 5.13× 10−2, 4.40× 10−2

Values for 22Na through Copper: 4.34× 10−2, 7.36× 10−2, 6.11× 10−2

Values for 22Na through Lead: 1.08× 10−1, 1.13× 10−1, 0.98× 10−1

These values do not show optimal agreement, i.e. we should be getting the same mass attenu-ation coefficient regardless of the thickness. Especially the thinest pieces of metal seem to havecreated bad results. These values can be compared to the accepted values for photons of energies0.5 and 0.6Mev on the NIST webpage and the results are always on the same order of magnitudeand often within ten or twenty percent. For example, Lead for a photon of 0.6MeV, near like Ce-sium, has a mass attenuation coefficient of 1.248× 10−1, within 20% of our results.

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12 TREVOR DOLINAJEC PARTNER: YOUNG PYO HOUNG

Conclusion: Gamma ray spectrums and the equipment used in detect them have offer manyavenues to further understanding of nuclear processes, decay mechanism and energy exchanges.The annihilation following positron decay in 22Na, for example, offers an interesting experimentin coincidence. Minimization of the many possible secondary radiation occurrences and the effec-tive clean up on the spectra also offers the possibility of more precise results. Furthermore, with acatalog of known spectra one can feasible identify unknown radioactive sources, even those thatare not one particular isotope.

The errors in this lab are larger than anticipated and perhaps using the the 137Cs peak to cali-brate the spectra rather than the annihilation peak from 22Na would have lead to better agreementamong the experimental peak locations from the other isotopes and those documented in the liter-ature. Also, longer data acquisitions and a more consistent method for measuring FWHM wouldprobably lead to a much better demonstration of the dominance of statistical spreading on thewidening of photopeaks.

The NaI(Tl) scintillator, the photomultiplier tube and the PHA will undoubtable remain main-stays of any scientific endeavor that relies on gamma ray detection for results. The reliability andprecision of such instrumentation is quite remarkable. Indeed, more precise methods exist suchas the improved resolution of Germanium detectors but NaI(Tl) scintillators in particular offereffective results and high light output.