Neutron Activation AnalysisTrainingship at the Nuclear Physics Institute, Rez, CZ

Steven Peetermanssummer 2009

Contents

1 The Nuclear Physics Institute at Rez, Czech Republic 2

2 Technical report 42.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Basic formulas in NAA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.1 Production of radio-isotopes . . . . . . . . . . . . . . . . . . . . . . 52.2.2 Detection of radio-isotopes . . . . . . . . . . . . . . . . . . . . . . . 62.2.3 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Efficiency calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3.1 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3.2 Full peak efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3.3 Total efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.4 Neutron flux absorption in gold foils . . . . . . . . . . . . . . . . . . . . . 152.4.1 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4.2 Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . 152.4.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.5 Geometric correction factor . . . . . . . . . . . . . . . . . . . . . . . . . . 202.5.1 Experimental method . . . . . . . . . . . . . . . . . . . . . . . . . . 202.5.2 Spectral analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 Personal evaluation 23

A 25

B 26

1

Chapter 1

The Nuclear Physics Institute atRez, Czech Republic

The Nuclear Physics Institute or Ustav Jaderne Fyziky was founded in 1955 with theobjective to conduct basic nuclear research, to produce radio-isotopes and to instruct youngscientists. After a short period of management by the Czechoslovakian government, thefacilities were transferred under the auspices of the Czechoslovak Academy of Sciences.Over the years, the institute grew bigger and in 1972 it was split into the Nuclear ResearchInstitute (NRI) - which provides industry related nuclear research and services - and theNuclear Physics Institute (NPI), aiming at basic research in nuclear physics.

On 1 Januari 1993, the dissolution of Czechoslovakia into the Czech Republic andSlovakia was a fact and the NPI would henceforth fall under the Academy of Sciences of theCzech Republic (ASCR). This period is also characterized by the growth of internationalscientific cooperation, which was added to the NPI objectives as well [4]. It became possiblefor physicists from the NPI to spend time in laboratories abroad as well as for foreignscientists to work for a while at the NPI.

Today the NPI consists of several departments. The Nuclear Theory department isdevoted to hypernuclear physics, interactions of hadrons and elementary particles withnuclei and mathematical physics.

The department of Nuclear Reactions focuses on reactions with light nuclei and exoticlight nuclei - i.e. light nuclei with extreme shell configurations - as well as light induceddrift applications and radiation induced mutagenesis.

The Neutron Physics division investigates neutron diffraction and neutron analyticalmethods such as Rutherford Backscattering Spectrometry (RBS), Elastic Recoil DetectionAnalysis (ERDA), . . . Its main research tools are a Tandetron, a Van de Graaff acceleratorand the LVR-15 light-water reactor at the NRI where the NPI hires experimental channels.

The department of Radiopharmaceuticals focuses on discovering new medical applica-tions for radionuclides and the production of several short-lived positron emitters for usein Positron Emission Tomography (PET-scans).

To this end, it uses the 37 MeV U-120M cyclotron from the Accelerator department

2

Figure 1.1: Overview of the Rez Science and Technology Park, housing a.o. the NPI and NRI.

which also operates a 25 MeV microtron. The department of Radiation Dosimetry concen-trates its efforts mainly on low-level environmental and professional exposures e.g. aircrewexposure to cosmic radiation for which more than 25 in-flight measurements have beenperformed on board of CSA Czech Airlines aircraft.

The Spectroscopy department finally, spreads her activities over a much broader fieldthan nuclear spectroscopy alone. On the one hand, a lot of attention is paid to comparingsimulations and experimental results from activation detectors in the framework of the“Energy plus Transmutation” set-up to model an Accelerated Driven System (ADS) core.Close ties with JINR (Dubna, Russia) exist. On the other hand, there is the Relativisticand Ultra-Relativistic Heavy Ion Physics Group doing research on quark gluon plasmasvia the STAR collaboration at RHIC (BNL, USA). Measurements of magnetic moments ofnuclei are carried out as well in cooperation with the ISOLDE facility at CERN. Throughthe KATRIN collaboration, the department is involved in the attempted determination ofthe electron neutrino mass with a sensitivity of 0.2 eV.

3

Chapter 2

Technical report

2.1 Introduction

Neutron activation analysis

Neutron activation analysis (NAA) is a very precise technique mainly used to determinetrace concentrations of elements in samples [6] or to acquire information on the spatialdistribution of a neutron field via neutron activation detectors [9].

In NAA a sample is first irradiated with neutrons coming from e.g. a particle acceleratoror an experimental reactor. Depending on the neutron flux energy spectrum and reactioncross sections, the target nucleus undergoes a nuclear reaction and the resulting nucleuswill immediately de-excite under emission of characteristic prompt gamma rays into a morestable configuration. This configuration is in general a radioactive nucleus with a certainhalf-life t1/2 which will further decay under emission of characteristic delayed gamma raysinto a stable product nucleus. An illustration in the case of a neutron capture reaction isdepicted in figure 2.1.

Monitoring the emitted gamma photons with a detector then gives information on theconcentration of different elements in the sample or on the incoming neutron field if oneknows the nuclear reactions that result in the detected radio-isotopes. By using severalthin foils of known composition at different locations as sample, one can obtain informationon the spatial distribution of the neutron field. Such foils are called neutron activationdetectors, sometimes referred to as activation foils as well.

Trainingship objectives

There are however some specific issues connected to the use of neutron activation detectorsin spallation experiments such as at Dubna [9]. They were investigated with Monte Carlocodes MCNPX and FLUKA by dr. Mitja Majerle as part of his PhD [10].

During my trainingship, I was assigned to the department of spectroscopy under thesupervision of Vladimir Wagner and Marek Fikrle. I conducted experiments and performednuclear data analysis in order to investigate those issues and to verify several of those

4

Figure 2.1: Overview of the (n, γ) neutron capture reaction.

simulations.In this report I will first derive the basic formulas describing the production rate of

radio-isotopes in a sample from the detected delayed gamma photons after irradiation.The statistics one has to take into account when analysing experimental data are brieflytreated as well.

Some correction factors and considerations will arise and are treated in the sections thatfollow thereafter. They will be experimentally determined and compared to simulations.

2.2 Basic formulas in NAA

2.2.1 Production of radio-isotopes

If a sample is subjected to a neutron flux Φ(E), radio-isotopes are formed at a rate

P = N0

∫Φ(E)σ(E)dE (2.1)

With N0 denoting the number of nuclei prior to irradiation and σ the reaction cross sectionfor the production of corresponding radio-isotopes.

The time dependence of the number of radio-isotopes in the sample is determined bythe balance between the rate of new isotopes being formed and the radioactive decay ofthe ones already formed:

dN

dt= P − λN (2.2)

With λ denoting the decay constant which is related to the half-life as t1/2 = ln(2)λ

. This first-order differential equation can easily be solved by taking into account following boundaryconditions:

N(0) = 0[dNdt

]t=∞ = 0

(2.3)

5

At t = 0, the radio-isotopes are yet to be created and at t = ∞ a state of equilibriumexists. The solution to (2.2) becomes:

N(t) =P

λ(1− e−λt) (2.4)

So at the end of irradiation, at tirr, the sample is left with N(tirr) radio-isotopes.

2.2.2 Detection of radio-isotopes

In order to determine the initial rate P, the irradiated sample is measured by the detectorfor some time treal starting at t0, the time since the end of irradiation tirr. The number ofradio-isotopes decaying in that time interval is

s = N(t0)−N(t0 + treal) (2.5)

= N(tirr)(e−λt0 − e−λ(t0+treal)

)(2.6)

=P

λe−λt0

(1− e−λtirr

) (1− e−λtreal

)(2.7)

It is clear that the number of photons emanating from the radioactive decay that aredetected, S, will be a lot smaller. One has to take into account several effects:

The peak efficiency εp(E) is defined as the probability that the full photon energyis deposited in the detector. The efficiency callibration procedure is examined more thor-oughly in section 2.3.

The gamma emission probability Iγ(E) reflects the fact that there is only a certainprobability, between all possible transitions between excited states, that a photon of energyE is emitted in the γ-decay. These probabilities are tabulated and can be found for instanceat [13]. An example is depicted in figure 2.2.

There is a correction for cascade coincidences (COI) as well. The decaying radio-isotope can turn into a stable nucleus by emitting photons as it passes through severaltransition states. These photons have different energies and escape angles. It is howeverpossible that several photons reach the detector simultaneously. This is called a cascadecoincidence. We speak of true coincidences when the cascading photons are emitted in thesame decay of a radio-isotope with a very small time delay. The other case is refered to as afalse coincidence, they are in general negligible unless the activity of the radioactive sampleis very high. With increasing distance between the radioactive sample and the detector, theprobability that two photons are emitted in the same diminishing solid angle that coversthe detector decreases and cascade coincidences become negligible. Let us use figure 2.2 asan example to further clarify this and discuss the influence on the spectrum. From the levelscheme we expect three gamma-peaks in our spectrum: at 412 keV, 676 keV and 1088 keV.However, a transition energy of 1088 keV can be released in a single transition (2+ → 0+)or in two consecutive transitions (2+ → 2+ → 0+) that will be recorded together as a truecascade coincidence. As such the area of the 412 keV and 676 keV full energy peak willdecrease and the 1088 keV peak area will increase.

6

When dealing with only two excited states, the calculation of the cascade correctionfactors is very straightforward, see e.g. [10], [7]. In more complicated level schemes, otherpeaks at the sum of transition energies for which there is no single transition energyalternative, might arise as well. For more than two excited levels the calculation quicklyturns into a cumbersome and tedious task [5] and the use of tables and automated macrosbecomes advisable.

Figure 2.2: The gamma emission probabilities and decay level scheme for 198Au. Taken from [13]

The geometric correction factor Cg takes into account the finite size of the sample.Photons from decaying nuclei at the edge of the source will see a smaller solid anglecovering the detector than the ones emitted at the centre. As the distance between sourceand detector increases, the source can be regarded as a point source and the geometriccorrection factor will approach to unity.

The self-absorption correction factor Cs corrects for the absorption of gammaphotons inside the source sample itself.

Furthermore, a correction for beam instabilities Ct should be applied in case theaccelerator beam output isn’t stable in time.

Finally, a correction for the dead time of the detector is added in the form of afactor tlive

treal.

7

So the total number of detected photons becomes:

S = s.εp(E).Iγ(E).COI.Cg.Cs.Ct.tlivetreal

(2.8)

From (2.7) and (2.8) we can find an expression for the rate P:

P =S.λ

εp(E).Iγ(E).COI.Cg.Cs.Ct

tlivetreal

eλt0

(1− e−λtirr) (1− e−λtreal)(2.9)

The production rate B is the number of produced radio-isotopes per gram of material andper accelerator beam particle and is often used as an alternative for P in spallation physicswhere the neutron flux is created by bombarding a heavy target with e.g. a proton beamcoming from a particle accelerator.

B =1

m

∫Φ(E).

tirrNp

σ(E)dE (2.10)

=tirrm.Np

P (2.11)

2.2.3 Statistics

The total number of detected photons in one peak or a derived physical quantity is neverexactly defined. Deviations between the measured value and the true value - i.e. the errorof the experiment - will arise due to small variations in background, in source-detectorpositioning, in ones reading of a scale, in the random emission of photons from a radioactivesample,... When all deviations are random by nature they will lead to a certain distributionof the measured values: the Poisson distribution in case we are determining a discretenumber of counts.

f(x) =mxe−m

x!(2.12)

For high count numbers, this distribution will approach a Gaussian distribution

f(x) =1

σ√

2πe−

(x−m)2

2σ2 (2.13)

where m denotes the expectation value and σ2 the variance of the distribution.

If we have a set of N values xi, we can determine the mean value x as a weightedaverage with the square of the inverse uncertainties of these values taken as weights:

x =

∑Ni=1

1s2(xi)

xi∑Ni=1

1s2(xi)

(2.14)

The uncertainty on the average, s(x), is then given by:

s(x) =

√1∑N

i=11

s2(xi)

(2.15)

8

And if this set of values follows a Poisson or Gaussian distribution, then x will approachto m and s2(x) to σ2 if N is large.

So in general we will give the result of a (set of) measurements as x±u, where u denotesthe uncertainty on x. Usually, u = s(x) is taken and the probability of the true value ofthe measured quantity lying in the confidence interval [x − u, x + u] becomes 68% for aperfectly Gaussian distribution.

A simple test to find out if the set of values follows a Poisson distribution is to check ifs2(x) = x since for a true Poisson distribution σ2 = m. To find out if the deviation froma real Poisson distribution is significant, the so-called χ2-test is often applied.

χ2R =

1

N − 1

N∑i=1

(x− xis(xi)

)2

(2.16)

Equation (2.16) is the relative χ2-value of the set of values. As long as it is smaller thanor equal to one, the supposition that the values follow a Poisson distribution is valid. If itis bigger than one, a rescaling of the uncertainties can be applied in accordance to [3].

Often, one is more interested in a physical quantity that is the result of applying severalformulas on the measured data. In that case the error propagation law of Gauss will givethe uncertainty of the physical quantity.

σ2(f(z1, .., zN)) =N∑k=1

(∂f

∂zk

)2

σ2(zk) (2.17)

2.3 Efficiency calibration

2.3.1 Experimental set-up

The detector set-up used for the efficiency calibration measurements and all following mea-surements is a HPGe detector installed in a shielding vault in order to decrease backgroundradiation influence on the measurements. The vault is made out of lead and covered withthe low-Z material aluminum on the inside. Its purpose is to reabsorb X-rays emitted inthe relaxation of Pb atoms after low-shell electrons have escaped due to incident gammarays from the radioactive sample. This will lead to the subsequent Rontgen emission in alower energy range, interfering less with the spectrum from the sample.

2.3.2 Full peak efficiency

The full peak efficiency εP (E) is defined as the ratio of all photons who deposit their fullenergy in the detector, over all photons emitted by the source in the decay.

To determine the energy dependence of εP (E), we will calculate it for a number ofcalibration sources with well know characteristics. These calibration sources are very small

9

point-like radioactive sources encapsuled in a glass frame that emit photons isotropicallyduring their decay.

The number of photons emitted during the measurement time treal, starting at t0 isthen given by:

s = N(t0)−N(t0 + treal) (2.18)

=A0

λe−λt0

(1− e−λtreal

)(2.19)

By applying (2.8), we can solve for an expression allowing us to determine εP (E) withthe help from a calibration source with initial activity A0 at t = 0 and a peak in itsspectrum at energy E.

εP (E) =S.λ.eλt0

A0.Iγ.COI.Cg.trealtlive

.1

1− e−λtreal(2.20)

Because the used calibration standards are in good approximation point sources, wecan state Cg ≈ 1. The half-life of the calibration sources is in general on the order ofyears, while measurement times in general only take a few hours up to one or two days(λtreal << 1). Using the Taylor expansion of (2.20) and keeping only the first term, weget:

εP (E) =S.λ.eλt0

A0.Iγ.COI.

1

1− e−λtlive(2.21)

An overview of the used calibration sources and their most important energy peaks withcorresponding gamma emission probabilities is presented in appendix A.

The calculated peak efficiencies are presented in figure 2.3. The error flags containuncertainties on the peak area S, on A0 and Iγ. In order to obtain a continuous efficiencyspectrum from these discrete datapoints, we will interpolate them by means of a fittedεP (E) curve which is of the analytical form:

εP (E) = ea ln(E)2+b ln(E)+c (2.22)

The ratios of the experimentally determined εP values over the corresponding fittedvalues (Figure 2.4) reveal an excellent agreement. We only have to take a 5% uncertaintyinto account if we work with fitted peak efficiency values.

The experimental efficiency curves were determined for 4 different distances betweensource and detector and are shown in figure 2.5. We can ask ourselves now if we can notfind a relation between the efficiency curves at different distances. This would mean thatwe wouldn’t have to perform a new efficiency callibration for each new source-detectordistance. As a first order approach, one can simply state that

εP (x)

εP (x0)=

Ω(x)

Ω(x0)(2.23)

10

Figure 2.3: Experimental and fitted peak efficiency spectrum for a source located at 53mm fromthe detector

With εP (x) the unknow full peak efficiency spectrum to be interpolated from the knowspectrum at x0 and

Ω(x) = 2π

1− 1√1 +

(rD

x+wD

)2

(2.24)

where rD and wD denote the respective detector crystal radius and window thickness.This method assumes however that the intrinsic detector efficiency - i.e. the ratio of

all registered photons over all photons incident on the detector sufrace - is independentof the source-detector distance, an approximation which should only be applied for largedistances x, x0 >> rD or x ≈ x0. This can be easily seen from the situation depictedschematically in figure 2.6 where photon 1 and 2 hit the detector surface at the sameposition, but photon 1 will deposit more energy in the detector because its longer pathlength results in a higher reaction probability.

Experimental confirmation of this hypothesis can be found from figure 2.7. We cansee clearly how for geometries closer to x, x0 >> rD and x ≈ x0, equation (2.23) holdsbetter. The same is true for lower incoming photon energies: low energy photons alreadydeposit most of their energy near the detector surface, whereas for higher energy photonsthe deposition takes place over a larger distance and the dependence of intrinsic efficiencyon source-detector distance will be more pronounced.

A more advanced method to calculate the unknow efficiency spectrum at a certaindistance out of only a few known spectra can be found in [11].

11

Figure 2.4: Ratio between the experimentally determined peak efficiencies and the values de-termined from the fit as a measure for the uncertainty on the fitted peak efficiencyspectrum for a source located at 53mm from the detector.

Figure 2.5: Overview of the full peak efficiency spectrum at several source-detector distances

2.3.3 Total efficiency

The total peak efficiency εT (E) is defined as the ratio of all photons that deposit at leasta part of their energy in the detector over all photons emitted by the source in the decay.The calculation of the total efficiency follows more or less the same procedure as the fullpeak efficiency, one only has to take for S in (2.20) the total number of detected photonscoming from the radioactive source for all energies up to and including the full energy peak.This leads to a few extra measurement requirements: a background measurement has tobe performed, so the background counts can be subtracted from the energy spectra of thecalibration sources. From these sources only the ones with a single full energy peak in theirspectrum (or two very close to each other so they can be regarded as one) can be used. Inthe case of calibration sources with multiple full energy peaks, it isn’t possible anymore to

12

Figure 2.6: Schematical clarification of how the intrinsic efficiency of the detector depends onthe source-detector distance

Figure 2.7: Shortcomings of the efficiency spectrum interpolation through solid angle ratios(equation (2.23)). The active crystal diameter was 51.5mm and the thickness ofentrance window and dead layer was 5.5mm.

accurately distinguish between counts corresponding to a certain full energy peak and thesuperposed counts corresponding to Compton scattering of photons belonging to a higherfull energy peak. One also has to pay attention to the decay type. The 22Na callibrationsample for instance undergoes β+ decay. The annihilation of the positron within the sourcesample will give rise to 511 keV photons hitting the detector, where a strong 511 keV fullenergy peak will arise and again we find ourselves with a spectrum with multiple full energy

13

peaks.Following these restrictions, we will only take into account for the total efficiency calli-

bration the spectra from 57Co, 65Zn, 109Cd, 137Cs and 241Am from all callibration sampleslisted in appendix A. The resulting experimental total efficiency values are presented infigure 2.8. A fit of the form εT (E) = ea ln(E)+b is included for the high energy tail as well,with the ratios of experimental values over fitted values as a measure of the fit uncertaintygiven in table 2.1. Again we can state that fitted data agree within a 5% uncertainty toexperimental values.

The absence of sufficient number of data points to obtain a good representation of thelow energy peak area in the total efficiency spectrum is of secondary importance only. Thiscan easily be seen from a small numerical example. The total efficiency only contributesto the production rate through the cascade coefficient COI, which is usually within a 5%range around unity, occasionally 10%. So even uncertainties of 20% would only contributeto the uncertainty of the production rate by 10%.20% = 2%.

Figure 2.8: Total efficiency spectrum for a source-detector distance of 23mm.

Energy [keV] 123.7 661.7 1115.5Ratio exp/fit 0,989 1,048 0,964

Table 2.1: Ratio of experimental over fitted total efficiency values for a source-detector distanceof 23mm.

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2.4 Neutron flux absorption in gold foils

It is desirable for the activation foils to be thin enough not to disrupt the neutron flux. Inthis section we will investigate the evolution of the neutron flux through a gold activationfoil. For this purpose, three Au foils were irradiated together and subsequently analysedapart from each other.

2.4.1 Experimental set-up

When the U-120M cyclotron is active for the creation of radiopharmaceuticals, the nuclearreactions induced by the proton beam will lead to the creation of a lot of secondary particlesas well. As such, a.o. a neutron field is created which we have used here to irradiate thegold foils. The gold foils are made from the 197Au isotope, which comes at 100% naturalabundance.

Three seperate gold foils with dimensions 2cm x 2cm x 50µm, 1.5cm x 2cm x 50µmand 1.5cm x 2cm x 50µm were packed together in one paper envelope and irradiated. Thereason for the different foil geometries was only of practical nature and of no physical one -no other foils were simply at hand. The paper envelope allows easy handling of the sampleand will stop all radio-isotopes that might obtain enough energy from the (n,2n) reactionto leave the gold foil - even though this number is quite low, as can be seen from a simplecalculation to get an idea of the magnitude of the effect. The electronic mass stoppingpower S = 40MeV cm2

mg[12] at an energy of 10MeV. Now let’s for simplicity take S constant

during the slowing down of the particle, than from S.ρ = ∆E∆l

we find that a gold nucleuswith a kinetic energy of 10MeV will only be able to leave the sample if it is within a 0.13µmrange of the surface. For the foil dimensions stated above, this will only amount to 0.52%of the nuclei present.

The experimental set-up and foil configuration is given in figure 2.9.

2.4.2 Theoretical background

As a measure for the change in neutron flux as a function of the thickness of the activa-tion foil, we use the change in production rates in the three separate foils relative to theproduction rate of the first foil:

Bi

B1

=PiP1

m1

mi

(2.25)

=PiP1

V1

Vi(2.26)

=SiS1

V1

Vi

treal,itreal,1

tlive,1tlive,i

Cg,1Cg,i

eλ(t0,i−t0,1)

(1− e−λtreal,1

)(1− e−λtreal,i)

(2.27)

For which we have used (2.11),(2.9) and only considered relative production rates for thesame nuclear reactions (i.e. Bi(n, γ)/B1(n, γ) and Bi(n, 2n)/B1(n, 2n)) which allowed somesimplifications.

15

Figure 2.9: Experimental set-up for irradiating gold foils by a neutron field.

2.4.3 Analysis

In our spectral analysis we will use software tools such as Canberra1 or Deimos2 to fit aGaussian distribution to the recorded full energy peak and use the fitted values of m andσ2. Experience has shown that the Canberra fitting software can fit isolated and large fullenergy peaks very well, but when it comes to full energy peaks of low amplitude with a lotof other peaks in the spectrum nearby it starts to show considerable abberations. Deimoshas no problem with these spectral conditions because of the bigger user customizationpossibilities. It is possible to manually indicate all the peak locations, which Deimos willthen use as a basis for fitting. This results in better fitting of the background and thetaking into account of partially overlapping peaks. A screenshot of the fitting proces inDeimos is provided in figure 2.10.

Let’s take a look at the experimental set-up from figure 2.9 again. We expect theneutron flux spectrum to contain fast neutrons - a direct result from the nuclear reactionsin the radiopharmaceutical target by impinging high-energy protons. However, not all ofthese will hit the gold foils. The vast majority will be scattered around and moderated inthe concrete walls and the earth soil (which contain large amounts of water) that surroundthe experiment hall. So thermal and epithermal neutrons will show up in the spectrum aswell.

Figure 2.11 shows us the reaction cross sections for the 197Au(n,γ)198Au reaction andfor the 197Au(n,2n)196Au reaction [1], which shows a threshold around 8 MeV (the typical

1Canberra Industries, Inc. 800 Research Parkway, Meriden, CT 06450, U.S.A.2made by Jaroslav Frana, NPI Rez, CZ

16

Figure 2.10: Screenshot of the Deimos peak fitting window.

binding energy per nucleon). Looking at the magnitudes we can expect a considerable de-formation of the neutron flux in the (epi)thermal region as it passes through the three foils.The low cross section values for the 197Au(n,2n)196Au reaction predict little deformationonly for fast neutrons.

The relative production rates of the 198Au and 196Au are calculated using the numberof photons detected in the 411.80 keV and 355.68 keV decay lines respectively.

From equation (2.27) we obtain the relative production rates depicted in graphs 2.12and 2.13 for different distances between detector and sample. The relative production ratesare independent of this distance (see equation 2.27) and a mean relative production rateand uncertainty can be calculated using the statistical techniques explained in subsection2.2.3. They are presented in tables 2.2 and 2.3.

The relative production rate of 198Au drops to 76.4% in foil 2, indicating considerableabsorption of (epi)thermal neutrons when the neutron flux passes through the gold sample.The relative production rate of 196Au shows no significant absorption for fast neutrons. Thislies within the expectations from the cross sectional data.

Regarding the spatial distribution of the neutron flux, we notice that the relative pro-

17

Figure 2.11: Cross sections for 197Au(n,γ)198Au and 197Au(n,2n)196Au from the Jeffdatabase [1].

Figure 2.12: Relative production rates for 198Au in foils 1 to 3. A horizontal offset was providefor clarity.

18

Figure 2.13: Relative production rates for 196Au in foils 1 to 3. A horizontal offset was providefor clarity.

Foil 1 Foil 2 Foil 3Mean Brel 1 0.764 0.986Deviation 3,831.10−3 3,999.10−3 6,558.10−3

χ2R 0 4,165.10−27 1,287.10−27

Table 2.2: Statistical analysis of the relative production rate Bi(n, γ)/B1(n, γ)

Foil 1 Foil 2 Foil 3Mean Brel 1,000 0,940 1,001Deviation 0,027 0,030 0,034

χ2R 0,000 0,492 0,591

Table 2.3: Statistical analysis of the relative production rate Bi(n,2n)/B1(n,2n)

duction rates of 198Au and 196Au in foil 3 both lie within the uncertainty margins around1. With gold foil 1 facing the radiopharmaceutical target and foil 3 screened by the otherfoils, this means that scattering in the walls of the experimental hall is complete, as fromthe viewing point of the foils the neutron flux seems to be inbound from all sides in equalproportion.

As a conclusion we can compare these results with the simulations from [10] that aredepicted in figure B.2. We can clearly see how for the (n,2n) reaction the simulated neu-tron flux absorption is negligable as well. In order to compare the experimental relativeproduction rate for the (n,γ) reaction with the simulation, we calculate the average pro-duction rate in the [50µm,100µm] and [0,50µm] interval in figure B.2. For simplicity, apiecewise linear approximation of figure B.2 was used and the ratio of average productionrates yields a relative production rate of 76.3%. We can state that there is an excellent

19

agreement between experiment and simulation.

2.5 Geometric correction factor

The efficiencies calculated in section 2.3 hold for point-like sources. The activation foilstypically used have a finite size however. As a consequence, photons emitted along the edgesfrom the source will see the detector under a smaller solid angle than photons emitted fromthe center. As such, for radioactive samples of the same material and activity, the point-like source will give rise to more detected photons than the spatially extended one. Tocompensate for this, a geometrical correction factor Cg was introduced in (2.8).

2.5.1 Experimental method

In this section, we will experimentally determine the geometric correction factor for thethree gold foils from section 2.4. In order to do this, we will compare the productionrates of 198Au by (n, γ) reactions in the 2 cm x 2 cm and 1.5 cm x 2 cm gold foils with a1 mm x 1 mm irradiated gold-aluminum alloy. The experimental set-up for the irradiationof the activation foils is described in subsection 2.4.1. The 1 mm x 1 mm alloy was irradiatedduring 30 seconds in the LWR-15 research reactor of the NRI. The high neutron flux thatcomes with irradiation at the reactor is the main reason for the use of an alloy instead ofa pure 197Au 1 mm x 1 mm sample. It allows us to keep the activity of the produced 198Aulimited (since the amount of 197Au is limited), while the created radioactive 28Al (through(n, γ) reactions on 27Al, i.e. natural Al) with its half life of only 2.24 minutes will havenegligible influence on the activation spectrum if we wait for at least half an hour (i.e.already 13 half lives) between irradiation and measurements.

2.5.2 Spectral analysis

Using (2.11) and (2.9) we find for the ratio of production rates in the foil (Bf ) and the‘point’ source (Bpt):

Bf

Bpt

∝ PfPpt

=SfSpt

treal,ftreal,pt

tlive,pttlive,f

1

Cgeλ(t0,f−t0,pt)

(1− e−λtirr,pt

)(1− e−λtirr,f )

(1− e−λtreal,pt

)(1− e−λtreal,f )

(2.28)

Now all factors which are independent of the distance between source and detector can beabsorbed in the proportionality constant and we get following relation for the geometriccorrection factor:

Cg ∝SfSpt

treal,ftreal,pt

tlive,pttlive,f

eλ(t′0,f−t

′0,pt)

(1− e−λtreal,pt

)(1− e−λtreal,f )

(2.29)

Where we recall that t0 was the time between the start of the measurements and theend of irradiation, which we can write as t′0− t′irr with t′ denoting absolute time values, sothat

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eλ[t0,f−to,pt] = eλ[(t′0,f−t

′irr,f )−(t′0,pt−t′irr,pt)] (2.30)

= eλ(t′0,f−t′0,pt).eλ(t′irr,pt−t′irr,f ) (2.31)

Where the last factor is independent of the source-detector distance and can be absorbedin the proportionality constant as well in order to arrive at (2.29). Now we can eliminatethe proportionality if we set the geometric correction factor to unity for the sample foil inthe furthest source-detector position where it can be regarded as a point source.

(a)

(b)

Figure 2.14: Experimentally determined geometric correction factor for 2 cm x 2 cm irradiatedgold foils (a) and 1.5 cm x 2 cm (b) as a function of the source-detector distance.

The result is depicted in figure 2.14. The datapoints clearly follow the same behaviouras simulation results (see figure B.1). The main difference in size between the experimentaland simulation results is caused by the set-up used in the experiment (see figure 2.9). Foil 1is partially shielded by foil 2 and 3 that absorb a fraction of the incoming thermal neutron

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flux. As a result, activity in foil 1 will be higher at the edges then in the center, so moreemitted gamma photons will see the detector under a smaller solid angle than would bethe case if the activity was uniformly distributed and Cg will be lower. Foil 2 on theother hand is more or less homogeneously shielded and the corresponding Cg values arein closer agreement to figure B.1. The simulation from figure B.1 was also carried outwith a slightly different detector model, which could contribute to some extent to the sizedifference but isn’t enough to explain it entirely [8]. We can conclude that although thechoice of foil dimensions was at first purely out of practical reasons and did not hamper theinvestigation of neutron flux absorption, it is most unfortunate for the proper investigationof the geometric correction factor and a new experiment is due.

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Chapter 3

Personal evaluation

The seven weeks I spent in Prague at the NPI in Rez for my trainingship have been veryrewarding. For the first time, I was really able to handle radioactive samples myself,perform measurements on them and analyse the resulting data. As a result I gained a lotof experience and knowledge in the field of nuclear spectroscopy. I was surprised to see theamount of effort that hides behind such things as an efficiency callibration, that are easilytaken for granted when going through papers and books.

The relevance of the work I did was an important aspect to me as well and it wasvery satisfying that my results were used for the PhD defense of Mitja Majerle[10] on 2September and the paper that is being prepared on the different effects one has to takeinto account when using neutron activation detectors where the influences are investigatedbased on Monte Carlo simulations and where I have taken care of part of the experimentalverification of those simulations.

During the trainingship, I also had the chance to go on a lot of excursions to a.o. theU-120M cyclotron, the tandetron, the microtron in an underground laboratory, the Golemtokamak (formerly known as Castor), the LVR-15 experimental light-water reactor,... (fig-ure 3.1). It was very interesting to see such machines in reality, to get some informationfrom the people who operate them and to ask them questions. I also got to attend somelectures of the Spin Praha 2009 conference[2].

(a) (b) (c) (d)

Figure 3.1: View on the U-120M cyclotron (a), the tandetron (b), the microtron (c) and theLVR-15 research reactor (d)

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I would therefore like to say thanks to Vladimir Wagner, Mitja Majerle, Antonın Krasaand Marek Firkle who have assisted me during some measurements and were always thereto answer my questions.

Doing my trainingship abroad through the IAESTE program didn’t let me down again.After a trainingship in Athens last year, it became Prague this year. Next to the pro-fessional aspect mentionned above, there is an important social and cultural aspect toIAESTE trainingships. It left me with friends from Brasil on one side of the globe toChina and Japan on the other side. After two months in the Czech Republic, I reallygot to learn the local culture. I moved as freely through Prague as through Ghent. Thenthere were the sight-seeing trips to Dresden, Budapest, Vienna, Karlovy Vary, Kutna Hora,Karlstejn organized by IAESTE or among us, trainees. Not to mention the parties, lasershooting, carting and just strolling around through Prague. It was a very rich and fulfillingsummer!

Steven Peetermans23 September 2009

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Appendix A

Isotope Epeak [keV] Iγ[%]22Na 1274,53 99,94457Co 122,0614 85,6

136,4743 10,68860Co 1173,237 99,9736

1332,501 99,985665Zn 1115,546 50,6

109Cd 88,04 3,61133Ba 53,161 2,199

79,6139 2,6280,9971 34,06160,613 0,645223,234 0,45276,398 7,164302,853 18,33356,017 62,05383,851 8,94

137Cs 661,657 85,1152Eu 121,7817 28,58

244,6975 7,583344,2785 26,5411,1163 2,234778,904 12,942867,378 4,245964,079 14,6051085,869 10,2071089,737 1,7271112,074 13,6441212,948 1,4221408,006 21,005

241Am 59,5412 35,9

Table A.1: overview of the peak energies and gamma emission probabilities of the radioactivesources used for the efficiency callibration.

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Appendix B

This appendix contains the simulation results from [10] that are experimentally verified inthis report.

Figure B.1: Simulated geometric correction factor for 2cm x 2cm x 50µm irradiated gold foilsas a function of the source-detector distance.

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Figure B.2: Ratio between the production rates for (n,xn) and (n,γ) reactions in gold foils withdifferent thicknesses and the production rates in the foils filled with air (to simulatean absence of absorption).

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