Analysis of some important parameters in gamma spectroscopy based on theoretical and experimental calculations
There are two types of radioactivity namely, Artificial Radioactivity and Natural Radioactivity. Artificial radioactivity samples have large activity which can be easily detected by High Purity Germanium (HPGe) detector but environmental samples contain very less concentration of primordial radionuclides having activity of ~2-3 Bq. Hence, in order to obtain accurate and reliable data using HPGe detector, the device needs to be well calibrated. The present work explains the various aspects of radioactivity, gamma spectroscopy, radiation detection and instrumentation, utility of HPGe detector and its comparison with Sodium Iodide (NaI (Tl)) scintillation detector. The measurements of FWHM/resolution, energy and efficiency calibration has been done using GENIE 2K software and the calibration has been checked with theoretically calculated values. For performing energy calibration, single point sources of artificial radioisotopes have been used and for efficiency calibration, in-house prepared standards of bulk sources having very low activity ~2-5 Bq have been used. The results were obtained and verified showing that the instrument has been properly calibrated according to our requirements and can provide reliable data for radioactivity measurements.
Keywords: radioactivity, natural radioactivity, artificial radioactivity, energy calibration, efficiency calibration
|HPGe||High Purity Germanium|
|NORM||Naturally Occurring Radioactive Material|
|TeNORM||Technologically enhanced Naturally Occurring Radioactive Material|
|FEP||Full Energy Peak|
|FWHM||Full Width at Half Maximum|
|FWTM||Full Width at Tenth Maximum|
|CPS||Counts Per Second|
|DPS||Disintegrations Per Second|
|NaI(Tl)||Sodium Iodide (Thallium)|
|CsI(Tl)||Cesium Iodide (Thallium)|
|LiI(Eu)||Lithium Iodide (Europium)|
Radioactivity is the phenomenon of spontaneous emission of radiation from radioactive materials, which are substances with unstable nuclei emitting highly energetic charged particles and radiations. It is the property of an individual nucleus. The phenomenon of radioactivity was discovered by Henri Becquerel in 1896 while studying the properties of X-rays using natural fluorescent materials. The term radioactivity was first coined out by Marie Curie, who discovered radioactive substances, Radium and Polonium. Radioactivity is the key process to understand the structure, stability and behaviour of different nuclides.
Nuclides and symbols
A nuclide is an atom/nucleus characterised by a specific number of nucleons i.e. protons and neutrons or the atomic number (A) and the mass number (Z). If the nuclide is radioactive then it is called a radionuclide. The symbol for nuclide is AZX.
Classification of nuclides
Nuclides may be classified in several ways. On the basis of stability, nuclides are of two types: stable nuclides and radionuclides.
Stable Nuclides are those which do not show any radioactive decay.
14N, 12C, 16O, 90Zr, 19F, 89Y, 40K, 153Eu, 107Ag, 56Fe, 203Tl, 135Ba, 52Cr and many more.
Unstable Nuclides or Radionuclides undergo radioactive decay and are further of the following types: Natural Radionuclides and Artificial Radionuclides.
1. Natural Radionuclides: Natural Radionuclides are those which are radioactive in their natural state. They are further of the following types:
Primary natural radionuclides are those natural radionuclides which have present on Earth since the origin of the solar system. These radionuclides have very long half-lives comparable to the age of Earth.
Examples: 238U (T1/2 = 4.5 x 109 a), 40K (T1/2 = 1.28 x 109 a), 232Th (T1/2 = 14.05 x 109 a), etc.
Secondary natural radionuclides are those which have been produced by the decay of primary radionuclides and have shorter half-lives.
Examples: 226Ra (T1/2 = 1600 a), 234Th (T1/2 = 24.1 days).
Induced natural radionuclides are produced by the action of cosmic radiation in Earth's atmosphere. Examples: 3H (T1/2 = 12.3 a), 14C (T1/2 = 5730 a).
2. Artificial Radionuclides: These are man-made radionuclides and do not occur naturally in the environment.
Example: 60Co (T1/2 = 5.26 a), 137Cs (T1/2 = 30.17 a), 24Na (T1/2 = 14.9 h), etc.
Natural decay series
There are four natural decay series:
1. Thorium Series, 4n+0
2. Uranium Series, 4n+2
3. Actinium Series, 4n+3
The fourth decay series is neptunium decay series (4n+1) which is extinct now because its parent atom, 237Np has half life of 2.14 x 109 a which is shorter than the age of Earth which is 4.7 x 109 a .
Radioactive decay is the process of spontaneous emission of radiation or energetic particles from an unstable atom. This process is completely random and exoergic in nature.
The three basic types of radioactive decay are alpha, beta and gamma decay. Other types of decay also exist but they are less probable as compared these three. They are spontaneous fission, delayed neutron emission, delayed proton emission, two-proton decay, double β decay and composite particle emission.
In α-decay, a nucleus emits 4He nucleus consisting of two protons and two neutrons.
Mainly three types of processes occur which we classify as β decay: Negatron decay, positron decay and electron capture.
When a nucleus transitions from a higher excited state to lower excited state or the ground state, then γ-radiations are emitted by the nucleus. During γ decay, there is no change in the A or Z of the parent nucleus.
There are three modes of γ decay: pure γ-ray emission, internal conversion and pair-production
Units of radioactivity
The SI unit of radioactivity is the Becquerel (Bq). 1 Bq = 1 dps
Another unit of activity is Curie (Ci). 1 Ci = 3.7 x 1010 Bq
This type of equilibrium is possible when the half-life of the parent nuclei is a few times greater than the half-life of daughter nuclei.
When the parent and daughter achieve the transient equilibrium, the ratio of their activities becomes constant and activity of the daughter becomes greater than the activity of the parent at equilibrium.
When the half-life of the parent nuclei is much longer than the half-life of the daughter nuclei, then secular equilibrium can be established between them.
The activity of the parent is greater than daughter and stays essentially constant whereas the activity of the daughter increases and becomes equal to the activity of the parent. Ratio of their activities is unity.
Equilibrium cannot be obtained when the half-life of daughter is greater than the half life of parent. In this case the activity of parent decreases and goes to zero whereas the activity of daughter goes on increasing and then starts decreasing.
Interaction of radiation with matter
Some basic modes in which radiation interacts with matter are: Ionization, molecular and atomic excitation, radiative processes, kinetic energy transfer and nuclear reactions.
Heavy charged particles interactions: Alpha particles are heavy charged particles. They have shorter range and interact with matter primarily through ionization processes.
Beta-particle interactions: The range of β-particles is greater than α-particles. Main modes of interaction are: bremsstrahlung radiation, Cerenkov radiation, beta backscatter, positron interactions.
Interaction of Gamma Radiation with matter
Gamma rays are electromagnetic radiations consisting of photons which are charge-less and have zero rest mass and very high energies. Due to which their interaction with matter is different from the way alpha and beta radiation interact with matter. They have high penetration and are emitted when unstable nuclei transition from high energy state to a low energy state. Gamma rays do not lose energy continuously like charged particles and are unaffected by Coulomb interactions. The ways in which γ-radiations interact with matter is such that they either lose all their energy or a part of it.
The major modes of interaction of γ-rays with matter are: the photoelectric effect, Compton scattering, and pair production. 
1. Photoelectric Effect
In photoelectric effect, a photon interacts with an electron in the atom, transferring all its energy to the electron, part of which is utilised in knocking out the electron and rest is imparted as kinetic energy to the knocked out electron, i.e. the electron receives all the energy of the γ-ray, minus its binding energy:
Ee,PE = Eγ - BEe
High energy γ-rays manage to knock out electrons from the inner shells of the atom which in turn leads to the production of X-rays when outer orbit electrons get de-excited to the empty inner shell in the place of the knocked out electron.
The probability of occurrence of the photoelectric effect is
(i) directly proportional the atomic number Z of the absorber element,
(ii) inversely proportional to the energy of the incident γ-ray.
This implies that photoelectric effect is more probable when we have low energy γ-rays and high-Z absorbers.
The electrons produced as a result of photoelectric effect are detected by the detector. Following plot shows the number of γ-rays detected versus the energy of the γ-ray when only photoelectric effect takes place.
2. Compton Scattering
A γ-ray incident on an orbital electron of an atom, instead of losing all its energy, may lose a part of its energy transferring it to electron. As a result the electron gains kinetic energy and gets scattered whereas the direction of the γ-ray changes. This process is called Compton scattering, named after its discoverer Compton.
The probability that Compton scattering will occur is:
(i) directly proportional to the atomic number Z of the element, i.e. for an element with high atomic number there will large number for electrons present for scattering thus there is a greater probability for the Compton scattering to occur.
(ii) inversely proportional to the energy of the incident γ-ray.
The electron scattered by the γ-ray is then detected by the detector.
Fig. 7 shows the γ-spectrum in the case of Compton scattering. It is possible that some γ-rays escape the detector and their energies go undetected which ranges from 180° backscatter energy to the total energy of the γ-ray. Compton continuum corresponds to the range of energies imparted by the γ-ray to the scattered electrons. If the γ-ray loses all its energy in the detector then we get a FEP in addition to the Compton distribution. 
In practise, the γ-rays can also interact with the shielding material due to their high penetration which results in a peak which appears as following.
3. Pair Production
When the energy of the γ-ray is greater than 1.02 MeV then near an atomic nucleus, it can get converted into positron and electron. This process is called pair production and is only possible for high-energy photons in the vicinity of a nucleus.
The probability that this process shall occur is directly proportional to the atomic number Z of the absorber and the energy of the incident γ-photons.
The positron released during the process may get annihilated with an electron producing two annihilation photons.If one of these photons escapes the detector than we get what is called the first escape peak. Its energy is equal to 0.511 MeV and we get a peak at this energy. If both the annihilation photons escape the detector taking with them 0.511 MeV x 2 = 1.02 MeV energy. Then we get a peak at 1.02 MeV called the second escape peak.
We may get another peak at high energy called sum peak. It corresponds to the sum of the energies of two gamma rays released at the same time and detected as a single event by the detector.
In order to detect a radiation, it must interact with the detecting material through one of the ways described above.
There exists a different types of detectors used for detecting different types of radiation.
Examples are Ionization chamber, Geiger-Muller counters and proportional counters.
All of these work on the process of ionization of fill gas when any radiation passes through them. This ionization is converted into a signal by applying external voltage.
Scintillation detectors are different from gas-filled detectors in the respect that instead of a gas we have something called scintillator. The incident radiation interacts with scintillator absorbing the radiation exciting the electrons to higher level. These electrons de-excite and emit energy in the visible region. This process is called fluorescence. These pulses of light are very small so we use what is called a photomultiplier tube. Its purpose is to amplify the light incident on its dynodes.
On the basis of the nature of the fluorescent material, there are two types of scintillation detectors.
1. Inorganic scintillation detectors: These constitute the detectors made of alkali halides. Examples: NaI(Tl), CsI(Tl), LiI(Eu), CsF. When radiation passes through these detectors, electron transitions take place between energy states of the atom. NaI is the most commonly used scintillation detectors, but it cannot be used in its pure form because the band gap is very large and photons emitted are of very high energy beyond the visible region. To solve this issue, we use activator Tl which creates additional energy levels between the original levels of NaI giving photons in the visible region. This is then called NaI(Tl) scintillation crystal. This scintillator has high efficiency but poor energy resolution. CsI(Tl) has the highest efficiency compared to other crystals.
2. Organic scintillation detectors: Organic molecules like anthracene and stilbene are also used as scintillants(liquid/solid). Here the electron transitions take place between molecules. Since these molecules are composed of elements with low Z, they are not used in detection of γ-rays but used for α and β detection.
The basic principle of semiconductor detectors is the generation of electron-hole pairs in the depletion region of a p-n junction when radiation is incident on it. The diode is used in reverse bias since the width of the depletion layer is larger in this case which provides greater area for detection. But this width can be increased even more by drifting. In this technique ions with opposite charge are drifted into the diode which neutralise the charge on both sides thus increasing the width of the depletion region. Li is used for drifting because of its small size and high mobility. It is diffused to one end of the p-type semiconductor. A drifted semiconductor material needs to be cooled because Li may drift out of the semiconductor. Examples: Si(Li), Ge(Li) 
The main characteristics of semiconductor γ-ray detectors are: resolution, efficiency and peak-to-Compton ratio. Drifted semiconductors have good energy resolution and efficiency.
High-purity germanium detectors
With latest techniques, it has become possible to produce Ge crystals having very low concentrations of impurities. It is called Intrinsic Germanium or High-Purity Germanium(HPGe). Since Ge has a small band gap, thermal excitations at room temperatures can give false readings and add error to the observed value due to which these detectors are cooled down using liquid nitrogen.
A HPGe detector has following components:
Statement of the Problems
In order to get reliable data for radioactivity measurement by an HPGe detector, the device needs to be properly calibrated properly with respect to energy of the γ rays and efficiency of the detection of the detector. Improper calibration can lead to faulty results for measurement of radioactivity especially in natural samples, where activity is nearly negligible.
Objectives of the Research
- To understand the fundamentals of γ-spectrometry.
- Learning the applications of two important γ detectors: NaI(Tl) and HPGe in measuring natural and artificial radioactivity.
- Theoretical and experimental calculations of FWHM/resolution for HPGe detector having 80% relative efficiency.
- Energy calibrating the same HPGe detector with single point source activities of 133Ba, 60Co and 137Cs.
- Plotting the efficiency calibration for measurement of low-level radioactivity using bulk sources of 2-5 dps 238U and 2-5 dps 232Th.
- Understanding the complex γ-spectra of the point sources, the bulk sources and to identify the respective photopeaks from the spectra.
From the present study, ideas about radioactivity, γ-spectrometry, different types of detectors for detection of different types of radioactivity, the mechanism of detection, utility of associated electronics and software could be achieved. Through intense theoretical and experimental approaches, the present study helped in getting knowledge about the three important parameters related to γ-spectrometry i.e. FWHM/resolution, energy calibration using point sources and efficiency calibration using bulk sources.
Hence, the scope of the present study lies in the appropriate application of efficiency calibration for measuring radioactivity. Proper efficiency calibration is required especially for measurement of natural radioactivity in environmental samples where activities are present at very low or trace level of 1-2 Bq in 50 g of environmental sample. Detection of such low level radioactivity requires several parameters to work in synchronization. Also, sample geometry is an important parameter in such cases. Thus, a proper efficiency calibration ensures reliable data for low-level natural radioactivity.
Gamma spectrometry is practised much more as compared to α-spectrometry and β-spectrometry but different laboratories have different detector types, procedures of calibration and different sample geometries which leads to huge variation in results obtained from different places .
There are three main aspects of calibration of a γ-spectrometer: energy, FWHM and efficiency which are individually the functions of number of channels . The purpose of energy calibration is to identify the energy of the γ-ray in the spectrum obtained by the system . The initial efficiency calibration of the system is not affected by energy and resolution calibration . The detection efficiency has a complex dependence on energy of γ-rays, sample geometry, type of detector, etc. 
The efficiency and resolution of HPGe detector has been compared with that of NaI(Tl) scintillation detector in Hossain et al 2010. The HPGe detector can resolve two close energies much more efficiently than NaI(Tl) detector but its disadvantage is that its detection efficiency is much lower as compared to NaI(Tl) detector. Also the detection efficiency of HPGe detector decreases which increase in γ-ray energy .
In case of low level NORM measurements, instead of performing efficiency calibration, Naskar et al 2017 has compared the area counts of photopeaks of standard with samples having the same geometry and composition.
Calin & Druker 2011. observed that at high energies, there is a displacement of amplification of the system and movement in peaks and if similar behaviour is also observed in the background spectrum then recalibration should be done.
Different laboratories have used different techniques of calibration[9-13]. Morera-Gomez et al 2016. has first calibrated the device and then checked the accuracy of calibration using Monte-Carlo simulation methods. Daza et al 2001 has used a method with two different experimental inputs. First, it measures radioactive sources emitting γ-rays of many energies. Then it measures sources emitting γ-rays in order of single energies and gives a general function of dependence of efficiency on energy.
Energy and efficiency calibrations are essential prerequisites for the proper functioning of detectors to be used for γ-spectrometry and different researchers have used different techniques and methods to calibrate the γ-spectrometers and validate their calibrations.
As we have discussed in the literature review that there are three important concepts of calibration required in HPGe detectors that include:
- FWHM/resolution as a function of the channel number.
- Energy of the γ rays as a function of the channel number.
- Efficiency as a function of channel number.
1. FWHM/Resolution: FWHM is a parameter in γ-spectrum which defines the resolution of a peak by the detector. It gives the spread of a peak between two values of energy at which the number of counts is equal to half of the maximum value. It is calculated as follows:
We take the half of centroid value and find the energies on either side of the peak where the count is half of the maximum value. The difference in these two energies gives us FWHM of that peak.
FWTM gives the full width of the peak at tenth of the maximum value. It is also a useful parameter to calculate along with FWHM.
For a good detector the value of FWHM and FWTM should be small at high energies. This is because better the resolution through the energy range, better chance of resolving closely spaced photopeaks.
2. Energy calibration: Energy calibration is done in gamma detector in order to linearly assign energy values to all the channels which, are essential for accurate measurement of the γ-energies by the software. Also this enables the software to identify the unknown photopeaks from the energy calibration plotted with known point sources.
3. Efficiency calibration: Efficiency of a detector is defined as the ability of the detector to detect the incident γ rays.
CPS detected by the HPGe are directly proportional to
1. No. of gamma rays emitted by the sample per unit time.
2. Efficiency of the detector for detecting γ rays
3. Intensity of characteristic peaks
Therefore, CPS = DPS × Efficiency × Intensity
Then Efficiency for HPGe detector is numerically calculated as follows:
It is the ratio of the counts detected by the detector per second to the number of γ rays actually emitted by the source. Ideally the ratio should be unity i.e. 100% efficiency but it is not practically possible. So its value is always < 1. Efficiency obtained in this way is the absolute efficiency of the detector.
As we know that a HPGe detector is less efficient than a NaI(Tl) scintillation and its efficiency is always defined relative to the efficiency of a 3'' x 3'' NaI(Tl) detector. This is the relative efficiency of the HPGe detector.
Generally, efficiency decreases with increase in energy/channel number. Efficiency calibration is always done after doing the energy calibration of the gamma detectors. Efficiency shows a decreasing trend with increasing energy. This is especially required for measurement of natural radioactivity.
FWHM and Energy calibration
In order to perform energy calibration of the HPGe detector having 80% relative efficiency, we need point sources emitting characteristic γ rays over a wide range of energy preferably the range over which the γ spectrum will come up.
We have used following single point sources to perform the energy calibration: 133Ba, 152Eu, 60Co and 137Cs where the photopeaks of respective Region of Interest (ROI) are having Gaussian shape. The range of γ energies emitted by these nuclides is given in the following tables. The tables show the characteristic γ energies and their relative intensities. 
|γ-peaks [keV]||Iγ [%]|
|γ-peaks [keV]||Iγ [%]|
|γ-peaks [keV]||Iγ [%]|
|γ-peaks [keV]||Iγ [%]|
However, out of all these photopeaks/γ energies not all are useful because of their varying intensities. Only those energies have been used which have detectable intensities and are resolvable by the detector. All used energies have been bolded in the tables.
For example, 152Eu emits a large number of γ energies but only those energies have been used that are marked bold. Energies 39.522 and 40.118 keV have measurable intensities but since these values are close to each other, their respective peaks overlap with each other which the detector may not be able to resolve properly. Same is the case with 1085.885 and 1089.706 keV. So we ignore these peaks and use only those which are intense as well as properly resolved.
If we take the spectra of these sources together then the peaks of 133Ba and 152Eu may interfere with each other because they have several photopeaks and some may overlap with each other. So, we obtained the spectra of 133Ba, 60Co and 137Cs together and that of 152Eu separately to check the calibration. Since these are artificial radioisotopes, they possess high activity and short preset times are sufficient to obtain a good spectra with Gaussian shaped peaks. So, the spectra for all these sources have been measured for 500s each. Then we marked all the characteristic peaks and calibrated them. Finally on calibrating, we obtain a plot of channel number with γ energies.
We also obtain a plot of FWHM with channel number.
In order to perform efficiency calibration, we have used bulk sources having very low activity of ~2-5 Bq. Here we made use of in-house built standards: 2 dps and 5 dps 238U and 2 dps and 5 dps 232Th. The γ energy and intensity of various peaks of these isotopes has been obtained from Shirley et al 1986 .
We obtained the spectra for above mentioned bulk sources as well as background for 75000s because this was found to be optimum time for HPGe 50% detector by Nasker et al 2017 . This concept has been extended for present work 80% HPGe detector. After stripping the background from all the experimental spectra, we calculate the efficiency of each characteristic peak in the spectrum by the formula mentioned above. We match these values with the efficiencies obtained by the software and finally obtain a plot in which efficiency shows a decreasing trend with increasing γ energy.
RESULTS AND DISCUSSION
- To energy calibrate HPGe detector using point sources of 133Ba, 60Co, 137Cs.
- To plot efficiency calibration using bulk sources of 238U and 232Th.
- To utilise these calibrations effectively in identifying different unknown photopeaks of U and Th and measure their activities from their area count by marking the ROI.
In order to check variation of FWHM and FWTM with energy of the γ rays, first we calculated FWHM and FWTM for all the characteristic peaks and compared the calculated values with those obtained by the GENIE 2K software that we are using. Results obtained are given in Table 3 and calculated and observed FWHM and FWTM have been plotted with respective γ energies in Fig. 13 and 14.
|Isotope||Gamma peak (keV)||FWHM calculated by formula||FWHM by GENIE 2K software||FWTM calculated by formula||FWTM by GENIE 2K software|
From these graphs we observe that
- With increase in γ energy, there is an increase in FWHM as well as FWTM which is exactly what is desired for these parameters. This is also the basic parameter of any gamma detector.
- Both the measured and calculated values of FWHM and FWTM are in good agreement with each other.
Using the point sources mentioned in previous section, the energy calibration was performed using GENIE 2K software and following energy calibration curve was obtained.
The graph shows a straight line passing through origin with all the measured points lying on the fitted line. This shows that energy calibration has been performed correctly. [GENIE 2K software from CANBERRA]
Following the procedure for efficiency calibration mentioned in the previous section, we first used in-house standards of 2 dps 238U and 2 dps 232Th to perform the calibration. Table 4 shows the values of efficiency for each characteristic peak Fig. 16 shows the calibration curve provided by the GENIE 2K software.
|Parent||Isotopes||gamma energy||intensity||dps||Area||preset time||CPS||efficiency|
We note in Table 4 that area count obtained for certain peaks is very small. For 214Bi, area count for 934.039 keV is very small, equal to 4. The reason for this is since we are using sample with very small activity of 2 dps, the detector is unable to detect this small activity efficiently which can affect our efficiency calibration. To solve this issue, we have extended the same phenomena taking standards of higher activity. So, we used 5 dps 238U and 5 dps 232Th in-house standards which gave good area counts for various energies as shown in Table 5 and hence obtained calibration curve shown in Fig. 17
|Parent||Isotopes||gamma energy||intensity||dps||Area||preset time||CPS||efficiency|
From the curve, we observe that efficiency decreases with increasing energy as expected and hence we can say that the efficiency calibration done is accurate. [GENIE 2K software from CANBERRA]
CONCLUSION AND RECOMMENDATIONS
From our calculations and observations for FWHM, FWTM, energy calibration and efficiency calibration, we can conclude that the gamma-detector being used for present study has been well calibrated. We also note that for measurements of natural and environmental samples which contain very small activity of about 2-3 Bq, proper energy and efficiency calibration are extremely important in order to get reliable data.
It is always recommended that before measuring any concentration of radioactivity in any γ-detector, the detector should be well-calibrated and all other parameters and electronics should be complimenting the detector mechanism. This is how a researcher who is new in the field of nuclear chemistry or physics can ensure reliable end result from his/her experimental setup.
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I would like to thank Indian Academy of Sciences for providing me this opportunity and necessary fellowship for pursuing this project.
I am indebted to my guide Professor Susanta Lahiri for his constant guidance, care, encouragement and support throughout the project. He has always made himself available to clarify my doubts. From interdisciplinary nature of his research, I learnt to appreciate the beauty of research and have developed a keen interest in experimental research. I am proud of being associated with him, and I consider it as an excellent opportunity to do my summer project under his guidance and to learn from his research expertise.
My special thanks to Nabanita Naskar (Nabanita Di), research scholar for guiding me and clarifying my doubts at every step during this internship and sharing with me her knowledge and experience that I shall always carry with me.
My parents always support me for my endeavours and let me pursue them against all odds. A simple 'thanks' would not be sufficient.
Also, I would like to thank all my colleagues and friends I met at SINP, Kolkata who made this two month internship a memorable and cherished experience.
Finally, I am thankful to Saha Institute of Nuclear Physics, Kolkata for giving me the opportunity to work in the radiochemistry laboratory.