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Transcript
VOLUME #, NUMBER # PHYSICAL REVIEW STYLE LETTER 11 DECEMBER 2007 _____________________________________________________________________________________________________________________ Gamma Spectroscopy and Detector Calibration Elizabeth Pollock University of Rochester I first explain the three main interaction of photons with matter: (1) Photoelectric effect, (2) Compton Scattering, and (3) Pair Production. Next, I explain how the spectra are obtained with the set-up in Advanced Lab. Finally, by analyzing the known spectra of three radionuclei, Na-22, Cs-137, and Co-60, I show how one can calculate the efficiency and resolution of a detector, as well as calibrate the detector channel number in relation to energy. Similar to the discrete energies observed when electrons transition from lower orbitals to higher orbitals, or higher to lower, the nucleus is also characterized by discrete energy levels. Analogous to the electron shell model, these discrete energies occur when the nucleus emits or absorbs electromagnetic radiation of the allowed energy, which is the energy difference between the allowed transitions of the nucleus. For γ-rays, this energy ranges from 0.01 to 10 MeV. Therefore, γ-rays show spectral lines characteristic of the emitting nucleus, and thus the γ-ray spectrum is unique to each nucleus (see Fig. 1) [1]. In this Letter I will describe the basic interactions of γ-rays with matter and also show how different known γ-ray spectrums can be used calibrate a detector. To do this, I will explain the spectrums of three γ-emitting nuclides: Sodium22 (Na-22), Cesiums-137 (Cs-137), and Cobalt-60 (Co-60). From these spectra, I will explain how the channel number of the detector corresponds to the energy of that channel, and thus describe detector calibration. To understand a γ-ray spectrum, it is critical to recognize that the interactions of charged particles, such as protons and electrons, are very different than the interactions of photons with matter. The primary interactions of photons, or γrays, in matter are the: 1. Photoelectric Effect 2. Compton Scattering 3. Pair Production. In the photoelectric effect and pair production the γ-ray is completely absorbed, where as in Compton scattering the gamma ray is scattered [2]. FIG. 1. Decay scheme of three radionuclides. The energies corresponding to the γ-rays emitted during transitions are given. Image Credit: [2]. Furthermore, the effects of these interactions are governed by the atomic number Z of the absorber and of the emitted γ-ray energy, , as seen in Fig. 2 on the following page. VOLUME #, NUMBER # PHYSICAL REVIEW STYLE LETTER 11 DECEMBER 2007 _____________________________________________________________________________________________________________________ The γ-ray-absorber interaction depends on the atomic number Z of the absorber and the γ-ray energy, . Image Credit: [2]. FIG. 2 (a) The first of the three interactions among photons, the photoelectric effect, occurs when the γ-ray is absorbed by an atomic electron, which then results in the emission of an electron (see Fig. 3(a)). This results in the ejected electron energy of: where E is the sum of the kinetic energy of the electron, K, and the atom, Ka, and B.E. is the binding energy of the electron [2]. From Eq. (1) one sees that the photoelectric absorption occurs when the energy of the incident γ-ray has an energy higher than the binding energy, B.E. of the electron that is ejected in the collision [3]. The next interaction mentioned is Compton Scattering, the scattering of photons on free electrons [1]. In this interaction, we assume that the energy of the photon, , is much greater than the binding energy of the electron, B.E., and therefore the electron is treated as a free electron. From the conservation of momentum and energy, it follows that the energy of the scattered γ-ray is given by: (b) (c) where . Similarly, the kinetic energy of the struck electron is by: Where the maximum energy transferred is called the Compton edge, which occurs when ϑ = 180°. FIG. 3. (a) Photoelectric absorption. An incident γ-ray with energy collides with a bound electron in an atom, and ejects the atom with energy K and momentum P, and the atom recoils with energy Ka and momentum Pa. (b) Compton Scattering. (c) Pair Production. Image Credit: [2]. VOLUME #, NUMBER # PHYSICAL REVIEW STYLE LETTER 11 DECEMBER 2007 _____________________________________________________________________________________________________________________ Finally, pair production occurs when a photon of sufficient energy is absorbed by matter and subsequently produces a pair of oppositely charged particle [4]. Thus, the γ-ray is transformed into an electron-positron pair. This interaction becomes important when an incident γray of energy MeV interacts with matter. Conservation of energy and momentum requires that this interaction cannot occur in free space, and thus there must be a nucleus or an electron for to satisfy conservation laws [3]. Now that I have explained the basic interactions between γ-rays and matter, I will explain how I obtained the spectrums of the three sources. The gamma spectroscopy set-up consists of a source placed a few centimeters from a backscatter plate (Lead or Aluminum), and a scintillation detector including a Photomultiplier Tube (PMT), connected to a linear amplifier, which then sends the signal to the Multi-Channel Analyzer (MCA), which converts the signal produced by the detector into a digital signal. From the MCA, the signal may then be viewed on the oscilloscope or computer screen using the acquisition program. The main obstacle of this lab required selecting a gain for the linear amplifier that did not result in oversaturation of the output voltage signals. Thus, to avoid saturation, I used the following settings for the linear amplifier: a coarse gain of 2, and a fine gain of approximately 3. Once these settings were determined, a background sample was taken for 10 minutes. After the background sample was recorded, my lab partner and I collected samples of the three sources, each with the two different backscatter plates (Lead and Aluminum), for 10 minute intervals. Analysis of the spectra was obtained via a C++ and Root program which in addition to plotting the Channel Number vs. Counts for each spectra, also displays the χ2, Constant, Mean, and σ values, see Fig. 4. Of these values, the ones pertinent to calibrating the detector include the Constant, which is the amplitude of the peak, the Mean, which represents the mean of the channel number, and the σ value, which is related to the full width half maximum (FWHM) value of each peak. The error in the Mean represents the error in the channel, and thus the error in the calibration of channel number to energy. As we can see from Fig. 2, the maximum error in the Mean is seen in the Na-22 Spectrum: 0.3795, which is a small fraction of the total number of channels, 1022, and thus is nearly negligible. The FWHM represents the resolution of the detector. The resolution of the detector is a measure of how good the detector is. The higher the resolution, the better the detector, that is, the easier it is to distinguish between energy peaks located next to each other. The value σ is a measurement of the distribution of the Gaussian at a particular peak. It is related to the FWHM, which represents the width of the gamma ray peak at half of the highest point on the peak distribution, by the following equation: Expressing the resolution in absolute terms, that is, expressing the resolution in terms of the specific γ-ray energies, we see, for example, the FWHM of the 0.511 MeV peak of the Na-22 spectrum (Fig. 4(a)) is approximately 2.35*401.9, which is 26.226. The other resolution values can be calculated similarly. In addition, from the FWHM calculations, the efficiency of the detector can be calculated, where the efficiency is defined as: While the detector resolution and efficiency is found from the FWHM, the correlation between the channel number and the energy still remains undetermined at this point. To find the relationship between channel number and energy value, one must analyze the spectra of the three known sources: Na-22, Cs-137, and Co-60. The first step towards analyzing each spectrum individually is to subtract the background spectrum from each of the three sources. This is trivially done by writing code in C++ that subtracts the background file from the file for each spectra. After this, one can use the decay schemes of the radionuclides given in Fig. 1 to relate the channel number of the detector to energy in MeV. As seen by the Na-22 spectrum (Fig. 4(a)), the 0.511 MeV peak, representing the positron annihilation of photons, is situated at channel 401 ± 0.09226, while the 1.275 MeV photo-peak VOLUME #, NUMBER # PHYSICAL REVIEW STYLE LETTER 11 DECEMBER 2007 _____________________________________________________________________________________________________________________ relates to channel 868.5 ± 0.3746. From the Cs137 spectrum, (Fig. 4(b)), the photo-peak of 0.662 MeV corresponds to channel number 509.7 ± 0.05068. Finally, as seen in the decay schemes of Fig1, Co-60 has emits two γ-rays and thus has two photo-peaks of energy 1.173 MeV, corresponding to channel 815.2 ± 0.1262 and 1.332 MeV, corresponding to channel 911.3 ± 0.08876. Representing this data as a graph, as seen in Fig. 5 below, we see the relationship between the channel number and the energy of the detector. (a) FIG. 5. Graph of relating the channel number to the energy in MeV. (b) (c) FIG. 4. Channel vs. Counts (a) Na-22 Spectrum with lead backscatter plate. (b) Cs-137 spectrum with aluminum backscatter plate. (c) Co-60 spectrum with aluminum backscatter plate. Thus, in conclusion, by understanding the three major interactions of photons with matter: (1) Photoelectric effect, (2) Compton Scattering, and (3) Pair Production, we can use known spectra, such as the spectra of the radionuclei, Na-22, Cs-137, and Co-60, to calibrate a detector and therefore gain a relationship between the channel number and the corresponding energy. [1] W.R. Leo. Techniques for Nuclear and Particle Physics: A How-to Approach. 2nd Edition. Germany: Springer-Verlag Berlin Heidelberg. 1994. Pages: 35,48,53-59 [2] D. Preston and E. Deitz. The Art of Experimental Physics. John Wiley & Sons, Inc. 1991. Pages: 316331, pic 317 [3] Emilo Segre. Nuclei and Particles. 2nd Ed. W. A. Benjamin, Inc. 1997. Pages: 54 [4] Ashok Das and Thomas Ferbel. Inroduction to Nuclear and Particle Physics. John Wiley & Sons, Inc. YEAR. Pages: 124-134 VOLUME #, NUMBER # PHYSICAL REVIEW STYLE LETTER 11 DECEMBER 2007 _____________________________________________________________________________________________________________________ Since PRL style articles are only four pages, I did not include analysis of the backscatter peak, which is observed around approximately channel 200. The aberrations, before the backscatter peak, are most likely due to the geometry of the system. The backscatter difference between the Aluminum and Lead plates can be seen in the figure below: Where the black line represents the lead backscatter plate, and the red line represents the Aluminium backscatter plate, plotted Channel Number vs. Counts. The backscatter difference is thus observed to be: VOLUME #, NUMBER # PHYSICAL REVIEW STYLE LETTER 11 DECEMBER 2007 _____________________________________________________________________________________________________________________ In addition, the Fig. 4 in the article is very small, so I have included bigger pictures below (these are the pictures I would have used in the presentation, and I have included them so that the small size does not hinder the interpretation of the results): Na-22 spectrum with lead backscatter plate Cs-137 spectrum with aluminum backscatter plate Co-60 spectrum with aluminum backscatter plate