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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.
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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].
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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
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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
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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:
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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