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The Basics of Gamma Ray Spectroscopy

Dr. Thomas Swan is a published physicist who received his PhD in nuclear astrophysics from the University of Surrey.

What Are Gamma Rays?

If you know that a dog whistle emits "ultrasonic" sound that is inaudible to the human ear, then you can understand gamma rays as a form of light that is invisible to the human eye.

Gamma rays are an ultra-high frequency of light that is emitted by radioactive elements, energetic celestial bodies (e.g., black holes and neutron stars), and high energy events such as nuclear explosions and supernovae. As they have the highest frequency of any light wave (see below), gamma rays carry a lot of energy (E = hf; the Planck-Einstein relation).

Gamma rays are the highest frequency of light. There is only a small region of the electromagnetic (light) spectrum that is visible to the human eye.

Gamma rays are the highest frequency of light. There is only a small region of the electromagnetic (light) spectrum that is visible to the human eye.

What Is Gamma Ray Spectroscopy?

Gamma rays are referred to as radiation because they can penetrate deep into the human body, causing harm when the energy they carry is deposited. Gamma ray spectroscopy is a way to identify the source of these potentially harmful gamma rays by allowing their energy to be deposited within detectors, measuring this energy, and comparing it to known sources.

For example, in recent decades, detectors have been placed aboard space telescopes, allowing scientists to determine the composition of other planets and stars by measuring their gamma ray emissions.

In this laboratory, gamma-ray detectors are plugged into circular slots around the reaction chamber to measure gamma rays emitted by nuclear reactions.

In this laboratory, gamma-ray detectors are plugged into circular slots around the reaction chamber to measure gamma rays emitted by nuclear reactions.

How Do Gamma Ray Detectors Work?

Gamma ray detectors are made from semiconductor materials, which contain atoms with orbiting electrons that can easily absorb the energy of a passing gamma ray. This absorption pushes the electron into a higher orbit, allowing it to be swept away in an electrical current. The lower orbit is called the valence band, and the higher orbit is the conduction band. These bands are close together in semiconductor materials such that valence electrons can easily join the conduction band by absorbing the energy of a gamma ray.

For example, germanium is a semiconducting element that is often used in gamma ray detectors. In germanium atoms, the band-gap is only 0.74 eV (electron volts). The small band-gap means that only a small amount of energy is required to produce a charge carrier, resulting in large output signals and high energy resolution.

To sweep the electrons away, a voltage is applied to the semiconductor to create an electric field. To help achieve this, the germanium may be infused (or "doped") with an element that has fewer valence band electrons. These are called n-type elements, having only three valence electrons compared with the semiconductor’s four. The n-type element (e.g., lithium) drags electrons away from the semiconductor material, becoming negatively charged.

By applying a reverse-biased voltage to the material, this negative charge can be pulled toward a positive electrode. The removal of electrons from the semiconductor atoms creates positively charged "holes" that can be pulled towards a negative electrode. This depletes charge carriers from the center of the material and, by increasing the voltage, the depletion region can be grown to encompass most of the material. An interacting gamma ray will create electron-hole pairs in the depletion region, which are swept up in the electric field and deposited on the electrodes. The collected charge is then amplified and converted to a voltage pulse of a measurable size that is proportional to the energy of the gamma ray, which can be recorded and plotted on a computer (see below).

As gamma rays are an extremely penetrating form of radiation, they require large depletion depths. This can be achieved by using large germanium crystals with impurities of less than 1 part in 1012 (a trillion). The small band-gap requires the detector to be cooled to prevent noise from leakage current. Germanium detectors are therefore placed in thermal contact with liquid nitrogen with the whole setup housed within a vacuum chamber.

Europium-152 gamma ray spectrum. The peaks show how frequently gamma rays of particular energies (in electron volts; eV) are emitted from the europium source.

Europium-152 gamma ray spectrum. The peaks show how frequently gamma rays of particular energies (in electron volts; eV) are emitted from the europium source.

Basic Gamma Ray Spectroscopy

Europium (Eu) is a metallic element that commonly emits gamma rays when it has a mass of 152 atomic units. The gamma ray spectrum above was observed by placing a small lump of 152Eu in front of a germanium detector. The wide range of gamma ray peaks in 152Eu means that it can be used to calibrate the energy scale of a Multi-Channel Analyzer (MCA) up to around 1.5 MeV. For example, five of the peaks were tagged in the MCA with their previously determined, known energies, thus calibrating the energy scale of the equipment. This calibration allows for the energy of gamma rays from unknown sources to be measured to an average uncertainty of 0.1 keV.

Measuring The Background Spectrum

With all laboratory sources shielded from the detector, a spectrum was recorded to measure gamma rays coming from the surrounding environment (i.e., the building and the Earth itself). This background data was allowed to accumulate for 10 minutes. Several gamma ray peaks were resolved and identified (see below) by referring to previously collected data.

The spectrum of background gamma rays within a normal concrete building.

The spectrum of background gamma rays within a normal concrete building.

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Looking at the spectrum, there is a prominent peak at 1.46 MeV that is consistent with 40K (potassium). The most likely cause is the concrete that makes up the laboratory building. Indeed, 40K accounts for 0.012% of all naturally occurring potassium, which is a common constituent in building materials.

214Bi and 214Pb (bismuth and lead) are produced following the decay of uranium within the Earth, and 212Pb and 208Tl (lead and thallium) follow the decay of thorium. 137Cs (cesium) can be found in the air as a result of past nuclear weapons testing. The small 60Co peaks (cobalt) can be attributed to less than perfect shielding of the detector from this intense laboratory source.

Identifying X-Rays in the Europium Spectrum

As described above, gamma-rays are the most energetic form of light. X-rays are the second most energetic, which means that some gamma-ray detectors can resolve x-rays at the lower end of their detectable range.

At around 40 keV, several x-rays were detected in the europium spectrum (above). In the spectrum below, these are resolved in a magnified image. The two large peaks have energies of 39.73 keV and 45.26 keV, which correspond to the x-ray emission energies of 152Sm (samarium), which is formed through the capture of an inner electron from 152Eu in the reaction: p+e → n+ν.

X-rays are emitted as other electrons descend to fill the vacancy of the captured inner electron. The two energies correspond to electrons that come from two different shells, known as the Kα and Kβ shells.

Zooming in at the low energy end of the europium spectrum to see samarium x-rays.

Zooming in at the low energy end of the europium spectrum to see samarium x-rays.

Measuring X-Ray Escape Peaks

The small peak at even lower energy (~30 keV) in the spectrum above is likely to be an x-ray escape peak. X-rays are relatively low energy, which increases the chance of them being photoelectrically absorbed by the germanium detector. This absorption results in a germanium electron being excited to a higher orbit, from which a second x-ray is emitted by the germanium to return it to it’s ground-state electron configuration.

The first x-ray (from samarium) will have had a low penetration depth into the detector, thus increasing the chance that the second x-ray (from germanium) will escape from the detector without interacting at all. As the most intense germanium x-ray occurs at an energy of ~10 keV, the detector records a peak at 10 keV less than the samarium x-ray that was absorbed by the germanium.

An x-ray escape peak is also evident in the spectrum of 57Co, which has many low-energy gamma rays. It can be seen (below) that only the lowest energy gamma ray has a visible escape peak.

Gamma ray spectrum for cobalt-57 showing an x-ray escape peak.

Gamma ray spectrum for cobalt-57 showing an x-ray escape peak.

Identifying Examples of Peak Summing

Peak summing occurs when a detector can't keep up with a high-activity source. For example, a relatively high activity 137Cs (cesium) source was placed very close to the detector, producing a large count rate and the spectrum below. The energies of a barium x-ray (32 keV) and a cesium gamma ray (662 keV) have occasionally summed to produce a peak at 694 keV. The same is true at 1324 keV for the summing of two cesium gamma rays.

Peak summing occurs when a second ray penetrates the detector before the charge from the first ray is fully collected. The minimum time that must separate two events is called the pile-up resolution time. If the amplifier's shaping-time is too long, the signals are summed. Even worse, if the detected signal pulse is is not rectangular, the peak will be poorly resolved and will not sum at the full amplitude of the signal.

The above examples of peak summing are called random summing because, other than their coincidental detection, the two signals are unrelated. A second kind of summing is true summing, which occurs when there is a nuclear process dictating a quick succession of gamma ray emissions. This is often the case in gamma ray cascades, where a nuclear state with a long half life decays to a short-lived state that quickly emits a second ray.

Evidence of peak summing in a high activity cesium-137 source.

Evidence of peak summing in a high activity cesium-137 source.

Measuring Annihilation Photons

An isotope of sodium, 22Na, decays by positron emission (β+) in the reaction: p → n+β++ν. The daughter nucleus is 22Ne (neon), which is left in an excited state (99.944% of the time) at an energy of 1.275 MeV, and which subsequently decays via gamma rays to its ground state, producing a gamma ray peak at that energy. However, the emitted positron (antimatter) will annihilate with an electron within the source material to produce back-to-back annihilation photons with energies equal to the rest-mass of an electron (511 keV; although an annihilation photon can be shifted down in energy by a few eV due to the binding energy of the electron involved in the annihilation).

Annihilation photons from a sodium-22 source.

Annihilation photons from a sodium-22 source.

The width of the annihilation peak is uncharacteristically large. This is because the positron and electron occasionally form a short-lived orbiting system, or exotic atom (similar to hydrogen), called positronium. The positronium has a finite momentum, meaning that after the two particles annihilate each other, one of the two annihilation photons may possess slightly more momentum than the other, with the sum still being twice the rest-mass of the electron. This Doppler effect increases the energy range, broadening the annihilation peak.

The Energy Resolution of the Detector

The percentage energy resolution is calculated using: FWHM ⁄ Eγ (×100%), where Eγ is the gamma ray energy. The full width at half maximum (FWHM) of a gamma ray peak is the width (in keV) at half the height.

For a 152Eu source at 15 cm from a germanium detector, the FWHM of seven peaks were measured (below). The FWHM (blue line) increases linearly as the energy increases. Conversely, the energy resolution (red line) decreases. This occurs because high energy gamma rays produce a large number of charge carriers, leading to increased statistical fluctuations. A second contributor is incomplete charge collection, which increases with energy because more charge needs to be collected in the detector.

Electronic noise provides a minimum, default peak width, but it is invariant with energy. Also note the increased FWHM of the annihilation photon peak due to the Doppler broadening effects described above.

Full width at half maximum (FWHM) and energy resolution for europium-152 peaks.

Full width at half maximum (FWHM) and energy resolution for europium-152 peaks.

Measuring the Dead Time and Shaping Time

The dead time is the time for the detection system to reset after one event in order to receive another event. If radiation reaches the detector in this time then it will not be recorded as an event. A long shaping time for the amplifier will increase energy resolution, but with a high count rate there can be a pile-up of events leading to peak summing. Thus, the optimum shaping time is low for high count rates.

The graph below shows how with a constant shaping time, the dead time increases for high count rates. The count rate was increased by moving the 152Eu source closer to the detector. Distances of 5 cm, 7.5 cm, 10 cm, and 15 cm were used. The dead time was determined by monitoring the MCA computer interface and assessing the average dead time by eye.

How dead time varies with count rate at four different gamma ray energies.

How dead time varies with count rate at four different gamma ray energies.

Absolute Total Efficiency

The absolute total efficiency (εt) of the detector is given by: εt = Ct ⁄ Nγ (×100%). The quantity Ct is the total number of counts recorded per unit time, integrated over the whole spectrum. Nγ is the number of gamma rays emitted by the source per unit time.

For a 152Eu source, the total number of counts recorded in 302 seconds of data collection was: 217,343 ± 466, with a source-detector distance of 15 cm. The background count was 25,763 ± 161. The total number of counts is therefore 191,580 ± 493, with this error arising from a simple propagation of errors calculation √(a2+b2). Thus, per unit time, Ct = 634 ± 2.

The number of gamma rays emitted per unit time is: Nγ = DS.Iγ(Eγ). The quantity Iγ(Eγ) is the fractional number of gamma rays emitted per disintegration, which for 152Eu is 1.5. The quantity DS is the disintegration rate of the source (the activity). The original activity of the source was 370 kBq in 1987. After 20.7 years and a half-life of 13.51 years, the activity at the time of this measurement was: DS = 370000 ⁄ 2(20.7 ⁄ 13.51) = 127.9±0.3 kBq.

Therefore, Nγ = 191900±500, and the absolute total efficiency is εt = 0.330±0.001%.

Intrinsic Total Efficiency

The intrinsic total efficiency (εi) of the detector is given by: εi = Ct ⁄ Nγ'.

The quantity Nγ' is the total number of gamma rays incident on the detector, and is equal to: Nγ'= (Ω/4π)Nγ. The quantity Ω is the solid angle subtended by the detector crystal at the point source, equaling: Ω = 2π.{1-[d ⁄ √(d2+a2)]}, where d is the distance from the detector to the source and a is the radius of the detector window. For this study: Ω = 2π.{1-[150 ⁄ √(1502+302)]} = 0.039π.

Therefore Nγ' = 1871±5, and the intrinsic total efficiency, εi = 33.9±0.1%.

Intrinsic Photopeak Efficiency

The intrinsic photopeak efficiency (εp) of the detector is: εp = Cp ⁄ Nγ'' (×100%).

The quantity Cp is the number of counts per unit time within a peak of energy Eγ. The quantity Nγ'' equals Nγ' but with Iγ(Eγ) being the fractional number of gamma rays emitted with energy Eγ. Data and Iγ(Eγ) values are listed below for eight of the more prominent peaks in 152Eu.

Eγ (keV)CountsCounts/secNγ''Efficiency (%)

45.26

16178.14

53.57

0.169

210.8

25.41

121.78

33245.07

110.083

0.2837

354

31.1

244.7

5734.07

18.987

0.0753

93.9

20.22

344.27

14999.13

49.666

0.2657

331.4

14.99

778.9

3511.96

11.629

0.1297

161.8

7.19

964.1

3440.08

11.391

0.1463

182.5

6.24

1112.1

2691.12

8.911

0.1354

168.9

5.28

1408

3379.98

11.192

0.2085

260.1

4.3

The graph below shows the relationship between gamma ray energy and intrinsic photopeak efficiency. It is clear that efficiency decreases for higher energy gamma rays. This is due to the increased probability of rays not stopping within the detector. The efficiency also decreases at the lowest energies due to an increased probability of rays not reaching the depletion region of the detector.

A typical efficiency curve (intrinsic photopeak efficiency) for a europium-152 source.

A typical efficiency curve (intrinsic photopeak efficiency) for a europium-152 source.

Summary

Gamma ray spectroscopy provides a fascinating look into the world beneath the scrutiny of our senses. To study gamma ray spectroscopy is to learn all the tools that are needed to become a proficient scientist. One must combine a grasp of statistics with a theoretical understanding of physical laws and a familiarity with experimental equipment. Discoveries continue to be made with gamma ray detectors in the domains of nuclear physics and astrophysics, and this trend looks set to continue well into the future.

© 2012 Thomas Swan

Comments

Thomas Swan (author) from New Zealand on May 04, 2013:

Hi Rocket City Writer, this wasn't really research; it was some work I had to do in the lab to demonstrate an understanding of gamma-ray spectroscopy so that I would be able to do my research. Ultimately, I used some of these skills later though. My research was looking at nuclear isomers (which emit gamma rays).

I don't think I've used the same detectors as you have. I used silicon particle detectors during my research year to detect protons from a (d,p) reaction. It was nice to get an experience of more than one type of detector.

It's good to find a fellow physicist here. I'll check out some of your hubs. Thanks for commenting.

RocketCityWriter from Alabama on May 03, 2013:

Wow, so I stumbled onto one of your other hubs about quitting physics and then this one caught my eye.

Was this part of your research?

I've also done work in gamma ray spectroscopy, but not with direct gamma ray detectors. We use inorganic scintillators and silicon photomultipliers in an all-sky survey concept.

So cool to see an article like this on here. Thanks!

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