Gamma-Ray Spectroscopy: A Laboratory Guide

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 light of ultra-high frequency, which means they carry significant energy (E = hf; the Planck-Einstein relation). They may pass through matter, but if they interact with it, they can deposit this energy, ionizing atoms and damaging biological material.

Gamma rays are emitted by high-energy events such as nuclear explosions and supernovae, and by energetic celestial bodies such as neutron stars and the edges of black holes. Some of these events also produce radioactive elements or isotopes that are unstable, taking nanoseconds or billions of years to decay into stable elements—a process that often involves gamma-ray emission. These radioactive sources of gamma rays can be collected and studied in a shielded laboratory environment.

What is Gamma-Ray Spectroscopy?

Gamma-ray spectroscopy is a technique for identifying and quantifying gamma-ray emissions from radioactive sources. The technique is often used to identify the source, such as within a rock sample or supernova remnant. Strong sources may be shielded behind lead to protect the researcher. Weaker sealed sources (e.g., Europium-152) may be handled with tongs.

The technique is used in laboratories, such as to identify naturally occurring background radiation from terrestrial sources, and on space telescopes to identify astronomical sources. In a laboratory, gamma-ray spectroscopy typically involves placing radioactive sources in front of a gamma-ray detector. The detector is used to measure the energy and intensity of the gamma rays, allowing for identification by comparison with known sources.

How Do Gamma-Ray Detectors Work?

There are three common types of gamma-ray detector. Gas-filled detectors such as Geiger counters are only effective for detecting the presence of radiation. Scintillation detectors emit light when struck by gamma rays, which is converted into measurable electrical signals, providing a cost-effective way to identify sources. Semiconductor detectors, which will be discussed here, offer the best energy resolution and are used in research and spectroscopy applications.

Typically, the electrons in an atom are in discrete energy levels (i.e., orbitals around an atomic nucleus). However, in semiconductors such as germanium, atoms behave more collectively. The electrons from a particular orbital in all of the atoms form a collective energy level called a "band." When a gamma ray is absorbed by electrons in this band, the electrons "jump" into a higher band. An applied electric field then sweeps these electrons to the electrodes, producing a current pulse proportional to the gamma ray's energy that can be measured and studied.

The lower band is called the valence band, and the higher one the conduction band. These bands are close together in semiconductor materials. For example, the band-gap in germanium is only 0.74 eV (at the cryogenic temperatures used in detectors) and the average energy required for the "jump" is only ~3 eV, so a single gamma ray produces hundreds of thousands of charge carriers, resulting in large output signals and high energy resolution.

Without an electric field, the electrons would rejoin the valence band before they can be collected. To create this field, the semiconductor is doped with an element with fewer valence electrons, such as gallium. The dopant atoms accept electrons from the semiconductor, becoming negatively charged and leaving behind mobile positive holes (making the material "p-type"). If a thin contact layer doped with an element that donates electrons (called n-type, e.g., lithium) is then deposited on one face, forming a p–n junction, a reverse-biased voltage can be applied—negative on the p-side, positive on the n-side. This sweeps electrons toward the n-side and holes toward the p-side, depleting the region between them of mobile charge carriers.

By increasing the voltage, this depletion region can be grown to encompass most of the detector. A gamma ray interacting within the depletion region creates electron-hole pairs that are swept to the opposite electrodes before they can recombine. The collected charge is amplified and converted to a voltage pulse proportional to the gamma ray's energy, which can be recorded and plotted on a computer (see below).

As gamma rays are an extremely penetrating form of radiation, detecting them requires 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. 

The Basics of Gamma-Ray Spectroscopy

Europium (Eu) is a metallic element that emits gamma rays when it has a mass of 152 atomic units. The computer plot below is a gamma ray spectrum that was recorded by placing a small lump of 152Eu in front of a germanium detector. The spectum was produced by a Multi-Channel Analyzer (MCA), with higher energies to the right, and taller peaks representing a greater number (or "count") of gamma rays at that energy.

The energies of the peaks in this spectrum are well known, which means that 152Eu can be used to calibrate the MCA's energy scale up to around 1.5 MeV. Here, five peaks were tagged with their known energies to calibrate the MCA. This calibration allows 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 air, the building, and the Earth). This background data was allowed to accumulate for ten minutes. Several gamma ray peaks were resolved and identified by referring to previously collected data (see below).

For example, a prominent peak at 1.46 MeV was consistent with 40K (potassium). The most likely cause was 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.

Additionally, 214Bi and 214Pb (bismuth and lead) are produced by the decay of uranium in the Earth, while 212Pb and 208Tl (lead and thallium) follow the decay of thorium. Finally, 137Cs (cesium) can be found in the air due to past nuclear weapons testing, while the small 60Co (cobalt) peaks 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. This is the natural decay of 152Eu.

As other electrons descend to fill the vacancy of the captured inner electron, they must give up energy, which occurs via x-ray emission. The two energies correspond to electrons that come from two different shells (a shell is a set of orbitals) into the lowest "K" shell. They are known as Kα and Kβ transition energies and they equal the difference in energy between the electron's original shell and the K shell.

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 germanium atoms in the detector. This absorption ejects a K-shell electron from the germanium atom. An electron from a higher shell then drops into the vacancy, and the energy difference is emitted as a germanium x-ray.

The first x-ray (from samarium) has a low penetration depth into the detector due to its low energy, increasing the chance that the second x-ray (from germanium) escapes the detector without being reabsorbed. 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 (i.e., 40 - 10 = 30).

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 (i.e., 14.4 - 10 = 4.4). 

Identifying Examples of Peak Summing

Peak summing occurs when a detector can't keep up with a high-activity source. For this laboratory guide, a relatively high activity 137Cs (cesium) source was placed very close to the detector, producing a large count rate and the spectrum below. It is clear that 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 not rectangular, the peak will be poorly resolved and will not sum at the full amplitude of the signal.

The examples of peak summing in this spectrum 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 a nuclear process dictates 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. 

Measuring Annihilation Photons

A 22Na (sodium) source was placed in front of the detector. It 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 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 in the source material. This process produces 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).

In the spectrum, the annihilation peak is slightly broader than the detector resolution alone would predict. This is due to the Doppler effect: the positron–electron pair has a non-zero momentum at the moment of annihilation (primarily from the electron's momentum in the source material), so the two photons are shifted slightly above and below 511 keV, broadening the line by a few eV.

The Energy Resolution of the Detector

The percentage energy resolution is calculated using: FWHM ⁄ Eγ (×100%), where Eγ is the energy of a gamma ray. 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 as the energy increases. Conversely, the energy resolution (red line) decreases. This occurs because high energy gamma rays produce large numbers of charge carriers, causing greater 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 (data included from the 22Na spectrum). 

Measuring the Dead Time and Shaping Time

The dead time per event (τ) is the time for the detection system to process one event before it can accept the next; it is determined primarily by the amplifier shaping time. If radiation reaches the detector during this interval, the event is not recorded. Although a longer shaping time improves energy resolution, it also increases τ, which at high count rates leads to a larger dead time fraction (mτ) and a higher probability of pile-up. Thus, the optimum shaping time is shorter for high count rates.

The graph below shows how, for a constant shaping time (and therefore constant τ), the dead time fraction increases linearly with count rate. The count rate was increased by moving the ¹⁵²Eu source closer to the detector, at distances of 5, 7.5, 10, and 15 cm. The dead time fraction was read from the MCA software display.

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 from 20.7 years ago. With 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 laboratory guide: Ω = 2π.{1-[150 ⁄ √(150 2+30 2 )]} = 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. 

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 greater 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. 

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.