Gamma spectroscopy

Gamma spectroscopy detectors are passive materials that are able to interact with incoming gamma rays. The most important interaction mechanisms are the photoelectric effect, the Compton effect, and pair production. Through these processes, the energy of the gamma ray is absorbed and converted into a voltage signal by detecting the energy difference before and after the interaction (or, in a scintillation counter, the emitted photons using a photomultiplier). The voltage of the signal produced is proportional to the energy of the detected gamma ray. Common detector materials include sodium iodide (NaI) scintillation counters and high-purity germanium detectors.

To accurately determine the energy of the gamma ray, it is advantageous if the photoelectric effect occurs, as it absorbs all of the energy of the incident ray. Absorbing all the energy is also possible when a series of these interaction mechanisms take place within the detector volume. With Compton interaction or pair production, a portion of the energy may escape from the detector volume, without being absorbed. The absorbed energy thus gives rise to a signal that behaves like a signal from a ray of lower energy. This leads to a spectral feature overlapping the regions of lower energy. Using larger detector volumes reduces this effect. More sophisticated methods of reducing this effect include using Compton-suppression shields and employing segmented detectors with add-back (see: clover (detector)).[4]

The voltage pulses produced for every gamma ray that interacts within the detector volume are then analyzed by a multichannel analyzer (MCA). In the MCA, a pulse-shaping amplifier takes the transient voltage signal and reshapes it into a Gaussian or trapezoidal shape. From this shape, the signal is then converted into a digital form, using a fast analog-to-digital converter (ADC). In new systems with a very high-sampling-rate ADC, the analog-to-digital conversion can be performed without reshaping.

Additional logic in the MCA then performs pulse-height analysis, sorting the pulses by their height into specific bins, or channels. Each channel represents a specific range of energy in the spectrum, the number of detected signals for each channel represents the spectral intensity of the radiation in this energy range. By changing the number of channels, it is possible to fine-tune the spectral resolution and sensitivity.[5]

The MCA can send its data to a computer, which stores, displays, and further analyzes the data. A variety of software packages are available from several manufacturers, and generally include spectrum analysis tools such as energy calibration (converting bins to energies), peak area and net area calculation, and resolution calculation.[6]

A USB sound card can serve as a cheap, consumer off-the-shelf ADC, a technique pioneered by Marek Dolleiser. Specialized computer software performs pulse-height analysis on the digitized waveform, forming a complete MCA.[7] Sound cards have high-speed but low-resolution (up to 192 kHz) ADC chips, allowing for reasonable quality for a low-to-medium count rate.[8] The "sound card spectrometer" has been further refined in amateur and professional circles.[9][10]

Gamma rays detected in a spectroscopic system produce peaks in the spectrum. These peaks can also be called lines by analogy to optical spectroscopy. The width of the peaks is determined by the resolution of the detector, a very important characteristic of gamma spectroscopic detectors, and high resolution enables the spectroscopist to separate two gamma lines that are close to each other. Gamma spectroscopy systems are designed and adjusted to produce symmetrical peaks of the best possible resolution. The peak shape is usually a Gaussian distribution. In most spectra the horizontal position of the peak is determined by the gamma ray's energy, and the area of the peak is determined by the intensity of the gamma ray and the efficiency of the detector.

The most common figure used to express detector resolution is full width at half maximum (FWHM). This is the width of the gamma ray peak at half of the highest point on the peak distribution. Energy resolution figures are given with reference to specified gamma ray energies. Resolution can be expressed in absolute (i.e., eV or MeV) or relative terms. For example, a sodium iodide (NaI) detector may have a FWHM of 9.15 keV at 122 keV, and 82.75 keV at 662 keV. These resolution values are expressed in absolute terms. To express the energy resolution in relative terms, the FWHM in eV or MeV is divided by the energy of the gamma ray and usually shown as percentage. Using the preceding example, the resolution of the detector is 7.5% at 122 keV, and 12.5% at 662 keV. A typical resolution of a coaxial germanium detector is about 2 keV at 1332 keV, yielding a relative resolution of 0.15%.

Not all gamma rays emitted by the source that pass through the detector will produce a count in the system. The probability that an emitted gamma ray will interact with the detector and produce a count is the efficiency of the detector. High-efficiency detectors produce spectra in less time than low-efficiency detectors. In general, larger detectors have higher efficiency than smaller detectors, although the shielding properties of the detector material are also important factors. Detector efficiency is measured by comparing a spectrum from a source of known activity to the count rates in each peak to the count rates expected from the known intensities of each gamma ray.

Efficiency, like resolution, can be expressed in absolute or relative terms. The same units are used (i.e., percentages); therefore, the spectroscopist must take care to determine which kind of efficiency is being given for the detector. Absolute efficiency values represent the probability that a gamma ray of a specified energy passing through the detector will interact and be detected. Relative efficiency values are often used for germanium detectors, and compare the efficiency of the detector at 1332 keV to that of a 3 in × 3 in NaI detector (i.e., 1.2×10 ⁻³ cps/Bq at 25 cm). Relative efficiency values greater than one hundred percent can therefore be encountered when working with very large germanium detectors.

The energy of the gamma rays being detected is an important factor in the efficiency of the detector. An efficiency curve can be obtained by plotting the efficiency at various energies. This curve can then be used to determine the efficiency of the detector at energies different from those used to obtain the curve. High-purity germanium (HPGe) detectors typically have higher sensitivity.

Thallium-doped sodium iodide (NaI(Tl)) has two principal advantages:

1. It can be produced in large crystals, yielding good efficiency, and
2. it produces intense bursts of light compared to other spectroscopic scintillators.

NaI(Tl) is also convenient to use, making it popular for field applications such as the identification of unknown materials for law enforcement purposes.

Electron hole recombination will emit light that can re-excite pure scintillation crystals; however, the thallium dopant in NaI(Tl) provides energy states within the band gap between the conduction and valence bands. Following excitation in doped scintillation crystals, some electrons in the conduction band will migrate to the activator states; the downward transitions from the activator states will not re-excite the doped crystal, so the crystal is transparent to this radiation.

An example of a NaI spectrum is the gamma spectrum of the caesium isotope ¹³⁷
Cs
—see Figure 1. ¹³⁷
Cs
emits a single gamma line of 662 keV. The 662 keV line shown is actually produced by ^137m
Ba
, the decay product of ¹³⁷
Cs
, which is in secular equilibrium with ¹³⁷
Cs
.

The spectrum in Figure 1 was measured using a NaI-crystal on a photomultiplier, an amplifier, and a multichannel analyzer. The figure shows the number of counts within the measuring period versus channel number. The spectrum indicates the following peaks (from left to right):

1. low energy x radiation (due to internal conversion of the gamma ray),
2. backscatter at the low energy end of the Compton distribution, and
3. a photopeak (full energy peak) at an energy of 662 keV

The Compton distribution is a continuous distribution that is present up to channel 150 in Figure 1. The distribution arises because of primary gamma rays undergoing Compton scattering within the crystal: Depending on the scattering angle, the Compton electrons have different energies and hence produce pulses in different energy channels.

If many gamma rays are present in a spectrum, Compton distributions can present analysis challenges. To reduce gamma rays, an anticoincidence shield can be used—see Compton suppression. Gamma ray reduction techniques are especially useful for small lithium-doped germanium (Ge(Li)) detectors.

The gamma spectrum shown in Figure 2 is of the cobalt isotope ⁶⁰
Co
, with two gamma rays with 1.17 MeV and 1.33 MeV respectively. (See the decay scheme article for the decay scheme of cobalt-60.) The two gamma lines can be seen well-separated; the peak to the left of channel 200 most likely indicates a strong background radiation source that has not been subtracted. A backscatter peak can be seen near channel 150, similar to the second peak in Figure 1.

Sodium iodide systems, as with all scintillator systems, are sensitive to changes in temperature. Changes in the operating temperature caused by changes in environmental temperature will shift the spectrum on the horizontal axis. Peak shifts of tens of channels or more are commonly observed. Such shifts can be prevented by using spectrum stabilizers.

Because of the poor resolution of NaI-based detectors, they are not suitable for the identification of complicated mixtures of gamma ray-producing materials. Scenarios requiring such analyses require detectors with higher resolution.

In a real detector setup, some photons can and will undergo one or potentially more Compton scattering processes (e.g. in the housing material of the radioactive source, in shielding material or material otherwise surrounding the experiment) before entering the detector material. This leads to a peak structure that can be seen in the above shown energy spectrum of ¹³⁷
Cs
(Figure 1, the first peak left of the Compton edge), the so-called backscatter peak. The detailed shape of backscatter peak structure is influenced by many factors, such as the geometry of the experiment (source geometry, relative position of source, shielding and detector) or the type of the surrounding material (giving rise to different ratios of the cross sections of Photo- and Compton-effect).

The basic principle, however, is as follows:

• Gamma-ray sources emit photons isotropically[11]
• Some photons will undergo a Compton scattering process in e.g. the shielding material or the housing of the source with a scattering angle close to 180° and some of these photons will subsequently be detected by the detector.
• The result is a peak structure with approximately the energy of the incident photon minus the energy of the Compton edge.

The backscatter peak usually appears wide and occurs at lower than 250 keV.[12][13]

For incident photon energies E larger than two times the rest mass of the electron (1.022 MeV), pair production can occur. The resulting positron annihilates with one of the surrounding electrons, typically producing two photons with 511 keV. In a real detector (i.e. a detector of finite size) it is possible that after the annihilation:

• Both photons deposit their energy in the detector. This results in a peak with E, identical to the energy of the incident photon.
• One of the two photons escapes the detector and only one of the photons deposits its energy in the detector, resulting in a peak with E − 511 keV, the single escape peak.
• Both photons escape the detector, resulting in a peak with E − 2 × 511 keV, the double escape peak.

The above Am-Be-source spectrum shows an example of single and double escape peak in a real measurement.