Physical principles of radiation detection in sample counters

Gamma rays passing through the crystal are initially attenuated by photoelectric, Compton, or pair-production interactions.

The photoelectric effect is an event in which the gamma ray transfers all its energy to an inner orbital electron of an atom, resulting in the ejection of a bound electron. The electron is slowed down in the sodium iodide crystal by collisions with other electrons and becomes part of the general electron population. Some of this kinetic energy is transformed into light, as described in more detail below.

Compton scattering occurs when a gamma ray interacts with an outer orbital electron, which is regarded as a free electron. The photon is scattered with reduced energy and its energy loss is transferred to the electron as kinetic energy.

Pair production is an event which occurs in the high electric field close to the nucleus of an atom. The gamma-ray energy is converted to mass and creates an electron–positron pair. This can only occur for gamma-ray photons with a minimum energy of 1.02 MeV, the energy equivalent of the rest mass of the electron–positron pair. Any energy in excess of 1.02 MeV is partitioned as kinetic energy between the two particles. Both the electron and positron are slowed down, rapidly losing their kinetic energy in collisions with absorber electrons. The positron then undergoes annihilation with one of the electrons. The mass of the two particles is converted into energy, producing two gamma photons, each with an energy of 511 keV which are emitted at approximately 180° to each other. In crystals of the typical size used in gamma counters, these annihilation photons have a reasonably high probability of escaping from the detector without interaction.

The relative importance of these absorption processes for various gamma-ray energies is shown figure 1.1, which is a plot of the respective absorption coefficients against gamma-ray energy for both NaI(Tl) and organic liquid scintillators (sections 1.3 and 1.4).

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Each of the primary interaction processes produces an energetic secondary electron, which loses energy by exciting other electrons in the crystal from the ground state to the conduction band, creating electron–hole pairs. As these excited electrons return to the ground state, they give rise to photons in the wavelength range of 300–500 nm. This range is partly in the visible region of the electromagnetic spectrum and partly in the near-UV region. About 20–30 photons are produced per keV of energy loss. Most of the rest of the energy is dissipated as heat. The number of photons produced is proportional to the energy lost by the gamma ray in the crystal. The intensity of luminescence is temperature dependent, with an energy peak that increases in size with decreasing detector temperature. For NaI(Tl) the decay time of luminescence is 0.23 μs. The light photons are detected by a PMT which converts their energy to a pulse in an electrical circuit, the size of which is proportional to the light detected by the photocathode (section 2.2).

A spectrum of pulses is produced as a result of the different interaction processes undergone in the detector. The voltage values of the pulse heights are converted to energy losses in keV. A typical spectrum for ¹³⁷Cs obtained from a 50 mm × 50 mm NaI(Tl) crystal is shown in figure 1.2, which illustrates some of the common features listed below. For further information on the pulse size spectrum, see chapter 10 of Physics in Nuclear Medicine (Cherry et al 2012).

• 1.  
  Photopeak: two main processes contribute to the photopeak:

  • (a)  
    Photoelectric: the total energy of a gamma ray is absorbed in the scintillator by the initial photoelectric event, followed by absorption within the scintillator of any resulting scattered electrons and x-rays, giving rise to a full-energy peak (photopeak).
  • (b)  
    Compton: the total energy of a gamma ray is absorbed in the scintillator by a single or multiple Compton scattering events, followed by a photoelectric event. The probability of such absorption increases with crystal thickness.
• 2.  
  Compton plateau: during Compton scatter events, when the scattered photon escapes the detector without further interaction, the energy deposited in the crystal is less than that of the photopeak and depends on the scatter angle. This process gives rise to the Compton continuum. The continuum includes a broad spectrum of pulse sizes, corresponding to the variable energy of the secondary electrons produced by the Compton scattering process. The upper limit of the secondary electron energy corresponds to a photon scattering angle of 180° and gives rise to a feature known as the Compton edge.
• 3.  
  Barium x-ray peak: many gamma-emitting radionuclides have an alternative decay path by internal conversion which results in the emission of a characteristic x-ray from the daughter nucleus. In the case of ¹³⁷Cs, this is a barium x-ray at 37 keV.
• 4.  
  Backscatter peak: this occurs when the gamma rays are backscattered into the scintillator after undergoing a Compton scattering event in the surrounding materials. The energy of the backscatter peak is approximately equal to the energy of a 180° Compton-scattered photon and approaches a maximum of 0.25 MeV as the energy of the incident gamma ray increases. Lead peak: Photoelectric interaction with nearby materials, such as detector shielding, can produce characteristic K x-rays from the shielding material. In the case of lead shielding these K x-rays lie in the energy range of 72–88 keV (NIST 2020). However, these lead peaks are not always seen in practice (see figure 10.6).
• 5.  
  X-ray escape peak: a characteristic x-ray may be produced following the photoelectric absorption corresponding to the K x-ray of iodine (28 keV). In most cases the x-ray is reabsorbed; however, if the photoelectric absorption occurs near the surface region, the x-ray can escape, which results in a decrease of the deposited energy. This x-ray escape peak is most likely to be observed with lower-energy gamma rays since, in this case, most events occur close to the surface of the crystal.
• 6.  
  Summation peak (true coincidence): if radionuclides emit two gamma rays from the same disintegration, a coincidence or summation peak may occur. This peak corresponds to the sum of the gamma-ray energies and arises because of the simultaneous absorption of both gamma rays in the scintillator. Summation peaks are routinely used, for example, when counting ¹¹¹In or ¹²⁵I. These can additionally help to correct the counting efficiency, as described in section 6.8.
• 7.  
  Summation peak (random coincidence): Summation peaks may also occur for radionuclides emitting monoenergetic gamma rays when there is a high count rate. When two gamma rays are emitted by different nuclei within the time resolution of the electronic detection system (random coincidence), they result in a single event with a summed energy. The probability of random coincidence increases as the count rate increases. This summation peak leads to loss of events for individual gamma-ray responses at high count rates. These can be corrected for, as described in section 2.5.2., although samples can ideally be diluted or left to decay before counting to reduce count losses due to random coincidences. Alternatively, some modern counters have a high-count-rate mode, which uses a robotic arm to lift the sample partly off the well to reduce counting efficiency and therefore random coincidences.

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When a NaI(Tl) detector is exposed to a monoenergetic beam of gamma rays, all photoelectric events (except for a few in which the iodine x-ray escapes) have the same energy loss in the detector. However, as can be seen from figure 1.2, the photopeak comprises of a spread of pulse sizes. This results from random variations in the various energy conversion steps in the detection process. The width of the peak is primarily determined by the statistical variation in the number of photoelectrons produced at the photocathode of the PMT. The energy resolution is usually measured using the full width at half maximum (FWHM) of the photopeak and is often expressed as a fraction of the photopeak energy. For ¹³⁷Cs the energy resolution of the 662 keV peak is typically about 7% (i.e. the FWHM is ~45keV). As the resolution is statistically limited, it improves with increasing gamma-ray energy proportional to 1/E^1/2. The relatively good energy resolution of NaI(Tl) detectors means that it is possible to count samples containing a mixture of more than one radionuclide by using dual energy window counting and making appropriate correction for crosstalk between channels (section 9.7).

The counting of a sample is achieved by setting an appropriate pulse size window, which is often centered around the photopeak of the spectrum of the radionuclide. The counting efficiency (E) is defined as:

$$\begin{eqnarray*}&&E=\frac{c}{d}\times 100\end{eqnarray*}$$

where c is the number of counts per second detected and d is the number of disintegrations per second in the sample. It depends on several factors, which can be described by the following equation:

$$\begin{eqnarray*}&&E=A\cdot G\cdot D\cdot W\cdot (1-S)\end{eqnarray*}$$

where A is the abundance of gamma photon production by the radionuclide, G is the geometric efficiency of photon detection, D is the intrinsic efficiency of the detector, W is the fraction of counts detected in the selected energy window, and S is the fraction of photons attenuated in the sample or vial wall.

The geometric efficiency is maximised by surrounding the sample as completely as possible with the detector. Fortunately, NaI(Tl) can be machined into a variety of shapes; those most commonly used are a well, first described by Anger (1951), and a diametric through hole (see figure 1.3), both of which give a geometric efficiency of almost 100 % with small volume samples. However, geometric efficiency is very dependent on the sample volume, particularly if activity extends near to or beyond the edge of the detector, and this must be taken into consideration when carrying out measurements (see section 4.6.13 for sample volume effects).

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The size of the sample also influences the self-absorption fraction, S. This effect is more marked for low-energy emitters such as ¹²⁵I (with energy peaks at 27 keV and 35.5 keV). For a particular application, the use of a constant sample volume and shape ensures that the geometric efficiency remains fixed. The intrinsic efficiency, D, is defined as the ratio of the number of pulses interacting in the detector to the number of gamma-ray photons which enter it. It increases with increasing crystal size and decreasing gamma-ray energy (figure 1.4(a)). The intrinsic efficiency value is close to unity for gamma-ray energies of less than 200 keV and medium-sized crystals.

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The counting efficiency is also affected by the fraction of the detected spectrum which is used. It is common practice to eliminate rays scattered within the sample by counting only the photopeak, although in many applications this is not essential. Increasing the window width increases the relative contribution of background counts. If background contributions are substantial then a photopeak window should be used.

This is also the case when counting more than one radionuclide simultaneously. In this situation, the fractional detection in the window (W) is referred to as the photofraction, which is the fraction of the total number of pulses occurring in the spectrum that lie in the total energy peak. The photofraction increases with increasing crystal size and decreasing gamma-ray energy (figure 1.4(b)).

Typical counting efficiencies for commonly used radionuclides using a 3-inch diameter well-shaped crystal and an open energy window are shown in table 1.1.

Gamma counters are normally used to assay sample counts relative to counts for a standard. By relating the standard counts to a traceable absolute measure of activity, the counting efficiency can be determined and therefore the sample activity can be calculated.