Design optimization of a truncated cone-shaped LaBr₃:Ce/NaI:Tl phoswich detector based on GEANT4 simulation Open Access

Scintillation detectors are widely used in many fields because of their excellent detection efficiency and portability.^1,2 However, due to the unavoidable existence of the Compton continuum in the measured gamma-ray energy spectrum, the applications of scintillation detectors in low-energy and low-intensity radiation detection are greatly limited.³ 

Therefore, to improve the performance of the scintillation detectors and expand their application, it is necessary to reduce the height of the Compton plateau. To do this, one common way is to select scintillators with better performance, such as better energy resolution, higher light yield, and shorter decay time, and the other way is to use external methods or devices to suppress the generation of the Compton continuum in the measured spectrum. For example, the Compton continuum suppression (CCS) spectrometer combining multiple detectors has been invented, which uses peripheral secondary detectors, or so-called guard detectors, to detect photons that escape from the primary detector after Compton scattering.^3–5 It has proved to be useful in reducing the height of the Compton platform and, thus, improving the peak to Compton $P/C$ plateau ratio.⁶ 

Despite its many advantages, the CCS spectrometer still has some drawbacks. First, those secondary detectors used as the “anti-Compton detectors” need additional photomultiplier tubes and more signal channels, which correspond to a more complex electronic system that not only increases the overall cost but also makes the whole detection system extremely bloated and, therefore, makes the transfer and redeployment of the detection system extremely complex. In addition, the excessive volume and irregular shape may also limit the use of those detectors in forming detector arrays for the detection of low-level radionuclides. Finally, when two gamma rays generated at the same time are detected coincidently by both the primary and secondary detectors, it may also be determined as a Compton event and rejected so that this kind of anti-Compton spectrometer with multiple detectors will lose the full-energy peak (FEP) and lead to reduce the sensitivity of the detector.⁷ 

To ameliorate the problem of FEP loss, there has been a scheme to correct it through digital data processing methods.⁸ However, this method can play a very limited role in the other two issues mentioned above. Therefore, a more simple solution is to stop using those external guard detectors and, as an alternative, nest and combine two scintillators with different optical properties together to form a composite scintillator and couple it to a single photomultiplier tube to form a so-called phoswich detector. Since additional guard detectors are no longer required, this design not only reduces the overall cost and complexity considerably but also reduces the probability of accidental coincidences and, hence, the FEP loss.

First, the idea of the phoswich detector was applied in particle discrimination, which uses the difference between different scintillators to realize the function of detecting different kinds of particles in the mixed radiation field.^9,10 Similarly, the anti-Compton phoswich (ACP) detector also uses the different rise and decay time between different scintillators as the characteristic factors to identify the deposition of gamma rays in different scintillators, which is so-called pulse shape discrimination (PSD).¹¹ In this way, photons generated from different scintillators can be distinguished by their different scintillator properties, and then, the same functionality as in the CCS spectrometer can be realized.

Noticeably, unlike particle discrimination detectors, ACP detectors are designed to reduce the Compton continuum and improve the performance, and thus, their design idea is naturally different. For example, as the most crucial part of the construction of the phoswich detector, the choice of the shape of the secondary scintillator becomes important when coupling different scintillators into a composite scintillator. Embedding the primary scintillator into a well-shaped secondary scintillator or coupling it to an annular secondary scintillator will certainly have a significant impact on the final performance of the detector. Hull et al. reported that the energy resolution of the phoswich detector became worse when coupling the bottom of LaBr₃:Ce with other scintillators.¹² It showed that the value of the measured energy resolution of the LaBr₃: Ce/NaI:Tl phoswich detector is 30% bigger than the stand-alone LaBr3:Ce detector.

In this study, a program for simulating the ACP detector based on the GEANT4 (Geometry ANd Tracking 4) toolkit was developed. The functionality of this simulation program is mainly based on the transport of optical photons in the scintillator and has been compared to experimental data to ensure the reliability of the simulations. The PSD method is also introduced, which is used in both experiments and simulations. During the simulation, we turned the shape of the secondary scintillator into a truncated cone, and changed two size parameters to study the influence of the size change on the energy resolution, FEP address, peak-to-Compton plateau ratio of the ACP detector, and give the design suggestions to meet different needs, as well as put forward a more ideal size selection.

GEANT4 is a toolkit for the simulation of the passage of particles through matter, which is widely used in high-energy physics, nuclear physics, accelerator physics, and medical physics.¹³ Because of its good performance in simulating the response of detectors to particles, many studies have used GEANT4 to simulate the response of the detector in recent years and fit well with the experiment.^14–16 

Using GEANT4 to simulate the anti-Compton phoswich detector requires the following steps. As C++ using object-oriented programming, first, the class of physical list needs to be set, then the geometric model of the detector needs to be established in the class of detector construction, and the data processing method is also integrated into the output. As for the physics list, the G4RadioactioveDecayPhysics, the G4Empenelope, and the G4DecayPhysics are used during the simulation, and the optical surface between the reflector and scintillator is set to dielectric metal. Meanwhile, the G4Opticalphysics is also set up according to experimental optical properties of different materials.^17,18

As shown in Fig. 1, the phoswich detector we used comprised a φ35.0 × 70.0 mm² cylindrical Ce-doped LaBr₃ scintillator and a φ75 × 90 mm² well-shaped Tl-doped NaI scintillator, which has a φ36.0 × 70.0 mm² well in it. The primary scintillator is embedded into the well of the secondary scintillator, and the reflective material (Teflon) is used between the scintillators. This design was obtained by GEANT4 simulation and optimization after taking into account production costs and detection efficiency.

Due to the deliquescence of NaI (Tl) and LaBr₃(Ce), the two scintillators are encapsulated in an aluminum alloy shell with a thickness of 1.5 mm and fitted with a piece of K9 glass at the bottom as the exit window. The space between the scintillator and the shell was filled with 0.5 mm thick Teflon as reflective material. The exit window is connected to a photomultiplier tube, where the scintillator photons are collected and recorded to form a pulse shape, and the pulse shape discrimination method is used for anti-coincidence processing to obtain the final gamma energy spectrum.

Figure 2 shows the energy spectrum obtained from the experimental measurement and theoretical simulation of the ¹³⁷Cs radioactive source by the LaBr₃/NaI phoswich detector. The simulated energy spectrum was obtained by using GEANT4 after simulating the complete photon transport response of the scintillator. For the detection efficiency, which is not of interest in this study, a normalization is then applied for comparison. It can be seen that the simulated spectrum is in good agreement with the experimental spectrum, which indicates that the P/C ratio obtained by the experiment(=14.4) is very close to the theoretical value obtained by simulation(=13.8), which proves the reliability and authenticity of the parameter setting of simulation.

To distinguish the signals from different scintillators, the rise and decay time discrimination (R&D) method is used in both experiments and simulations, which mainly uses the difference in the rise/decay time between different scintillators to identify the signals.¹³ During the comparison between the shape of the generated pulses, those coincident signals generated by multiple scintillators at the same time are determined as Compton signals or interference signals, and then the anti-coincidence method is used to remove those events, so as to reduce the Compton plateau and subtract the background radiation counts.¹⁹ 

In this study, t_rise is defined as the time taken for each signal to rise from 30% to 90% of the maximum value as the rise time, and t_decay is defined as the time taken to decay from 90% to 30% of the maximum value as the decay time. Taking these two factors as the x and y axes, respectively, one obtains the distribution of the temporal features of the signals, which can be used for PSD. As shown in Fig. 3, we can see the trend of the distribution of different signals according to their rise/decay time, and thus identify which signal is generated by which scintillator.

According to the properties of the scintillators and the distribution trend, we specify that signal with t_rise less than 20 ns and t_decay less than 50 ns is the primary scintillator signal,^17,20 and consider other signals as rejected signals, in this way, the fast signals generated only by the LaBr₃(Ce) can then be picked out and counted into the energy spectrum.

To intuitively show the influence when changing the size of the secondary scintillator on the overall Compton suppression ability of the ACP detector, we define a factor I_s as the Compton events suppression ratio,

where N_Compton is the number of all detected events with incomplete energy deposition in the primary scintillator in a simulation, which is considered as the Compton events. N_suppression is the number of events with energy deposition in both primary and secondary scintillators, which is considered as the Compton events that can be successfully identified and rejected by the ACP detector. Their ratio can be used to show the Compton suppression capability of the ACP detector when detecting gamma rays at a certain energy.

For the same scintillator, the increase in the number of photons arriving at the photocathode in each event may improve the energy resolution in the energy spectrum. At the same time, changing the shape of the secondary scintillator and thus forming a focusing effect due to the presence of the reflective layer may improve the overall photon collection capability to some extent. According to the Geant4 simulation results, the truncated conical design with narrow top and wide bottom can effectively enhance the photon collection capacity compared with the cylindrical design, which is mainly manifested in the movement of the FEP address in the energy spectrum, as shown in Fig. 4.

In Fig. 4, the height and bottom diameter of the truncated cone are fixed, and then, we gradually reduced the diameter of the upper plane to constantly change the inclination (upper diameter/bottom diameter) of the truncated cone, and finally obtained the changing trend of the FEP address and suppression ratio. When the inclination is 1.0, the diameters of the upper and bottom planes are equal, which means the scintillator is a cylinder, and its suppression ratio and FEP address are defined as 1.0. It can be seen that with the continuous reduction of the upper diameter, the location of FEP increases, which means more scintillation photons reach the PMT in each event. As a result, the signal-to-noise ratio may also increase and the energy resolution becomes better. At the same time, the Compton suppression ratio also decreases due to the reduction of the volume of the secondary scintillator, in agreement with our conjecture.

Therefore, ACP detectors with different purposes need to be designed for their respective uses. If better Compton suppression is the primary concern, a larger cylindrical-shaped phoswich scintillator may need to be considered. However, if a better energy resolution and signal-to-noise ratio are desired, the phoswich scintillator should be designed with a truncated cone shape. If one wants to take into account both the Compton suppression ratio and light collection capacity, we might recommend an inclination value of 0.8 in the case of this experiment.

For the ACP detector, when the shape of the secondary scintillator is a well-shaped cylinder, the presence of the bottom of the secondary scintillator between the primary scintillator and the photomultiplier tube may make the light collection capability worse. Therefore, the well-shaped design of the secondary scintillator may make the ACP detector have a worse energy resolution than when there is only a stand-alone primary scintillator.¹² At the same time, as a representation of the light collection capability, if the light collection becomes worse, the location of the FEP will also decrease, as shown in Fig. 5.

In Fig. 5, we study the influence of the bottom thickness of the secondary scintillator. The FEP channel address is normalized according to the case when there is no bottom (thickness = 0 mm). Due to the relatively low variation of the Compton suppression ratio, it is not plotted here, and its value will be given in the subsequent comparison. Compared with 20 mm thickness, an ACP detector without bottom has 120.2% FEP address, 120.2% signal-to-noise ratio, 96.69% Compton suppression ratio, and 89.98% energy resolution. As a result, after fully considering the changes in performance, we suggest that it may be better to choose an annular shape rather than a well shape and that the bottom thickness should not exceed 5 mm when the well shape is chosen.

When two gamma rays are detected simultaneously by the primary and secondary scintillators, accidental coincidences will occur and the signal from the primary scintillator may be incorrectly considered as a Compton event and then rejected, resulting in a loss of FEP and an impact on the detection efficiency.

The volume of the scintillator is reduced after the second scintillator is transformed into a truncated cone shape. Although the Compton suppression ratio decreases at the same time, the probability of accidental coincidence misidentification may also decrease and lead to a decrease in the resulting FEP loss.

We simulated the energy spectrum of ⁶⁰Co radioactive source measured by a cylindrical ACP detector and truncated cone ACP detector. As shown in Fig. 6, it can be found that under the condition of simulating the same number of events (1 × 10⁶ events/run), the FEP value and peak area measured by the truncated cone ACP detector become larger. This may improve the sensitivity of the ACP detector and allow more accurate measurements of the activity of the radioactive source.

Compared to ordinary CCS spectrometers consisting of multiple detectors, ACP detectors using a composite scintillator coupled to single PMT have the advantage of a simpler system, lower cost, smaller volume, ease of carrying and deployment, and lower FEP losses. Therefore, the range of applications of scintillator detectors may be further extended to some extent, such as the detection of low-intensity radionuclides in complex outdoor environments.

While designing the secondary scintillator of the ACP detector into a truncated cone shape, the Compton suppression ratio is slightly reduced, it may not only reduces the overall volume and weight of the detector but also increases the channel address of the FEP in the measured energy spectrum, indicating that the number of scintillation photons reaching the photomultiplier tube increases in each event, which means the light collection efficiency is improved and signal-to-noise ratio also increases. For the same scintillator material, better light collection efficiency may be equivalent to increasing its light yield, or in other words, choosing a better scintillator material in design.

Correspondingly, if a well-shaped secondary scintillator is selected in design, although the increased volume can increase the Compton suppression ratio of the ACP detector, the existence of the bottom of the secondary scintillator between the primary scintillator and the photomultiplier tube may make the energy resolution of the detector worse, this is consistent with the experimental results of others,¹² which is equivalent to using a primary scintillator with lower light yield and poor energy resolution, even though the signal-to-noise ratio may decrease.

Then, according to our simulation and optimization, based on the LaBr₃(Ce)/NaI(Tl) phoswich scintillator selected, we suggest that the shape of the secondary scintillator designed as a circular truncated cone shape with an inclination of 0.8 may not only take into account the Compton suppression function but also ensures good energy resolution and reduces the FEP loss. At this size, the ACP detector will have an equivalent light yield and signal-to-noise ratio of 137%, a Compton suppression ratio of 89.62% (at 662 keV), 89.98% FWHM energy resolution (at 662 keV), and a volume reduction of 36.74% compared with the φ75 × 90 mm² cylinder composite scintillator used in source laboratory, which means that the weight of the detector is reduced by 2.107 kg, greatly improving the portability and may reduce the cost if the cut material is reused, which may need a matched production process.

It is shown that the choice of the shape and size of the secondary scintillator in the design of the ACP detector is necessary and efficient and that a proper choice can be equivalent to choosing a primary scintillator with better scintillator properties. In general, the design of a well-shaped secondary scintillator is always disappointing due to the reduced energy resolution and equivalent light yield, which is why we propose to design the secondary scintillator as a ring. The overall performance of the slightly inclined truncated conical composite scintillator in the ACP detector is better than that of the cylindrical composite scintillator. However, a second scintillator with too small a volume would also significantly decrease the Compton suppression ratio. At the same time, after reducing the FEP loss, the sensitivity of the ACP detector also increases, which makes the ACP detector better able to detect both low- and high-intensity radionuclides.

Therefore, it is necessary to adapt the shape design to the needs of the design purpose, and we hope that this study may serve as a reference for others designing ACP detectors.

National Natural Science Foundation of China (Grant No. U1867210).

The authors have no conflicts to disclose.

R.P.L. and H.D.W. contributed eqully to this work.

R. P. Li: Conceptualization (equal); Data curation (lead); Software (lead); Validation (equal); Visualization (equal); Writing – original draft (lead); Writing – review & editing (equal). H. D. Wang: Conceptualization (equal); Data curation (equal); Software (equal); Writing – review & editing (equal). Jingbin Lu: Project administration (equal); Writing – review & editing (equal). Chengqian Li: Validation (supporting); Writing – review & editing (supporting). Zirui Situ: Validation (supporting); Writing – review & editing (supporting). Huan Qu: Validation (supporting); Writing – review & editing (supporting).

The data that support the findings of this study are available within the article.