Calculation of NaI(Tl) detector efficiency using ²²⁶Ra, ²³²Th, and ⁴⁰K radioisotopes: Three-phase Monte Carlo simulation study

1 Introduction

The existence of ionizing radiation sources, both natural and man-made, illustrates that these sources are a part of our everyday lives and serves as an important motivator for researchers to minimise these sources’ damaging consequences on living biological structures. At this point, numerous measurement and evaluation procedures have been established in everyday activities and have formed an integral part of such investigations. Among the several evaluation techniques, gamma-ray spectroscopy is commonly employed in numerous labs across the world to identify and quantify natural and man-made radionuclides for radioactive measurements for environmental sample analysis and activation analyses [1,2,3,4,5]. This technique is advantageous in terms of determining the presence of radiation as well as the radioactivity level of various kinds of samples [6]. On the other hand, gamma-ray spectroscopy techniques can be performed using a variety of detector types, most notably high-purity germanium (HPGe) and thallium-activated sodium iodide NaI(Tl) detectors [7,8]. Among the mentioned detector types, HPGe detectors require advanced cooling systems for having excellent energy resolution for a Ge detector. Furthermore, long measurement is required for a Ge detector due to its low detection efficiency [9]. On the other hand, another promising detector type, namely, NaI(Tl) detectors, can be utilised for various gamma-ray spectroscopy studies at room temperature, which significantly provides a remarkably beneficial feature for users. Moreover, using large-area NaI(Tl) detectors significantly reduces the measurement time. Most importantly, these detectors have a better detection efficiency than HPGe detectors, making them the favoured choice for different types of radioactivity studies. For example, a typical gamma-spectroscopy detector is made of inert materials that react on receiving gamma rays [9,10,11]. The gamma ray’s energy is absorbed and transformed to a gamma-ray detector’s output (an electrical charge) through different gamma-ray matter interaction processes, which are detected by comparing the energy difference before and after the interaction [12]. The amplitude of the generated signal is proportional to the detected gamma ray’s energy. To estimate the gamma ray’s energy precisely, it is preferable if the photoelectric effect occurs since it absorbs the whole energy of the incident ray. It is also conceivable to absorb all energy when a succession of these contact processes occurs inside the detector container. However, a fraction of the energy may escape the detector volume due to Compton interaction or pair formation. Thus, the absorbed energy produces a signal that behaves similarly to that produced by a lower-energy beam. This results in a spectral pattern that overlaps the lower energy areas. Increasing the detector volume (larger NaI(Tl) scintillation crystal) mitigates this impact [13]. On the other hand, detector efficiency and energy resolution are critical characteristics to determine for gamma-ray spectrometry [14,15]. These characteristics are often calculated using a function that fits the efficiency across a broad range of energies due to the restricted number of energy peaks obtainable from radioactive sources. The review of the literature showed that several investigations of detector efficiency had been conducted using experimental and modelling approaches, and this research is currently continuing [16,17,18,19,20,21,22]. Meanwhile, in a previous study, El-Gamal et al. developed a novel experimental approach for calibrating the absolute efficiency of a NaI(Tl) detector in the absence of a standard source of interest and by using the known specific activity of a reference sample measured with an HPGe detector [9].

This three-phase investigation aimed to simulate a standard NaI(Tl) detector using the MCNPX (Monte Carlo N-Particle eXtended) code’s sophisticated modelling approaches. The study was carried out in three phases as follows.

• Simulation of a standard NaI(Tl) detector,

• Validation of the simulated detector for gamma rays emitted from ²²⁶Ra, ²³²Th, and ⁴⁰K radioisotopes, and

• Evaluating the measuring performance of a validated NaI(Tl) detector based on experimental and standard theoretical data

2 Materials and methods

2.1 Phase-I: simulation of NaI detector in MCNPX code

MCNPX version 2.4.0 [23] was used to develop and calculate the absolute efficiency of the NaI(Tl) detector in this investigation. MCNPX is a completely three-dimensional (3-D) general-purpose program that makes use of enhanced nuclear cross-section libs and physics models for different types of scientific applications from medical to nuclear physics [24,25,26,27,28,29,30]. As a preliminary stage in the simulation procedure, the geometry of the NaI(Tl) detector was modelled using the code’s INPUT file. MCNPX’s INPUT file comprises three primary components: a CELL card, a SURFACE card, and a DATA card. To begin, we characterised the equipment’s CELL structures using their covering surfaces and densities. Finally, in the DATA card section, we added the radioisotope energies (Table 1) as well as the geometry of the source as point isotropic. The entire geometry of the successfully modelled NaI(Tl) detector is shown in Figure 1a. It is worth mentioning that the physical specifications of the associated detector displayed in Figure 1 were obtained from Canberra Company. The mentioned specifications were previously used in many experimental assessments of detector-based investigations [31].

Table 1

Comparison of absolute detection efficiencies and deviation (%) between experimental and MCNPX results

Energy (keV)	Type of isotope	Experimental NaI(Tl) efficiency (ε) [26]	MCNPX NaI(Tl) efficiency (ε) (this study)	Deviation* (Δ) %
186.1	226-Ra	0.037611	0.038174	1.4858
295.22		0.095051	0.096128	1.1267
351.93		0.045937	0.046601	1.4351
609.31		0.029546	0.029679	0.4491
1120.29		0.016689	0.016807	0.7046
1764.49		0.011257	0.011469	1.8657
238.63	232-Th	0.080115	0.080986	1.0813
911.2		0.020305	0.020826	2.5334
2614		0.00771	0.007912	2.5861
1460.83	40-K	0.013542	0.013887	2.5156

* Δ ( % ) = | ε ( MCNPX ) − ε ( Experimental ) | [ ε ( MCNPX ) + ε ( Experimental ) ] / 2 × 100 .

Figure 1

(a) Schematic 2-D view and detailed coordinates of the modelled NaI(Tl) detector obtained from MCNPX Visual Editor (VE VisedX22S) and (b) 3-D view and basic parts of the modelled NaI(Tl) detector obtained from MCNPX Visual Editor (VE VisedX22S).

Additionally, we included a vital specification of the data collection technique, which is specified as TALLY MESH, to the DATA card. This study established the detector response function of modelled NaI(Tl) detector using the MCNPX’s pulse-height TALLY MESH, namely, F8 tally. F8 tally operates the energy distribution of radiation-induced pulses in a detector. The net response consists of a spectrum of pulses with heights proportional to the frequency of events occurring in discrete energy bins. The MCNPX input file specified all chemicals and pure materials used in the detector.

• Aluminium: 2.7 g/cm³

• MgO: 3.58 g/cm³

• NaI(Tl): 3.67 g/cm³

• SiO₂: 2.648 g/cm³

Figure 1b shows a three-dimensional snapshot of the modelled NaI(Tl) detector obtained from the Visual Editor of MCNPX (VE_VisedX22_S). As can be seen from Figure 1b, there is one cylindrical 3 × 3 inch NaI(Tl) detector (the crystal height of 7.62 cm and diameter of 7.62 cm) with a monoenergetic isotropic point source. Additionally, massive lead (Pb) blocks were utilised to shield the source and detector system against backscattered gamma-rays, ensuring the consistency of the top-level counting. The simulations were performed for gamma-ray sources of ²²⁶Ra, ²³²Th, and ⁴⁰K. Meanwhile, all the simulation studies were performed using Lenovo® ThinkStation-P620/30E0008QUS Workstation-1x AMD-Ryzen, Threadripper PRO Hexadeca-core (16 Core) 3955WX 3.90 GHz-32 GB DDR4 SDRAM RAM.

2.3 Phase III: evaluation of modelled NaI(Tl) detector with standard NIST data

We utilised the modelled detector to calculate the mass attenuation coefficients (µ) of Lead (Pb) and various traditional and new-generation radiation shielding concretes [33,34] as follows.

• Ordinary concrete (OC)

• Lead (Pb)

• Hematite-serpentine concrete (HSC)

• Steel-scrap concrete (SSC)

The mass attenuation coefficients of the above-mentioned materials were determined at 186.1, 295.22, 351.93, 609.31, 1120.29, 1764.49, 238.63, 911.2, 2,614, and 1,460.83 keV gamma energies that were also used in absolute detector efficiency calculations. To simplify the mass attenuation coefficient, it is essential to understand the Lambert-Beer law [35,36], which is shown in equation 2:

(2) I = I o e − μ t ,

where I ₀ represents the initial energy of the beam, μ is the linear attenuation coefficient, t signifies the absorber thickness, and I signifies the gamma ray intensity after transit through the absorber. The mass attenuation coefficient (µ _m) is the ratio of the linear attenuation coefficient to the density. It is generally represented in cm²/g [37,38,39,40] and is computed using the following equation:

(3) μ m = μ ρ ,

where μ is the linear attenuation coefficient, and ρ is the density of the sample. To evaluate the overall performance of the simulated NaI(Tl) detector, we created a typical gamma-ray transmission experiment setup, complete with all necessary information and physical placements for the equipment. The appearance of the simulated experiment setup, including the setup interface, is shown in Figure 2. The simulated NaI(Tl) detector was then put inside a large Pb block along with an attenuator material. Following the same abovementioned INPUT preparation as in the Section 2.1, we used the same radioisotope energies of efficiency validation phase as 186.1, 295.22, 351.93, 609.31, 1120.29, 1764.49, 238.63, 911.2, 2,614, and 1460.83 keV. The attenuator material has been defined as ordinary concrete material. In the third, the mass attenuation coefficients (µ _m) of the ordinary concrete were determined at the same radioisotope energies. The obtained results have been compared with the standard NIST data using XCOM [41]. The main aim of Phase-III was to assess the reliability of the modelled NaI(Tl) detector for frequently used gamma-ray transmission studies. Therefore, we compared the simulated mass attenuation coefficients with those of the standard NIST database. The consistency of the obtained results may provide important information in terms of the consistency of the simulated detector and the gamma-ray transmission setup (Figure 2).

Figure 2

3-D view of the modelled gamma-ray transmission experiment setup of MCNPX obtained from MCNPX Visual Editor (VE VisedX22S).

3 Results and discussion

As a consequence, we utilised the experimental NaI(Tl) detector efficiencies to validate our model across a broad range using 186.1, 295.22, 351.93, 609.31, 1120.29, 1764.49, 238.63, 911.2, 2,614, and 1460.83 keV gamma-ray energies (Table 1). Moreover, we calculated the deviation (Δ) % of the obtained efficiency values between the experimental and Monte Carlo studies using the next equation:

The absolute efficiency of a modelled detector was confirmed in this work using experimental efficiency data for ²²⁶Ra, ²³²Th, and ⁴⁰K radioisotopes. Figure 3 shows the variation in absolute detector efficiency as a function of increasing gamma-ray energies (keV). The efficiency curve between 186.1 and 2,614 keV exhibits two distinct zones, showing a variation in behaviour of detector efficiency caused by attenuation and absorption processes. At low-photon energy, absolute detector efficiency keeps increasing when the attenuation of the radioactive source decreases significantly. The gamma-energy shows a peak based on the properties of the detector and source. Above a few 100 keV, the efficiency steadily drops. For NaI(Tl) detectors, the absolute detection efficiency cannot be expressed in one stated value. The effectiveness of detection is highly reliant on the gamma-ray energy, the source location, activity, and the geometry and composition of the source-detector, all of which are situational variables. On the other hand, Figure 3 illustrates the correlation between experimental and MCNPX data. There is a strong link between the acquired findings. On the other hand, Table 1 contains numerical data as well as percentages of variation. As can be observed, the numerical results are relatively constant. However, there are slight discrepancies between the two results, which are somewhat higher at low gamma-ray energy. The differences noted above might be a result of conceptual differences between the experimental and Monte Carlo simulation contexts. On the one hand, experimental conditions include all physical variables that might impact the overall outcome, ranging from particles in the air to material deficiencies of the used experimental equipment. Additionally, any technical inconsistency encountered during the gamma-ray counting procedure may influence the experimental data achieved. Monte Carlo simulations promise an immaculate condition, which is physically difficult to achieve in real life. For example, all the simulation components’ material definitions are constructed using their elemental mass fractions (wt%) and densities (g/cm³), which indicates that the described materials are filled with elemental components. However, this is not feasible owing to the material’s atomic and molecular structures, potential micro-cracks, and minuscule air spaces inside the material body. However, we reported the deviation amounts in an acceptable range for ten gamma-ray energies. The modelled NaI(Tl) detector in MCNPX code exhibits very similar behavioural responses to the radioisotopes utilised in the experimental work [9]. As a consequence, the modelled detector may be employed in comparable energy ranges. Figure 4 shows the comparison of mass attenuation coefficients obtained from standard NIST data (XCOM) and modelled NaI(Tl) detector in MCNPX. It is seen that the obtained mass attenuation coefficients are rather consistent (Table 2). There are slight differences between the two results, which are somewhat higher at certain gamma-ray energies. The possible causes of the slight deviation rates between these numerical values have already been discussed in detail. It is expected that conceptual variations between the approaches utilised contributed to some of the discrepancies in the data produced in this section of the research. In accordance with our findings, the modelled NaI(Tl) detector is capable of creating different gamma-ray shielding properties that are consistent with existing data.

Figure 3

Comparison of absolute detector efficiency (ε) values obtained from experimental [26] and MCNPX simulation code.

Figure 4

Comparison of mass attenuation coefficients obtained from standard NIST data (XCOM) and modelled NaI(Tl) detector in MCNPX.

4 Conclusion

The primary goal of this work was to create a standard NaI(Tl) detector in general-purpose Monte Carlo radiation transportation code MCNPX for use in different types of research such as gamma-ray shielding studies, measuring of gamma-ray spectrum of different radioisotopes, and measuring of counting efficiency depending on source properties. A validation study of the modelled NaI(Tl) detector has been performed using experimental results for absolute detector efficiency values obtained from ²²⁶Ra, ²³²Th, and ⁴⁰K radioisotopes. We also used modelled detector for determination of mass attenuation coefficients of OC, Pb, HSC, and SSC at 186.1, 295.22, 351.93, 609.31, 1120.29, 1764.49, 238.63, 911.2, 2,614, and 1460.83 keV gamma-ray energies. The high degree of consistency between the coefficients obtained from the modelled detector and the standard data leads to the conclusion that such detectors, which can be derived by modelling, may be employed in the design and characterisation of radiation shielding materials. It can be concluded that continuous optimisation procedures are strongly suggested for sophisticated Monte Carlo simulations to maintain a high degree of simulation reliability. As a result, it can be concluded that the simulation model may be evaluated using experimental data available. Finally, it can also be concluded that the validated detector models are effective instruments for obtaining basic gamma-ray shielding parameters such as mass attenuation coefficients. Nevertheless, Monte Carlo simulation for radiation transport studies and associated codes such as MCNPX, Geant4, FLUKA, and EGSnrc exhibit several interesting features in terms of variance reduction and overall simulation improvement. It is advised that the scientific community conduct thorough investigations and validation stages on modelled detectors to attain greater success in radiation sciences.