1. Introduction
The issue of managing highlevel radioactive waste is emerging due to the saturation of domestic spent nuclear fuel storage capacity [1]. In February 2023, a briefing organized by the Ministry of Trade, Industry, and Energy revealed that 72,000 assemblies and 722,000 bundles of spent nuclear fuel are expected to be generated. The Hanbit Nuclear Power Plant storage facility is anticipated to reach saturation as early as 2030, followed by sequential saturation of the Hanul Nuclear Power Plant in 2031 and the Gori Nuclear Power Plant in 2032. These saturation points are attributed to the phenomena resulting from nuclear power plant construction and operational plans, as well as the increase in nuclear power utilization rates.
Consequently, there is a pressing need for the establishment of facilities for the disposal of highlevel radioactive waste. To address the concerns of residents regarding these facilities, proactive communication and swift enactment of the HighLevel Radioactive Waste Management Special Act are essential. However, even if these measures are promptly discussed, agreed upon, and legislated, a considerable amount of time will be required for site selection, disposal facility construction, and operation.
Therefore, it is inevitable to operate dry storage facilities temporarily to alleviate saturation. Dry storage facilities involve removing spent nuclear fuel from wet storage tanks and storing it aboveground. Accurate radiation measurement and analysis technologies are crucial to ensure the safe management, transportation, and storage of spent nuclear fuel [24]. The constituents of spent nuclear fuel include fertile materials, transuranium material, and fission products [5]. Particularly, gamma radiation can measure the burnup of spent nuclear fuel, with 137^{Cs} being dominantly influenced by this process [68].
In this study, we confirmed the extent to which results from gamma radiation measurement experiments using CZT sensors could be reflected by simulating identical conditions on MCNP.
2. Materials and Methods
2.1 Selection of Gammaray Detector: CZT
A CZT (Cadmium Zinc Telluride) semiconductor detector was selected to measure the energy and dose of gamma rays generated in the fuel assembly. The device accepts gammarays in the direction of a CdZnTe single crystal.
Table 1
Detector sensitive volume  500 mm^{2}  



Performance (at operation temperature +22℃)  


Energy resolution (FWHM) at 662 keV line  For CZT/500  ≤ 30 keV 
For CZT/500S  ≤ 18 keV  


PeaktoCompton ratio at 662 keV line  For CZT/500  ≤ 2.3 
For CZT/500S  ≤ 4.0  


Bias voltage requirements  


Detector high voltage  ≤ 1,500 V  
Detector high voltage polarity  Positive  


Dimensions  


Diameter  23 mm  
Length (without connector)  33 mm  
Distance between the top plane of the housing cover and the sensitive surface  7 mm 
The CZT detection unit was selected based on the quasi hemispherical geometry of ‘CZT/500S (Ritec SIA)’. The CdZnTe single crystal receiving the signal is 10 × 10 × 5 mm, with a detection area of 500 mm^{3}, and operates at a drive voltage of 1,500 V or below. In subsequent actual experiments involving CZT, the detection unit’s single crystal will be simulated to concentrate gammarays towards it, with the device enclosed in lead shielding to minimize the impact from gammarays.
2.2 Comparison of Gammaray Measurement Experiment and MCNP Simulation
The correctness of the calculations was verified by comparing the results of the gammaray measurement experiment with those obtained from the MCNP simulation. The energy spectrum was evaluated using standard radiation sources (85 μCi, Eckert & Ziegler) of representative gammaemitting isotopes, ^{134}Cs, and 137^{Cs}, generated from spent nuclear fuel. Gamma rays were emitted at a rate of approximately 3.145 × 10^{6} per second, considering an emission probability of 94.6%, resulting in an effective emission rate of 2.97517 × 10^{6} per second. A lead collimator was positioned between the radiation source and the CZT detector to ensure parallel incidence of incoming particles.
By examining the gammaray dose based on the thickness (3, 4 cm) and inner diameter (1–4 mm) of the lead collimator, results similar to those shown in Fig. 3 can be obtained [8]. The thickness of the collimator must be carefully determined to accurately measure the gamma dose of 137^{Cs}, which is the main nuclide of burnup measurement. The attenuation rate was about 84% compared to before the application of the collimator at the thickness of 4 cm and the inner diameter of 4 mm, and the main peak of 662 keV was confirmed while the attenuation rate was about 98% at the thickness of 4 cm and the inner diameter of 1 mm [9]. Therefore, accurate gamma dose measurement is possible if a gammaray measurement system is configured using the corresponding thickness and inner diameter.
However, it should be noted that there is an experimental limitation as the shielding configuration was not separately designed for the space surrounding the radiation source, excluding the inner diameter of the collimator. Consequently, there is a possibility of gammarays incident from directions other than the straightline distance being detected during measurement.
3. Evaluation of Gammaray Attenuation Rate
Before implementing the conditions of this experiment in the MCNP simulation, the phenomenon of radiation being detected by the collimator was modeled using mathematical expressions.
3.1 Pb Plate With a Collimeter (hole) Modeling: Direct Hit
When radiation reaches an object, the central line reaching perpendicularly and its corresponding shadow are respectively termed ‘Umbra’ and ‘Penumbra’ (Fig. 4). The initial radiation is assumed to be N_{0}. If f(r) represents a function for radiation within the penumbra, it can be expressed by the following Equation (1).
Where f(r): radiation flux at penumbra area, N_{0} at r = R, 0 at r = H
Therefore, the radiation N reaching through a direct hit collision can be expressed as follows.
The combined region H of the umbra and penumbra obtained through direct hit can be expressed as shown in the equation.
where $q=\frac{d}{L}$
When determining the radiation N reaching, it can be formulated as in Equation (4).
Simplifying Equation (4), the final expression for a direct hit can be presented as follows.
3.2 Penetration With Attenuation
Secondly, consideration was given to the phenomenon of radiation encountering lead shielding and undergoing attenuation. Radiation interacts with the medium as it passes through, losing energy, a process referred to as attenuation. Assuming the initial radiation is N_{0}, the remaining energy after passing through the shielding is expressed as follows.
Where

N = intensity after attenuation

N_{0} = incident intensity

μ = linear attenuation coefficient (cm^{−1})

L = thickness of the absorber
Considering both Equations (5) and (6), the radiation reaching the detector after passing through the lead collimator can be expressed by the following Equation (7). This formula can be used for comparative verification to derive clearer values when trying to obtain experimental values using collimators.
Gammaray measurement experiments were conducted as depicted in the left image of Fig. 6. A collimator made of lead was positioned between the radiation source and the CZT sensor, and measurements were obtained. Collimator thicknesses of 3 cm and 4 cm were prepared, and holes ranging from 1 to 4 mm were drilled, taking into account the possibility of variations in gammaray intensity based on the inner diameter.
4. Geometry Modeling in Cylindrical Concepts and Corresponding Result
To check the results for various thicknesses and hole inner diameters at once, it was simulated as shown in Fig. 7 through MCNP. Table 2 shows the information of each cell.
Table 2
Cell  Notation  Cell  Notation  Cell  Notation 



11  4 cm 1 mm  21  3 cm 1 mm  25  3 cm 0 mm 
12  4 cm 2 mm  22  3 cm 2 mm  26  4 cm 0 mm 
13  4 cm 3mm  23  3 cm 3 mm  10  5 cm 0 mm 
14  4 cm 4 mm  24  3 cm 4 mm 
F8 tally and 1,000 channels of energy bin cards were used to calculate the energy spectrum for particles p and e. The energy band for peak observation of 137^{Cs} was set to 10^{−5} to 0.8 MeV. Nps was set to 1e8. In addition, in order to obtain a result similar to the actual spectrum, Gaussian Energy Broadcasting (GEB) was set, and a result value was derived when GEB was not set. Figs. 8 and 9 below show some of the result values.
Comparing the actual experimental results in Fig. 3 with the corresponding results, the main areas such as the total energy peak from the interaction between gamma rays and the detector are well illustrated across the energy spectrum. Fig. 9, which is the result of not applying GEB, simulates the result more simply.
After simulating the experimental environment using MCNP, focusing on significant results with 3 mm and 4 mm collimators, the outcomes were confirmed as illustrated in Fig. 10.
Using the 0.662 MeV peak as a reference, the MCNP results were 0.47 times the CZT measurement values, indicating an efficiency of 47% for each peak coefficient efficiency concerning the MCNP results. Therefore, the correlation between the actual measurement values and MCNP can be expressed by the following equation.
For the peak coefficient efficiency,
When the reaction rate value is known by scanning the spent nuclear fuel using the nondestructive testing method through the gammaray measuring instrument, the reliability can be determined by comparing the value with the simulated MCNP value. Thus, applying the efficiency corresponding to Equation (8) to the reaction rates calculated by MCNP, a correlation equation for gammaray measurements can be established.
5. Conclusion
Utilizing this study, it is possible to predict the burnup of spent nuclear fuel from gammaray detector measurements based on the gammaray reaction rate. In the earlier comparison between gammaray measurement experiments and MCNP simulations, the MCNP results were 0.47 times the measured values using the 0.662 MeV peak counts as a reference.
Converting the values to weight per 1 MTU (Det. Total Counts or Det. Peak Counts), multiplying by the efficiency of 0.47 as indicated in Equation (8), and applying the resulting value to the total neutron reaction rate (RR) calculated by MCNP, we can predict the burnup of spent nuclear fuel by applying the RR value at that moment to the function in Equation (9).
With the MCNP results serving as a reference, the detector efficiency is indicated to be 47% concerning the peak counts. Therefore, if the value converted to weight per 1 MTU (Det. Total Counts or Det. Peak Counts) matches the value calculated by MCNP for the total neutron reaction rate (RR), multiplied by the corresponding efficiency of 0.47 as expressed in Equation (8), then applying the RR value at that moment to the function in Equation (9) enables the prediction of the burnup of spent nuclear fuel [10].
Therefore, by applying the gammaray reaction rate (RR) calculated by MCNP to the measured values obtained by the CZT gammaray detector, it is possible to predict the burnup of spent nuclear fuel using the method illustrated in Fig. 10.