# Design of a Low-Resolution Gamma-ray Spectrometer for Monitoring Radioactive Levels of Wastewater
## 2 Materials and Methods
### Monte Carlo Simulation  
In this study, the activity conversion factor (_ACF_) was applied to convert the counts measured by the detector into specific activity. Although the _ACF_ has the same physical meaning as detection efficiency, it was used to clearly distinguish the purpose of use.  
Because the _ACF_ is determined using the intrinsic characteristics of the scintillation detector and MCA, it cannot be obtained only by simulation; therefore, it must be obtained only experimentally or calculated by experiments and simulations [15]. Different departments use different isotopes in hospitals. The \({}^{18}\)F has been commonly used for nuclear medicine outpatients due to its short half-life and production convenience among proton-emitting nuclides. In our study, \({}^{18}\)F was used, and the sample was placed in the tank, as shown in Figure 1b. The count rates of the sample and background count rates were measured using a NaI(Tl) detector for one hour under the same experimental conditions. The _ACF_ was calculated by comparing the simulation results obtained under the same conditions.  
The decay tanks used in the field store tens to hundreds of tons of wastewater. In the experiment, the periphery of the detector, as shown in Figure 1b, was constructed and used instead of that in Figure 1a, and the detector was installed at the top of an actual-sized decay tank. A NaI(Tl) detector was installed inside a polyethylene bottle to prevent the detector from being immersed.  
The _ACF_ was calculated by comparing the counters in the full energy peak measured with a NaI(Tl) detector, and the specific activity was measured with a gamma spectrometry system using diluted \({}^{18}\)F as radioactive wastewater. A gamma spectrometry system using a semiconductor detector was calibrated using a radioactive certified standard material. The _ACF_ was calculated using the following equation, and the counts measured by the NaI(Tl) detector were converted to specific activities measured by a gamma spectroscopy system with an HPGe detector. In this equation, the units of _ACF_, \(N_{NaI}\), and \(C_{HPGe}\) were Bq\(\cdot\)s\(\cdot\)m\({}^{-3}\cdot\)counts\({}^{-1}\), counts\(\cdot\)s\({}^{-1}\), and Bq\(\cdot\)m\({}^{-3}\), respectively:  
\[ACF=C_{HPGe}/N_{NaI(Tl)}, \tag{2}\]  
The radius (\(R\)) and height (\(H\)) of the water tank used in the experiment were 12.5 and 29.5 cm, respectively, and 14 L of radioactive wastewater was used in the experiment. Because practical water tanks are usually much larger, the _ACF_ was calculated using a Monte Carlo simulation.  
Figure 1: Outline of real wastewater tank (**a**) and calculation model (**b**).  
Because water is a good shielding material, its efficiency varies according to the measurement radius [15]. Thus, by changing the radius (\(R\)) and height (\(H\)) of the water tank, as shown in Table 1, the change in _ACF_ was calculated by the MCNP 6.2 (Los Alamos, NM, USA) with the Monte Carlo code using the F8 tally with the GEB option [22].  
In this simulation, the geometry of the scintillation detector was designed based on the drawing provided by the manufacturer, and the density of the NaI(Tl) detector was 3.667 g\(\cdot\)cm\({}^{-3}\)[23]. In this case, the volume of radioactive wastewater used in the calculation ranged from 14 to 56.1 L.