# Design of a Low-Resolution Gamma-ray Spectrometer for Monitoring Radioactive Levels of Wastewater
## 2 Materials and Methods
### Experimental Calibration  
The experimental efficiency calibration was performed in a test water tank with a volume of 14 L, filled with water and reference source \({}^{18}\)F, which is most commonly used in positron emission tomography/computed tomography. It has a half-life of only 110 min and emits two 511 keV gamma rays.  
The absolute detection efficiency (\(\varepsilon\)) for \({}^{18}\)F was obtained using the following equation from previous research [19,20]:  
\[\varepsilon=N/(A\cdot I_{\gamma}\cdot T), \tag{1}\]  
where \(N\) denotes the net count. Here, \(A\) denotes the specific activity of the specific radionuclide obtained using a gamma spectroscopy system including an MCA (DSA-1000 Digital Spectrum Analyzer, Canberra Industries, Meriden, CT, USA), analyzing software (Genie 2000, Miron technologies, Atlanta, GA, USA) [21], and a high-purity germanium detector (GEM25P-PLUS, Canberra Industries, Atlanta, GA, USA) calibrated by the certified reference materials in a cylinder-type source (Table 2) certified by the Korea Research Institute of Standards and Science (KRISS), in units of Bq\(\cdot\)m\({}^{-3}\). In addition, \(I_{\gamma}\) denotes the emission probability of the gamma ray, and \(T\) denotes the live time of measurement.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Details** \\ \hline Scintillation crystal & \(1.5^{\prime\prime}\times 1.5^{\prime\prime}\) NaI(Tl) \\ Enclosure & Aluminum case with cylinder shape \\ Resolution & 6.5\% to 8\% at 660 keV \\ Gamma efficiency & Approx. 60\% at 662 keV \\ Input power & +5 V USB 2.0 \\ Current draw & \(<\)150 mA \\ ADC sample rate and bit rate & 48 kHz, 16 bit \\ Pulse length & Adjustable \\ Signal-to-noise ratio & 73.97 dB \\ High-voltage connector & SHV \\ Signal in connector & BNC \\ \hline \hline \end{tabular}
\end{table}
Table 1: Specifications of the monitoring system.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Nuclide**} & \multicolumn{2}{c}{**Half-Life (day)**} & \multicolumn{2}{c}{**Activity (Bq)**} & \multicolumn{2}{c}{**\(\gamma\)-ray**} & \multicolumn{2}{c}{**\(\gamma\)-ray Emission**} \\ \cline{2-7}  & **Half-Life** & **Uncert.** & **Activity** & **Uncert.** & **(keV)** & **Prob.** & **Uncert.** \\ \hline \({}^{241}\)Am & 158,004 & 219 & 1844 & 74 & 59.54 & 35.92 & 0.17 \\ \hline \({}^{109}\)Cd & 461.9 & 0.4 & 10,257 & 410 & 88.03 & 3.66 & 0.05 \\ \hline \({}^{57}\)Co & 271.81 & 0.04 & 489 & 20 & 122.06 & 85.49 & 0.14 \\ \hline \({}^{139}\)Ce & 137.641 & 0.020 & 594 & 24 & 165.86 & 79.90 & 0.04 \\ \hline \({}^{51}\)Cr & 27.704 & 0.004 & 63,635 & 2600 & 320.08 & 9.89 & 0.02 \\ \hline \({}^{113}\)Sn & 115.09 & 0.03 & 1515 & 61 & 391.70 & 64.97 & 0.17 \\ \hline \({}^{85}\)Sr & 64.850 & 0.007 & 2009 & 81 & 514.00 & 98.5 & 0.4 \\ \hline \({}^{137}\)Cs & 10,976 & 29 & 909 & 37 & 661.66 & 84.99 & 0.20 \\ \hline \({}^{60}\)Co & 1925.23 & 0.29 & 1251 & 50 & 1173.23 & 99.85 & 0.03 \\  & & & & 1332.49 & 99.9826 & 0.0006 \\ \hline \({}^{88}\)Y & 106.63 & 0.05 & 3156 & 130 & 898.04 & 93.7 & 0.3 \\  & & & & 1836.05 & 99.346 & 0.025 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Specifications of certified reference materials in cylinder-type source, certified by KRISS.