# Improving a PGNAA Technique to Detect Heavy Metals in Solid Samples
## 3 Results and Discussions  
Figures 3-5 show the normalized pulse height spectra of the CeBr\({}_{3}\) detector from heavy metals contained in soil samples. The characteristic gamma rays of Cr at 1.43 MeV were clearly observed, whereas those of Ti and Zn at around 1.00 MeV were being built upon the Br peaks at 0.97 and 1.022 MeV. The detector's resolution at 1.0 MeV is estimated to be around 30 keV. This clarifies the strong overlap between the two bromine peaks and the zinc or the titanium peak. Hence, the lack of CeBr\({}_{3}\) capabilities to differentiate between these peaks increases the statistical error in determining the minimum detection concentration (MDC). On the other hand, when the spectra of each element are superimposed as a function of their concentration in the soil, the elemental peak displays an increase in gross counts that is proportional to its abundance in the samples. Furthermore, as shown in Figure 3, the neutron flux that activated the Si and its measured gamma rays at 1.78 MeV showed a gradual decline in gross counts, which is indirectly proportional to the heavy metal concentration. The integrated net counts under the chrome's peak at 1.43 MeV were determined by subtracting the uncontaminated soil background spectrum from the gross counts under each soil-Cr sample shown in Figure 3. The net counts under the 0.984 MeV titanium and 1.005 MeV zinc peak regions were obtained using a similar approach. The net and background counts were then used to calculate the MDC using the relation reported in [28,29];  
\[\mathrm{MDC}=4.653\frac{C}{P}\sqrt{B} \tag{1}\]  
where \(P\), \(C\), and \(B\) were related to the net counts, element's concentration in (wt%), and the associated background counts, respectively, whereas the standard deviation (\(\sigma_{\mathrm{MDC}}\)) is given by  
\[\sigma_{\mathrm{MDC}}=\frac{C}{p}\sqrt{2B} \tag{2}\]  
Figure 3: Prompt gamma-ray pulse height spectrum of soil samples containing 2.23, 3.71, 5.20, and 7.43 wt% Cr superimposed upon background spectrum using CeBr\({}_{3}\) detector. The spectrum of a 250 g pure Cr sample overlays the other spectra. Figures 6-8 show the calibration curves for the analyzed elements and the MDC resulting from their characteristic gamma-ray energies using our PGNAA setup are presented in Table 2. In addition to the standard deviation error in the value of the MDCs, the error raised from fitting the data in order to compute the slope \(\left(\frac{\mathrm{C}}{\mathrm{P}}\right)\) was calculated using the inverse variance weighting scheme [30]. For the case of titanium, this scheme added around \(\pm\) 0.05 wt% to the standard error. Slightly larger amounts were found for Cr and Zn. Thus, the main error in determining the MDC is mostly due to the standard deviation error \(\sigma_{\mathrm{MDC}}\). Figure 4: Prompt gamma-ray spectra of three soil samples containing 3.66, 5.18, and 6.40 wt% Ti superimposed upon background spectrum using CeBr\({}_{3}\) detector. The spectrum of a 100 g pure Tir sample overlays the other spectra. Figure 5: Prompt gamma-ray spectra were acquired by the CeBr\({}_{3}\) detector, obtained from the background spectrum and superimposed upon four samples containing zinc with the following concentrations, 3.66, 7.62, 10.67, and 15.24 wt%. In this study, the MDCs for Cr, Ti, and Zn were determined to be 0.85 \(\pm\) 0.26 wt%, 0.68 \(\pm\) 0.18 wt%, and 1.53 \(\pm\) 0.47 wt%, respectively. When compared to the previously discussed values in [PERSON] [22] and [PERSON] [23], the following can be summarized: 3.29 MeV neutrons were created by the DD reaction in [PERSON] and [PERSON]'s experiment, which used a 400 kV Van de Graaff machine and a NaI detector to measure the prompt gamma rays [22]. The high beam current of 100 A and the activation time of 1430 s were the two key advantages of their work. This current intensity was two times that of Genie 16's beam current, having a considerable impact on the NIS cross-section. On the other hand, in [PERSON] et al.