Traditional spectral analysis method

In traditional spectral analysis methods, there are problems with each of the basic steps. When smoothing the spectrum according to a five-point smoothing algorithm ^[37], the processing causes the maximum value of the peak to decrease each time, and the counts on both sides of the bottom of the peak increase. Thus, the calculation of the peak area is inaccurate. At the same time, it is difficult to identify the nuclide because of the changes in the peak shape.

According to the GammaVision user manual ^[37], background subtraction methods include the straight-line, stepped, and parabolic background methods ^[38]. These methods provide only rough approximations of the background, thereby increasing the peak area calculation error. At the same time, Miroslav ^[39] showed that the parabolic background had very poor robustness ^[38].

The peak search method was proposed by Mariscotti ^[28]. This method has a limited ability to separate overlapping peaks ^[32], resulting in inaccurate nuclide identification; furthermore, it is highly susceptible to noise. Thus, it is necessary to smooth the spectrum multiple times before searching for the peak, which leads to changes in the peak shape and increases the error in the peak area calculation.

The final step is the quantitative analysis of overlapping peaks. In traditional methods, a preliminary library-based peak search of the spectrum is performed. The analysis assumes that all of the gamma rays listed in the library are present in the spectrum; therefore, an attempt is made to fit a peak at every gamma energy listed in the library. Therefore, as reported in Ref. ^[40], if the nuclide library is inaccurate, it will increase the error in the spectral analysis results.

Spectral analysis method proposed in this study

According to Knoll ^[41] and the IEC international standard ^[42], for a single overlapping peak composed of multiple full-energy peaks with similar energies, the only method to conduct an analysis is through deconvolution. The deconvolution method can be used to establish the relationship between the incident gamma ray spectrum and the energy deposition spectrum using the response function of the detector, as follows ^[43]: $y\left(t\right)={\displaystyle {\int }_{-\infty }^{\infty }x}\left(\tau \right)h\left(t-\tau \right)\text{d}\tau +n\left(t\right),$ (1)  where $x\left(\tau \right)$ is the incident spectrum, $y\left(t\right)$ is the energy deposition spectrum, $h\left(t\right)$ is the response function, $t$ is the channel, and $n\left(t\right)$ is the system noise. Therefore, the core concept of this method is to use the peak shape function, $h\left(t\right)$, as a filter, and then to obtain the incident spectrum through deconvolution to realize the decomposition of overlapping peaks.

For $h\left(t\right)$, because of the different attenuations of the medium during gamma ray measurement under different conditions, it is difficult to establish the full-spectrum response under such complex and variable conditions through experiments or Monte Carlo simulations. Because the full-energy peak areas of the different nuclides are regarded as regions of interest in this study, it was only necessary to determine the full-energy peak response. The full-energy peak of the HPGe detector can be represented by a Gaussian function. Theoretically, according to the full width at half maximum (FWHM) of the full-energy peak, the response can then be obtained via calculations. Therefore, before the spectral analysis, an experimental method was used to calibrate the FWHM. The FWHM is different for different energies; therefore, the following equation is used for parameter fitting ^[44]: $FWHM=a+b\sqrt{E+c\times E^2},$ (2) where E is the gamma energy. The HPGe detector used in this study was calibrated using the experimental method. When the energy unit is MeV, the values of a, b, and c are 0.00068, 0.00062, and 1.07, respectively.

For a discrete system, $h\left(t\right)$ can be expressed as a matrix ^[45]: $\left[\begin{array}{ccccc}{h}_1\left(1\right)& 0& 0& ⋮& 0\\ h_1\left(2\right)& h_2\left(1\right)& 0& ⋮& ⋮\\ h_1\left(3\right)& h_2\left(2\right)& h_3\left(1\right)& ⋮& ⋮\\ ⋮& h_2\left(3\right)& h_3\left(2\right)& ⋮& 0\\ h_1\left(A\right)& ⋮& h_3\left(3\right)& ⋮& h_m\left(1\right)\\ 0& h_2\left(B\right)& ⋮& ⋮& h_m\left(2\right)\\ 0& ⋮& h_3\left(C\right)& ⋮& ⋮\\ ⋮& ⋮& ⋮& ⋮& h_m\left(N-1\right)\\ 0& 0& 0& ⋮& h_m\left(N\right)\end{array}\right]$ (3) where each column of the matrix is the probability density function of the full-energy peak response, and the subscripts of h indicate the gamma rays emitted from that channel. Because the FWHMs of the different full-energy peaks are different, the values of a–n represent the peak widths of different full-energy peaks.

The solution to Eq. (1) is an ill-posed problem. According to Miroslav ^[46], iterative regularization has strong positive constraints and noise-suppression capabilities. Currently, the most effective method for gamma spectrum analysis is the boosted traditional iterative algorithm ^[47]. In this study, a boosted maximum-likelihood expectation-maximization algorithm ^[48] was used.

Through this deconvolution process, the deposition spectrum of gamma rays with different energies can be converted into the incident $\delta$ function spectrum; thus, nuclide identification can be easily performed. Its height corresponds to the area of the full-energy peak. However, in the realization of this process, another problem must be solved, i.e., the background must be effectively subtracted from the original spectrum to obtain a “net spectrum” containing only the full-energy peak.

Background subtraction methods include the linear method ^[30], approximate physical models for the background, the polynomial method ^[49], digital filtering ^[50], peak clipping ^[38], fast Fourier transform ^[51], and the sensitive nonlinear iterative peak (SNIP) method^[52]. Among these methods, the most effective background subtraction method is the improved SNIP method, i.e., adaptive SNIP ^[39].

The basic concept of the adaptive SNIP method is to divide the energy spectrum into two regions: the region where the peak is located, and the region where there is no peak. For the peak area, the SNIP filter is used for background subtraction, and for the non-peak area, all of the gamma counts are regarded as the background. Therefore, the problem is to determine how to calculate the peak position, peak width, and selection of the clipping filter.

This study proposes a calculation method for peak position identification based on CWT. The wavelet transform of a signal $x$ is given as follows ^[35]: $T\left(E,s\right)={\displaystyle {\int }_{-\infty }^{\infty }x}\left(t\right){\psi }_{E,s}^{*}\left(t\right)\text{d}t,$ (4) where $E$ is the gamma ray energy, $s$ is the scale of the wavelet, ${\psi }_{E,s}\left(t\right)$ is the mother wavelet, and $T\left(E,s\right)$ is the scalogram. The scale $s$ represents the stretching and shrinking of the wavelet, as expressed in the following equation ^[53]: ${\psi }_{E,s}\left(t\right)=\frac{1}{\sqrt{s}}\psi \left(\frac{t-E}{s}\right).$ (5)

The correct choice of wavelet is the key to obtaining the results of the spectrum analysis. As the full-energy peak of the spectrum is a Gaussian function, a Mexican hat wavelet (Mexh) is selected because its shape is similar to that of a Gaussian peak. The definition of Mexh is given as follows ^[54]: ${\psi }_{\text{Mexh}}\left(t\right)=\frac{2}{\sqrt{3\sigma }{\pi }^{1/4}}\left(1-{\left(\frac{t}{\sigma }\right)}^2\right)e^{-\frac{t^2}{2{\sigma }^2}}.$ (6)

By analyzing the scalogram, the position information of the peak can be obtained. The next step is to calculate the widths of the peaks based on their positions.

The peak width can be obtained directly from the scalogram obtained with Eq. (4), but because the peak widths of different scales are different, this method has large errors ^[55]. The peak width can be calculated using a Gaussian product function ^[33], but it is highly susceptible to noise interference. The width can also be determined from the shapes of the peaks using function fitting ^[56]. This approach is also difficult to use because the number of singlets comprising the overlapping peaks is unknown. In Refs. ^[55] and ^[56], a method for calculating the peak width based on the second convolution of the Gaussian first derivative was proposed.

The expression for the full-energy peak is as follows ^[57]: $G\left(x\right)=A\text{exp}\left(-\frac{{(x-a)}^2}{2{\sigma }^2}\right),$ (7)  where $x$ is the channel, $A$ is the count of the full-energy peak maxima, $a$ is the peak position, and $\sigma$ is the standard deviation of the full-energy peak.

The calculation result for the second convolution of the Gaussian first-order derivative of Eq. (7) is expressed as follows ^[54]: $C\left(x\right)=\frac{2\pi {\delta }^2\sigma \left({(x-a)}^2-{\sigma }^2-2{\delta }^2\right)}{{\left({\sigma }^2+2{\delta }^2\right)}^{5/2}}\text{exp}\left(-\frac{{(x-a)}^2}{2\left({\sigma }^2+2{\delta }^2\right)}\right),$ (8)  where $\delta$ represents the width of the filter.

Using Eq. (8), the crossing point of the zero value can be determined as follows ^[54]: $\sigma =\sqrt{{\left(x_0-a\right)}^2-2{\delta }^2},$ (9) where $a$ a is the peak position calculated with the CWT, and $x_0$ is the intersection point with the x-axis. Then, [$a-3\sigma ,a+3\sigma$] is the width of the area in which the peak is located.

However, other studies have shown that this method is not suitable for calculating overlapping peak widths that contain too many full-energy peaks ^[39]. Therefore, in this study, we propose an improved method.

For Eq. (8), the calculation of the width of the peak requires the determination of the parameter $\sigma$, while the parameter $\delta$ is also unknown. Thus, a method is required to determine parameters $\sigma$ and $\delta$. For $C\left(x\right)$ in Eq. (8), when $\frac{\text{d}C\left(x\right)}{\text{d}\delta }=0$, it is easy to obtain $\delta =\sigma$, and this is the maximum value of $C\left(x\right)$. Therefore, the absolute value of $C\left(x\right)$ is first computed, and then a matrix $M\left(x,\delta \right)$ is built. Its horizontal axis, $x$, represents different channels. The vertical axis of $M\left(x,\delta \right)$ indicates that for each $x$, the value of $C\left(x\right)$ is calculated for different δ. In other words, for each $x$, the calculation is performed by traversing the possible values of $\delta$ (for example, 0.1–100) and then calculating a $C\left(x\right)$ curve. This is carried out because at the maximum value of $C\left(x\right)$, $\delta =\sigma$, the value of $\sigma$ can be obtained based on the value of $\delta$, and the peak width can then be effectively calculated. In the application, the horizontal axis, $x$, only considers the peak position information calculated based on the CWT.

Next, the background of the peak area must be removed. For the SNIP method, first, to compress the dynamic range of each channel count in the spectrum to speed up the iteration, a linear least-squares operator is applied to the spectrum data ^[52]: $v\left(i\right)=\text{log}\left\{\log \left[\sqrt{y\left(i\right)+1}+1\right]+1\right\},$ (10) where $i$ is the channel, $y\left(i\right)$ is the count of each channel, and $v\left(i\right)$ is the working vector.

For the count $v\left(i\right)$ of each channel, the parameter m is selected, and then w = 2m + 1. The following equation is then used to iteratively calculate $v_1\left(i\right),v_2\left(i\right)$, …, $v_m\left(i\right)$ ^[52]: $v_p\left(i\right):=min\left\{v_{p-1}\left(i\right),\frac{1}{2}\left[v_{p-1}\left(i+p\right)+v_{p-1}\left(i-p\right)\right]\right\},$ (11)  where $p\in ［1,m]$, $i\in ［p,siz{e}_y]$, and $siz{e}_y$ is the size of spectrum $y$. For parameter w, when the value of w is too small, the background estimate will be too large, and the net peak area will be too small. If the value of w is too large, the background estimate will be small, and the net peak area will be large. Theoretically, the background should be removed as much as possible while preserving the net peak areas. The real width of an object (peak, doublet, or multiplet) that should be preserved is the best value of w ^[58]. In the proposed method, the width of each peak is calculated based on the second convolution of the Gaussian first derivative, and the clipping width, w, of each peak is obtained; that is, the value of w is dynamic. Then, the SNIP algorithm is utilized. Finally, a linear least-squares inverse operator operation is performed on $v_m\left(i\right)$ to obtain the background spectrum.

For the adaptive SNIP ^[39], the spectrum is divided into two areas: the non-peak and peak areas. In the non-peak region, all of the gamma counts are the background. In the peak region, the background is subtracted using the traditional SNIP method. Eq. (11) represents a second-order filter that can effectively remove the linear background. To solve the problem of the inability to subtract the background at the Compton edge for the full-energy peak as described in Sect. 2.1.1, a novel method is proposed.

Because the Compton edge can be approximated by a cubic function to some extent, and a cubic function can be removed by a fourth-order clipping filter, a fourth-order clipping filter is proposed for background subtraction in the peak area. The parameters of the equation were derived from Pascal’s triangle ^[59] formula. The fourth-order clipping filter is defined as follows: $\{\begin{array}{l}{V}_1=v_{p-1}\left(i\right)\hfill \\ V_2=\frac{v_{p-1}\left(i-p\right)+v_{p-1}\left(i+p\right)}{2}\hfill \\ V_3=\frac{-v_{p-1}\left(i-p\right)+4v_{p-1}\left(i-\frac{p}{2}\right)+4v_{p-1}\left(i+\frac{p}{2}\right)-v_{p-1}\left(i+p\right)}{6}\hfill \\ v\left(i\right)=min\left[V_1,max\left(V_2,V_3\right)\right]\hfill \end{array},$ (12) where the definitions of these parameters are identical to those in Eq. (11).

Through the peak searching and peak width calculations described above, the spectrum can be divided into peak and non-peak areas, which are combined with a fourth-order clipping filter in the peak area. Thus, effective subtraction of the background is realized and the net spectrum is obtained.

During the smoothing process in the traditional method, the peak count will decrease. This study uses a low-pass filter ^[52] to smooth the spectrum and effectively solve this problem.

Experimental configuration

The HPGe detector was an Integrated Cryocooling System produced by ORTEC. Its relative efficiency at 1.33 MeV is 30%. The detector crystal has a diameter of 51.8 mm and length of 60.9 mm. The cold finger has a diameter of 8.7 mm and a length of 38.2 mm. The dead layer at the front end of the crystal has a thickness of 0.03 mm. The DSPEC-50 multi-channel analyzer was manufactured by ORTEC.

GV 6.08 spectral analysis software was used. The analysis parameters of GV included the calibration (.CLB) file, peak background correction (.PBC) file, and nuclide library (.LIB) file; the analysis program was WAN32. The standard area of the peak was calculated by selecting the region of interest (ROI) in the GV; the peak width was three FWHM.

The experiments were conducted using the Tomographic Gamma System (SJTU-TGS), which was independently developed by Shanghai Jiao Tong University, as shown in Fig. 1(a). The detector was equipped with a lead collimator (liftable). The exterior dimensions of the collimator and collimation window were 25 cm (L)× 36 cm (W)× 40 cm (H) and 9 cm (L)× 20 cm (W)× 25 cm (H), respectively, and the thickness of the lead was 8 cm. The distance between the detector surface and drum center was 74 cm. The system had a liftable transmission source storage device. The waste drum could be moved and rotated. Therefore, the measurement system had detection functions of SGS and TGS and could also meet the requirements of 200 L and 400 L waste drums at the same time.

Fig. 1Full-screen View

(Color online) (a) SJTU-TGS System; (b) Canberra SGS System

Source test conditions

To verify the accuracy of the spectral analysis of the different nuclides, the radioactive sources used were standard point sources: monoenergetic gamma ray nuclide Cs-137 ^[60] (7.86×10⁵ Bq) and multi-energy gamma-ray nuclide Eu-152 ^[61] (2.74×10⁶ Bq).

To obtain the spectrum of the radioactive source attenuated by different densities, the radioactive source was placed in a 200 L drum filled with different materials for measurement. The materials used in the drum were air (the empty drum), water (1 g/cm³), and sand (1.6 g/cm³).

To explore the influence of different nuclide libraries on the GV analysis results, multiple verification experiments were conducted on 200 L drums. The radioactive source, Cs-137, was placed at different positions in the drum, as shown in Fig. 2, and the drum was not filled with material. The time for each measurement was 10 min.

Fig. 2Full-screen View

Schematic diagram of the locations of the radioactive source

SGS experiment

The purpose of spectral analysis is to measure the activity of LILW. Therefore, a 200 L standard drum was employed. The material in the drum was water. Cs-137 was placed at radii of 0, 6.25, 11.25, 16.25, 21.25, and 26.25 cm, and the height was 42.5 cm (half the height of the drum). SGS ^[7,16] was used for activity reconstruction based on the SJTU-TGS system.

The same standard drum was used for activity reconstruction with the Canberra SGS System ^[25], as shown in Fig. 1(b). The aim of this study was to compare and analyze the activity measurement results of the two systems. The spectroscopy software in the Canberra SGS System is Genie 2000 ^[30], and the software for measurement activity is NDA2000 ^[62]. To control for the variables, the SJTU-TGS System adopts the SGS method described in NDA2000 (refer to Refs. ^[7] and ^[61]). The efficiency calibration method of the SJTU-TGS system adopts the method described by Qian ^[12], which meets the ASTM standards ^[63]. Because the material was water, this was an easy task for efficient calibration. It was assumed that any calibration method would provide relatively consistent results. During the gamma scanning, the drum was vertically divided into eight layers, and the lifetime of each layer was 1 min. Considering the dead time and moving time of the detector, the measurement time for a drum was approximately 10 min, which was within the measurement time range for 200 L drums in nuclear power plants. The only difference is that the SJTU-TGS System adopted the novel spectral analysis method proposed in this study. For the Canberra SGS System according to Genie 2000, its method was very close to GV, and thus it represented the traditional spectrum analysis method.

Spectra of monoenergetic gamma ray nuclides

The original spectra of the Cs-137 nuclide without attenuation and those attenuated by water and sand are shown in Fig. 3(a); the normalized spectra are shown in Fig. 3 (b). The Compton plateau in the attenuated spectrum is significantly higher than that in the unattenuated spectrum. Three spectra were analyzed using the proposed method. For comparison, GV was used to establish an accurate nuclide library and the nuclide analysis results were obtained. The spectral analysis results obtained using different methods are shown in Fig. 4, and the quantitative results are presented in Table 1.

Fig. 3Full-screen View

(Color online) (a) Original spectra of Cs-137 attenuated by different materials; (b) Normalized spectra of Cs-137 attenuated by different materials

Fig. 4Full-screen View

(Color online) Analysis results of the Cs-137 spectrum with different methods: (a)–(c) spectra attenuated by different materials (air, water, and sand). Left: Standard peak area of ROI; middle: GV; right: Novel method

As shown in Fig. 4, through the deconvolution process, the proposed method converted the number of full-energy peak channels into one channel, making it very easy to identify nuclides. The results in Table 1 indicate that because of the simple task of single-peak nuclide identification, the results were similar to those of GV, and the errors for both methods were less than 3%.

Spectra of multi-energy gamma ray nuclides

Because the nuclides in LILW generally emit multi-energy gamma rays, the Eu-152 spectrum was used for analysis and verification. The original spectrum of Eu-152 is shown in Fig. 5 (a). Gamma rays for eleven energies with the largest peak areas were selected for analysis. Because the energy resolution of HPGe is very good, the overall spectral lines appeared very clear. However, in the zoomed-in details, such as the 778.90 keV full-energy peak shown in Fig. 5 (a), the peak width was approximately 20 channels. The results of the spectral analysis using the novel method are shown in Fig. 5 (b). It can be observed that the gamma rays occupied only one channel, as seen in the zoomed-in details of the 778.90 keV full-energy peak. Thus, the accurate identification of nuclides could be realized.

Fig. 5Full-screen View

(a) Original spectrum of Eu-152; (b) Spectrum analysis results for Eu-152 with the novel method. The percentages represent gamma ray emission probabilities.

The results of the quantitative analysis of the novel method and GV are compared in Table 2. For the calculation errors of the full-energy peaks with different energies, the proposed method was more accurate, with a maximum error of 8.28%, whereas the maximum error of GV was 18.40%. This is because in the energy spectrum analysis process of GV, spectral smoothing is first performed, leading to some changes in the peak shape, and the peak area is calculated by fitting these peak shapes. Therefore for peaks with large statistical fluctuations, particularly those with relatively small peak areas, significant errors can be introduced during the smoothing and fitting processes. However, in the novel method, the full-energy peak is directly used to calculate the peak area during the process of deconvolution; thus, there is almost no significant deviation in the calculation of the peak area. From the perspective of the mean error (average error from all the peaks), GV has an error of 5.43%, whereas the novel method has an error of 3.89%.

Verification of the accuracy of the Monte Carlo simulation method

The types of nuclides in LILW are complex, and it is difficult to obtain different overlapping peaks experimentally to verify the spectral analysis method. Therefore, a Monte Carlo simulation was used in this study to simulate the process of measuring the radioactive source with an HPGe detector. A geometric model was constructed using the Geant4 tool ^[65,66]. According to the certificate of calibration (SRS number: 116230 and product code: 8403-GF-PNT) corresponding to the HPGe detector provided by ORTEC, the hybrid source (a point source in tape in a 2-inch aluminum ring) was placed horizontally 30 cm from the front end of the detector, and the detection efficiency curve was obtained experimentally. A comparison between the Monte Carlo simulation efficiency ^[67–70] and the experimental efficiency ^[71] is shown in Fig. 9(a). Except for the relative error of the full-energy peak efficiency at an extremely low energy (46.52 keV), which was 9.89%, all of other calculation errors were less than 5%.

Fig. 9Full-screen View

(Color online) (a) Comparison between the Monte Carlo simulation and experimental efficiencies; (b) Comparison of Cs-137 spectra with different methods

The Cs-137 spectrum experiment was conducted according to the measurement standard requirements of ANSI ^[72] and IEEE ^[73]. The collected full-energy peak count exceeded 20,000. The gamma count of the environmental background within the same measurement time was subtracted using the channel-by-channel method to obtain the net spectrum. A comparison between the normalized spectrum of the experiment and the Monte Carlo simulation is shown in Fig. 9(b). In addition to certain statistical fluctuations in the experimental spectrum, the full-energy peak and Compton plateau were in good agreement, verifying the accuracy of the Monte Carlo simulations.

Spectral analysis of key LILW nuclide overlapping peaks

Based on the key nuclide types of the LILW provided by the Qinshan Nuclear Power Plant and through the comparison and analysis of nuclides and their characteristic energies, three nuclides with the closest characteristic energies were selected: Sb-125 (601 keV), Sb-124 (603 keV), and Cs-134 (605 keV).

Different peak area ratios were set for the compositions of the three overlapping peaks. Because the overlapping peaks are difficult to decompose, it is easier to identify the nuclide as a full-energy peak located in the middle channel of the overlapping peaks. Therefore, if the peak area at the middle energy is lower than that on both sides, thus forming a weak peak, it is easier to elucidate the performance of the spectral analysis methods. Therefore, three overlapping peaks were set with peak area ratios of 5:1:10, 10:1:20, and 20:1:40 for 601, 603, and 605 keV, respectively. For overlapping peaks with larger area ratios, because the activity calculated with this weak peak does not contribute significantly to the total activity of LILW and does not affect its final disposal, it was not necessary to continue studying these cases. At the same time, to illustrate the difficulty of identifying overlapping peaks, the CWT with the strongest performance in the traditional peak searching method was used for comparison. The results of the spectral analysis are shown in Fig. 10, and the quantitative results are summarized in Table 4.

Fig. 10Full-screen View

(Color online) Analysis results of overlapping peaks with different peak area ratios: (a)–(c) represent peak area ratios of 5:1:10, 10:1:20, and 20:1:40, respectively. Left: original spectra; middle: spectral analysis results with the novel method; right: scalogram of CWT peak searching

As shown in Fig. 10(a), through the precise deconvolution process, the novel method decomposed the overlapping peaks into three incident spectra whose shape was a $\delta$ function, and the positions of the three full-energy peaks were accurately identified without energy deviation. The maximum area calculation error of the strong peak was –0.28%, and the error of the weak peak was 0.48%. CWT was used to analyze the overlapping peaks, and three full-energy peaks were observed in the scalogram. However, one weak peak was located in the middle of the overlapping peaks; therefore, the weak peak was more difficult to identify. As shown in Fig. 10(b), there was no energy deviation in the positioning of the three full-energy peaks. The area maximum calculation error for the strong peak was –0.28% at most, and that for the weak peak was 1.72%.

As shown in Fig. 10(c), under the condition of a peak area ratio of 20:1:40, by zooming in on the details in the original spectrum, because the area ratio of the three full-energy peaks was very different, it was determined that the 603 keV full-energy peak in the middle was completely covered by the high-energy peaks on both sides. The 603 keV full-energy peak was submerged. In the CWT scalogram, the weak peak at 603 keV could not be identified, and only two strong peaks at 601 and 605 keV could be identified. With the novel method, accurate nuclide identification could still be achieved for overlapping peaks in such extreme cases. The largest area calculation error for the strong peak was −0.3%, whereas that for the weak peak was 3.34%.

As shown in Fig. 10, for overlapping peaks under some extreme conditions, it was difficult for CWT to achieve an accurate nuclide analysis. CWT in the novel method was used to determine the positions of the overlapping peaks and perform subsequent peak width IAEA calculations. At this point, it did not matter which nuclides constituted the overlapping peaks.