Net Peak Area Research Articles

System optimization study of hybrid K-edge/XRF densitometer for uranium–plutonium solution measurement

In this paper, a comprehensive hybrid K-edge/XRF densitometer (HKED) device model is constructed using MCNP simulation. After the modeling process, a systematic simulation study is conducted to analyze the physical parameters and material selection of KED and XRF. The simulation results reveal that the optimal parameters for the X-ray tube are an X-ray source voltage of 160 kV and a 1 mm Fe filter. The sample should be placed in a vial with an inner diameter of 1.4 cm and an outer diameter of 2 cm. For the KED technique, the determined main parameters are a 1.9 cm Fe filter rod and an inner diameter of 0.08 cm for the collimator. For the XRF technique, the determined main parameters are a 0.01 cm Gd filter and an inner diameter of 0.3 cm for the collimator, with a detector angle of 150°. After selecting appropriate parameters, the average calibration factor Δμ of the KED technique was found to be 3.301 cm2 g−1, with a relative standard deviation (RSD) of 3.36%. Additionally, the comparison between the simulated and calculated values of uranium concentration revealed a minimum measurement error of 0.4%. The minimum detection concentration of KED for uranium solutions is approximately 1 g/L. For plutonium solutions ranging from 0.5 to 20 g/L, linear fitting of the Ka1 net peak area and plutonium concentration showed a coefficient of determination (R2) of 0.999. The detection limit of XRF for plutonium measurement was 2.33✕10−4 g/L. The linear fitting coefficients (R2) of uranium concentration versus K-edge transmission rate and plutonium concentration versus Ka1 net peak area for the hybrid technique in measuring uranium-plutonium mixed solutions are determined as 0.999 and 0.996, respectively, demonstrating the response relationship of the HKED device to uranium and plutonium under different concentrations.

Determination of uranium-enrichment from gamma-spectra by linear least-squares

The analysis of high resolution uranium spectra occasionally reveals inconsistent enrichment fractions too large to be explained by stochastic uncertainties. This is particularly noticeable for depleted and highly enriched samples. To clarify this, we use a linear combination of library spectra to model the Kα region between 88 keV and 101 keV. We find, that the inconsistencies are best explained by systematic errors regarding the continuum background, the width of the detector’s response function and the intensity ratio of the self fluorescence peaks. While the true shape of the background can only be approximated, a careful calibration of the detector’s response function and the correct intensity ratio of the Kα1 and Kα2 self fluorescence peaks can help to reduce systematic errors, especially those affecting the net peak area of the 235U peak at 93.352 keV.

INVESTIGATION OF GAMMA-RAYSATTENUATION IN METALLIC POWDERS USING GAMMA- GAMMACOINCIDENCE METHOD

Gamma-rays attenuation in metallic powders is investigated using coincidence technique with two 3ʺx3ʺ NaI(Tl) scintillation detectors. Na-22 source isused with 0.4µCi activity and resolving time registered was 6.7 ns. Linear attenuation coefficient (L.A.C) measurements were carried out at 511keV energy for Fe3O4 and ZrSiO4 metallic powders with uniform 100µm grains size and Fe sheets locally available (for comparison) with different thicknesses. The L.A.C values (in cm-1) calculated from direct spectra were 0.2705, 0.2641and 0.6239 for the materials respectively. The L.A.C values calculated from coincidence spectra using net peak area NPA were 0.2363, 0.2152 and 0.6231 and with using gross peak area GA were 0.2092, 0.1974 and 0.5261 respectively. The mass attenuation coefficient M.A.C (in cm²/g) for Fe sheets from direct spectra was 0.0792 and from coincidence spectra was 0.0791 and 0.0660 for NPA and GA respectively. The ratio of L.A.C from coincidence spectrum / L.A.C from direct spectrum were 0.7733, 0.7474 and 0.8432 using GA and 0.8735, 0.8148 and 0,9987 using NPA respectively.

Polarization effect of Schottky-barrier CdTe semiconductor detectors after electron irradiation

Spectrometric properties of cadmium telluride (CdTe) radiation semiconductor detectors with Schottky-barrier contacts were studied after irradiation with a high energy electron beam of 5 MeV-energy. The total cumulative dose of 2.25 kGy was delivered stepwise and the response of detectors to 241Am radioisotope source was acquired using a standard spectrometric chain at reverse bias voltages of 300 V, 400 V and 500 V. To evaluate the radiation damage, the spectral parameters of the 59.5 keV-photopeak were determined, namely the peak position, the full width at half maximum (FWHM), the peak amplitude and the net peak area. The time evolution of these parameters was followed by recording the spectra in 30-seconds (or 2-minutes) intervals after applying the reverse bias voltages. The results demonstrated significant effect of high energy electrons on the spectral characteristics even after applying the lowest dose of 0.5 kGy. The shift of the photopeak to lower energies, the increase of the FWHM and decrease of the peak height and area were confirmed. The time evolution of the observed tendencies disclosed that electron irradiation results in earlier onset of the polarization mechanism. After irradiating with the highest dose of 2.25 kGy, the polarization effect occurs practically immediately after applying the bias voltage.

Comparison of relative and k0 neutron activation analysis methods at MA-R1 TRIGA MARK II Research Reactor of CNESTEN (Morocco)

Since the installation of the TRIGA MARK II reactors in the National Centre for Nuclear Energy, Science and Technology (CNESTEN), Neutron Activation Data Analysis software (NADA) for neutron activation analysis (NAA) based on the relative method was the first software used; Over the years, the neutron activation analysis laboratory has been seeking to develop other softwares based on k0-INAA standardization namely the K0-IAEA software and the k0 software for Windows. In this paper we will focus on the comparison between the performance of k0 software for Windows and NADA. We compared the results obtained by the NADA Software and k0 for windows for the same input parameters (sample mass, nuclear data, net peak area for the same gamma line and cooling measurement times). In the neutron activation analysis laboratory of the National Center for Nuclear Energy, Science and Technology (CNESTEN) we analysed several reference materials (RM) or certified reference materials (CRM) and WEPAL samples. In this analysis, only certified or recommended values were used to compare the two processes for the different elements.

Marine radioisotope gamma-ray spectrum analysis method based on Geant4 simulation and MLP neural network

The monitoring of marine 137Cs using a scintillation detector relies on the spectrum analysis method to extract the 137Cs concentration. However, when in a poor statistics situation, the calculation result of the traditional net-peak-area (NPA) method has large uncertainty. In this paper, therefore, a new machine-learning-based method is presented to better analyze gamma-ray spectra with low 137Cs concentration. A multilayer perceptron (MLP) is applied to analyze the 662-keV full energy peak of 137Cs in seawater spectra; the MLP can be trained with a few measured background spectra by combining the simulated 137Cs spectra with measured background spectra. Thus, the time to prepare and measure standard samples for generating the training dataset can be saved. To validate the MLP-based method, Geant4 and background gamma-ray spectra measured by a seaborne monitoring device are used to generate an independent test dataset for testing the results obtained by the proposed MLP-based and traditional NPA methods. It is found that the MLP-based method achieves a root-mean-square error of 0.159, 2.3 times lower than that of the traditional NPA method, indicating that the MLP-based method improves the precision of 137Cs concentration calculations.

Localization of nuclear materials in large concrete radioactive waste packages using photofission delayed gamma rays

The characterization of radioactive waste packages is mandatory for their transport, interim storage and final disposal. In this framework, the Nuclear Measurement Laboratory of CEA DES IRESNE Institute, at Cadarache, France, uses a high-energy electron linear accelerator (LINAC) to produce an interrogating bremsstrahlung beam with endpoint energies ranging from 9 to 21 MeV to perform X-ray imaging and high-energy photon interrogation on large concrete packages. In particular, highenergy photon beam induces photofission reactions in both fissile (235U, 239Pu, 241Pu) and fertile (238U, 240Pu, 232Th, etc.) actinides possibly present in the radioactive waste. In order to assess their mass, we use delayed gamma rays emitted by their photofission products, which are measured with a 50 % relative efficiency High-Purity Germanium (HPGe) detector. Actinide differentiation, which is important for the fissile mass estimation, is based on the ratios of gamma rays emitted by different photofission products and requires appropriate corrections for the gamma attenuation in concrete. To this aim, we report here a localization method of point-like nuclear materials in the concrete matrix, based on the differential attenuation of several gamma rays emitted by a same photofission product. We use here the 1435.9 and 2639.6 keV lines of 138Cs, with both experimental data and MCNP numerical simulations to determine the (r,θ) coordinates of nuclear materials. Then, the depth inside the concrete matrix, which is determined with a precision of a few percent, mainly depending on counting statistics on 1435.9 and 2639.6 keV net peak areas, is used to correct for the different gamma ratios used in the actinide identification method. Experimental tests with uranium samples have been performed to validate the localization method.

Peak shape calibration of a Cadmium Zinc Telluride detector and its application for the determination of uranium enrichment

Cadmium Zinc Telluride (CZT) detectors are portable, room temperature serviceable, medium-resolution gamma-ray spectrometers. Their full-energy peak shape exhibits a low energy tail which complicates the analysis of spectra with overlapping peaks. In this paper, we determined the peak shape parameters of a CZT detector from measurements with calibrated point sources from 0.06 MeV up to 1.332 MeV. The peak shape parameters were obtained by applying a peak fitting algorithm that includes a Gaussian and a tail with energy dependent parameters in the region around the gamma-ray peak. The net peak areas were used to verify the absolute detection efficiency obtained with a Monte Carlo model of the CZT detector and the agreement in absolute terms was within 10% over the considered energy range. The peak fitting algorithm was then applied to determine the net peak areas of the full energy peak in spectra recorded with certified uranium standards. The enrichment was then determined by using the so-called ‘peak ratio’ method. We observed a systematic bias in the net peak areas of the 0.258 MeV gamma-ray which therefore was not included in the analysis. Hence, the enrichment was underestimated by about 10%.

Ratio of spectral averaged cross sections measured in standard 252Cf(sf) and 235U(nth,f) neutron fields

The results of systematic evaluations of spectrum averaged cross section (SACS) measurements in the fission neutron fields of 252Cf and 235U are presented. The data form a complete database of high-threshold experimental SACS measured in the same installation under the same conditions and using the same high purity germanium gamma spectrometer. This is crucial to reduce the uncertainty of the ratio and the data scattering and therefore, to minimize discrepancies compared to cross section measured under different conditions in different laboratories. This new dataset complements and extends earlier experimental evaluations. The total emission of the 252Cf neutron source during the experiments varied from 9.5E8 to 4.5E8 neutrons per second. The emission was derived in accordance to the data in the Certificate of Calibration involving absolute flux measurements in a manganese sulphate bath. Concerning 235U fission neutron field, the irradiations were carried out in a specifically designed core assembled in the zero power light water LR-0 reactor. This special core has a well described neutron field. After the irradiation, the low volume irradiated samples to be measured by gamma spectrometry were placed directly on the upper cap of a coaxial high purity germanium (HPGe) detector in a vertical configuration (ORTEC GEM35P4). High volume samples were homogenized and strewn into the Marinelli beaker. The HPGe detector is surrounded by the lead shielding box with a thin inner copper cladding and covered with rubber for suppression of background signal and bremsstrahlung. The experimental reaction rates were derived for irradiated samples from the Net Peak Areas (NPA) measured using the semiconductor HPGe detector. The measured reaction rates are used to derive the spectrum-averaged cross sections. Furthermore, measured reaction rates are also compared with MCNP6 calculations using various nuclear data libraries, in particular IRDFF evaluations.

Characteristic X-ray yields and cross sections of thick targets of Al, Ti, Zr, W and Au induced by keV-electron impact

In this paper, pure thick Al (Z = 13), Ti (Z = 22), Zr (Z = 40), W (Z = 74) and Au (Z = 79) targets are bombarded by electrons in an energy range of 5–27 keV, and the experimental thick-target characteristic X-ray yields of K-shell and L-shell, the X-ray production cross sections and the ionization cross sections of inner shells are presented. The present experimental setup and data processing are improved, specifically, a deflection magnet is installed in front of the X-ray detector to prevent the backscattered electron from entering into the X-ray detector, and the bremsstrahlung background spectra calculated from PENELOPE Monte Carlo simulations are used to deduce the net peak areas. The X-ray detector used in this experiment is the XR-100SDD manufactured by Amptek Inc. with a 25 mm<sup>2</sup> C2 ultra-thin window which can detect the low-energy x-rays down to boron Kα line (0.183 keV). Standard sources (<sup>55</sup>Fe, <sup>57</sup>Co, <sup>137</sup>Cs and <sup>241</sup>Am) with an activity accuracy range of 1%–3% (<i>k</i> = 2), supplied by the Physikalisch-Technische Bundesanstalt, Germany (PTB), are used to perform the detector’s efficiency calibration, and in a low-energy range (< 3.3 keV) the efficiency calibration is accomplished by measuring characteristic X-ray spectra produced by 20 keV electron impacting various thickness solid targets (i.e. by the characteristic peak method). The uncertainty of the detector’s efficiency calibration obtained in this paper is ~1.6%. The experimental thick-target characteristic X-ray yield data with an uncertainty of 1.7%–6.2% are compared with the PENELOPE Monte Carlo simulations, in which the inner-shell ionization cross sections are based on the distorted-wave Born approximation (DWBA) calculations, and they are in good agreement with a difference of less than or ~10%. According to the measured thick-target characteristic x-ray yields, the K-shell ionization cross sections for Al, Ti and Zr and the L-shell X-ray production cross sections for Zr, W and Au are also obtained with an uncertainty of 5%–8% (except for Al due to large K-shell fluorescence yield uncertainty), the difference between the experimental and theoretical data is also less than or ~10%. Moreover, by comparing the thick-target characteristic X-ray yields obtained from the analytical model and the PENELOPE Monte Carlo simulations at the electrons’ incident angles of 45° and 90°, it is found that the degree of agreement between the results from the analytical model and the Monte Carlo simulations at the incident angle of 90° is better than at the incident angle of 45°. Moreover, the contributions of the secondary electrons and bremsstrahlung photons to the characteristic X-ray yield are also given based on the PENELOPE Monte Carlo simulations. As for the elements studied in this paper, for the low ionization threshold energy, the contribution of the secondary electrons is ~2%, and however, for the high ionization threshold energy, the contribution is ~10%–20%. These contributions depend weakly on the energy of the incident electrons and show that these contributions are closely correlated with atomic number.

CONTAMINATION DEPTH OF 137CS IN CONCRETE STRUCTURES.

Uncertainty analysis for nondestructive estimation of contamination depth is presented. The contamination depth was determined using the peak-to-peak method as an in-situ measurement in which gamma spectra were measured by an HPGe detector. Since exponential activity distribution is a crucial assumption of this method, the distribution profile was confirmed by laboratory tests of core drill samples. The main parameter influencing uncertainty of contamination depth is uncertainty of relaxation length. The uncertainty is composed for statistical error represented by the ratio of net peak areas and systematic error given detection efficiency of measurement setup. Systematic relative error was evaluated to be 7.45%. Statistical relative error was evaluated to 9.97% for the proposed optimum net peak area. Variability of relaxation length was identified to be very low with mean value 2mm with standard deviation 0.73mm. For fixed relaxation length, it should be possible to estimate contamination depth by nonspectrometric devices.

Performance assessment of a 500 mm3 CZT and a 2x2 inch LaBr3(Ce) detectors for the determination of the uranium enrichment using the enrichment-meter method and calibration standards for safeguards applications

Determination of the uranium enrichment is an important safeguards verification task, routinely carried out using non-destructive assay methods. The enrichment-meter method is one of the most widely used passive non-destructive X- and gamma-ray based methods used for such tasks. Among its advantages is the highly constrained physical nature of its underlying formalism, allowing it to be used with high-resolution HPGe detectors, as well as with low-resolution NaI detectors. Due to attractive features and spectroscopic performance, CdZnTe and LaBr3(Ce) detectors raised interest in their application to such tasks as well. However, their spectroscopic performance is different to that of the traditional detectors in many ways. Application of the enrichment-meter method requires determination of the net peak areas corresponding to 235U signature photopeaks. The latter requires an adequate algorithm to select the region-of-interest boundaries, which may be sensitive to asymmetrical photopeaks of CZT detectors. In this paper we conduct a performance assessment of a 500 mm3 CZT detector of a quasi-hemispherical design and a 2 × 2 inch LaBr3(Ce) scintillator with the enrichment-meter method using a set of certified uranium standards with enrichment degrees from 0.31% to 4.46% of 235U atomic abundance. We investigate the impact of different methods used for net peak area determination, statistical quality of acquired spectra and size of region-of-interest boundaries on accuracy and uncertainty. We propose an algorithm for symmetrical/asymmetrical region-of-interest boundaries determination and make recommendations on the best combinations of the region-of-interest size and method used for the net peak area determination for each of the detectors. The underlying routines of the algorithm and analysis procedures are described in detail and results are presented.

γ-Ray spectral analysis method for real-time detection of fuel element failure

Monitoring of fuel element failure in a nuclear reactor is an important process to ensure safe operation of the nuclear reactor. It is feasible to detect fuel element rupture by analysing the radionuclides of fission products and activation products in the primary coolant. To identify the radionuclides in the primary coolant, the most convenient method to measure their activity concentrations is γ-ray spectrometry. A γ-ray spectral analysis method for real-time detection of fuel element failure is proposed in this paper. The method aims to implement a Gaussian smoothing processing for spectral data, extract peaks of spectral data through mathematical morphological transformation, determine left and right peak boundaries with a gradient descent algorithm and finally estimate net peak area with an image method. The method can rapidly recognize a designated key radionuclide from an obtained spectrum and extract peak information to meet the demands of real-time monitoring of fuel element failure in pressurized water reactors.

Investigation of 127I(n,2n)126I and 23Na(n,2n)22Na Reactions Using 252Cf Neutron Source

This work deals with 23Na(n,2n)22Na and 127I(n,2n)126I reactions in the 252Cf spontaneous fission neutron source. 252Cf neutron source with approximate emission of 6·× 108 n/s was employed for the irradiation of sodium iodide. The spectrum-averaged cross sections (SACS) were then inferred from experimentally determined reaction rates and compared with calculations in MCNP6 using various nuclear data libraries. The experimental reaction rates were derived from the net peak areas (NPAs) measured using the high purity germanium spectroscopy. The measured SACS for the 23Na(n,2n)22Na reaction in the 252Cf spectrum was determined as equal to (8.98±0.32)·× 10−6 b. The resulting SACS for the 127I(n,2n)126I reaction in the 252Cf spectrum was derived as (2.044±0.0072)·× 10−3 b. These experimental data can be used for nuclear data libraries validation and to specify high energy tail of the 252Cf neutron spectrum.

Determination of the uranium enrichment without calibration standards using a 500 mm3 CdZnTe room temperature detector with a hybrid methodology based on peak ratios method and Monte Carlo counting efficiency simulations

Room temperature semiconductor detectors of CdZnTe type have been proposed as possible alternatives to spectrometers based on HPGe and NaI detectors. Attractive spectroscopic performance and portability, as well as continuous improvements in their design and availability in different sizes make them especially competitive in various radiation measurement applications where absence of cooling, small size and significantly better resolution compared to other room temperature detectors are an asset. Among these applications are nuclear safeguards that include uranium and plutonium isotopic composition determination tasks. This paper focuses on the investigation of possibilities and limits of a net peak area based methodology used for the determination of the uranium enrichment without use of calibration standards. Tests are conducted on a room temperature medium resolution spectrometer based on a 500 mm3 CdZnTe sensor of a quasi-hemispherical design using which spectra of different statistical quality are obtained from certified uranium standards. Gamma-ray peaks in the 143–1001 keV energy range are used as uranium gamma-ray signatures. Performance assessment of an intrinsic calibration of the counting efficiency curve is conducted. A hybrid methodology based on a combination of the peak ratios method with Monte Carlo simulations of the counting efficiency curve is proposed for poor quality spectra. Implemented algorithms and analysis routines are described in detail and presented.

Determination of the uranium enrichment without calibration standards using a 2 × 2 inch LaBr3(Ce) room temperature detector and Monte Carlo sampling approach for uncertainty assessment

In recent years room temperature medium resolution scintillation devices, such as LaBr3(Ce), have attracted much interest as possible alternatives to traditional spectrometers based on HPGe and NaI detectors, for the determination of the uranium enrichment in safeguards applications. This paper focuses on the investigation of possibilities and limits of a net peak area based methodology used for the determination of the uranium enrichment without use of calibration standards and introduces the isotopic code MCSIGMA for LaBr3(Ce) scintillators. Tests are conducted with a room temperature, medium resolution spectrometer based on a 2×2 inch LaBr3(Ce) scintillator using which spectra of different statistical quality are obtained from certified uranium standards. Gamma peaks in the 143-1001keV energy range are used as uranium gamma-ray signatures. Results indicate a promising performance of the applied methodology with a room temperature medium resolution scintillator of the LaBr3(Ce) type, however at a cost of significantly higher uncertainty budget on the derived enrichment compared to HPGe, especially for natural and depleted uranium samples. This uncertainty budget is primarily influenced by the statistical quality of the measured spectra. Implemented algorithms and analysis routines are described in detail and presented.

Step-approximation SNIP background-elimination algorithm for HPGe gamma spectra

A step-approximation, statistics-sensitive nonlinear iterative peak-clipping background elimination algorithm with a clipping window adaptive to the full width at half-maximum is proposed. The calibration of the full width at half maximum was expressed as a square root of a quadratic function of energy. The relative differences of the background areas under a peak in successive iteration steps were used as the condition to end the iteration. The background area under a peak is calculated as a weighted sum of the background under the peak and the background in the immediate vicinity of the peak, obtained by the clipping method. The weights are given by the background under the peak and the number of counts in the original spectrum. The proposed algorithm was applied in 152Eu and 137Cs gamma spectra measured with a high-purity-germanium spectrometer. After background subtraction, the net peak area can be obtained from the net spectrum. It can be universally used for the gamma spectra given by a fixed detector, as long as the full width at half-maximum has been calibrated.

Validation of differential cross sections by means of 252Cf spectral averaged cross sections

The results of systematic evaluations of the spectrum-averaged cross section measurements performed in the spontaneous fission 252Cf neutron field are presented. The Following threshold reactions were investigated: 23Na(n,2n)22Na, 54Fe(n,p)54Mn, 54Fe(n,α) 51Cr, 27Al(n,p)27Mg, 27Al(n,α)24Na, 19F(n,2n)18F, 90Zr(n,2n)89Zr and 89Y(n,2n)88Y. The spectrum-averaged cross sections for 23Na(n,2n)22Na, 54Fe(n,α)51Cr and 89Y(n,2n)88Y reactions were measured for the first time. This quantity is compared with calculations carried with the IRDFF-v1.05 library. There is a notable disagreement exceeding uncertainties only for 54Fe(n,p)54Mn and 54Fe(n,α) 51Cr reactions. The spectrum-averaged cross sections were inferred from experimentally determined reaction rates. The experimental reaction rates were derived for irradiated samples from the Net Peak Areas measured using the semiconductor high purity germanium spectroscopy. The presented experimental data can be used to validate nuclear data libraries and reactions used in the practical reactor dosimetry and to specify high energy tail of the 252Cf neutron spectrum.

Detection limit calculations for peak evaluation methods in HPGe gamma-ray spectrometry according to ISO 11929

Two peak area estimation methods in gamma-ray spectrometry, the total peak area (TPA) and the background step function (BSF) methods are re-considered first. For least-squares (LS) peak fitting then, a new net peak area uncertainty model is established. It results in a new function fB replacing a TPA method internal design factor. This allows applying the TPA-related decision threshold (DT) and detection limit (DL) formulae, based on ISO 11929(2010), also for peak fitting. Linear LS adapted to Poisson counting data is suggested to derive fB values for a single peak and different combinations of background shape components including a fitted BSF. fB is then adapted to penalized non-linear fitting including Poisson maximum likelihood estimation by MC simulations. Within the DL iteration the fB method is much faster than with non-linear re-fitting. The fitted peak area uncertainty can be safely modeled for peak areas up to 10 DT which is sufficient for DL calculations. The extension for peak multiplets is indicated.

Applying ISO 11929:2010 Standard to detection limit calculation in least-squares based multi-nuclide gamma-ray spectrum evaluation

The concepts of ISO 11929 (2010) are applied to evaluation of radionuclide activities from more complex multi-nuclide gamma-ray spectra. From net peak areas estimated by peak fitting, activities and their standard uncertainties are calculated by weighted linear least-squares method with an additional step, where uncertainties of the design matrix elements are taken into account. A numerical treatment of the standard's uncertainty function, based on ISO 11929 Annex C.5, leads to a procedure for deriving decision threshold and detection limit values. The methods shown allow resolving interferences between radionuclide activities also in case of calculating detection limits where they can improve the latter by including more than one gamma line per radionuclide. The co"mmon single nuclide weighted mean is extended to an interference-corrected (generalized) weighted mean, which, combined with the least-squares method, allows faster detection limit calculations. In addition, a new grouped uncertainty budget was inferred, which for each radionuclide gives uncertainty budgets from seven main variables, such as net count rates, peak efficiencies, gamma emission intensities and others; grouping refers to summation over lists of peaks per radionuclide.