In-toto non-destructive assay methodology for the elimination of metallic waste from particle accelerators after melting

The operation of high-energy particle accelerators like the ones at CERN can lead to the unavoidable production of radioactive material via well-known activation mechanisms. The activation is the result of the interaction of the primary beam or the shower of the secondary particles with the surrounding matter. Consequently, the maintenance, upgrade, and dismantling activities lead to the production of radioactive waste. Prior to the disposal of such waste at dedicated repositories, a radiological characterization is required. At CERN, the radioactive waste is disposed of via the authorized elimination pathways at the Host State’s (France and Switzerland) final repositories. This paper proposes a new non-destructive assay methodology to radiologically characterize ferrous, solid metallic waste that can be classified as low-and intermediate-level (LILW) primary waste before melting. The latter will be dis-patched to the melting facility to be transformed into homogeneous ingots and other melting process-related waste, such as slag. The radiological characterization of LILW primary waste has the purpose to establish the radionuclide inventory and the associated activity values of the candidate waste items. These waste items are often subjected to significant activity heterogeneity due to the activation mechanisms and waste packaging. The quantification of the gamma emitters is commonly carried out by gamma spectrometry assuming homogeneous activity distribution within the waste item. This assumption can be burdened by important uncertainties of the measured activities. In order to estimate the uncertainty introduced by this assumption, a new pragmatic non-destructive assay technique is developed using the geometry model optimization technique. Additionally, the new operational methodology to predict the activity of the major gamma emitter based on the average dose rate measurements for LILW waste produced at CERN is proposed. This methodology allows the optimization of the radioactive waste packaging step by considering the radiation protection dose optimization, and limitation objectives and ensuring meeting the requirements of the melting facility. The results of the new methodology applied to the primary waste have been validated with a sampling analysis of the waste after melting.


Introduction
CERN's accelerator complex uses a variety of particle types and energies. It is characterized by a wide range of different radiation fields, that can induce radioactivity in the machine components and surrounding material. If the activated material cannot be reused or recycled, it needs to be disposed of in dedicated final repositories. The radioactive waste produced at CERN is disposed of in France or Switzerland in accordance with the existing elimination pathways following the tripartite agreement between CERN, France and Switzerland (Host States) [1].
In the present paper, we introduce a new characterization methodology that allows the safe disposal of legacy low-and intermediate-level (LILW) waste produced at CERN after melting. Melting of metallic radioactive waste offers a number of advantages: volume reduction, immobilization of contamination (if present) and radioactivity homogenization. The radiological characterization process relies on extensive Monte Carlo and analytical calculations in order to perform the preliminary radiological inventory predictions for solid metallic waste items.
The radiological characterization presents several challenges. Items of waste that are candidates for elimination as LILW present contact dose-rate levels up to 1 mSv/h, a radiation level which is challenging in terms of operational radiation protection during the phases of handling and measurements. In addition, these waste items often exhibit highly heterogeneous activity distributions. Hence, it can be difficult to obtain accurate results from in-toto gamma spectrometry (GS), especially if the analyses are performed under the simplistic assumption that the activity distribution is uniform. In order to overcome such difficulties, we propose a novel Non-Destructive Assay (NDA) technique that estimates and reduces the uncertainties introduced by this assumption. We use geometry model optimization to quantify the expected activity concentration values to the best of our knowledge using multi-line and multi-count consistency constraints as described in the rest of this paper. Section 2 gives a general overview of the primary radioactive waste candidates for disposal after melting. In Section 3, we describe the new operational methodology to predict the activity concentration of the main gamma emitter (Co-60), as well as the new NDA technique using the optimization approach. Additionally, the experimental validation of the activity values before and after melting is presented.

LILW Radioactive waste at CERN
During the operation of the accelerators, particles interact with matter, which might lead to the activation of the CERN machine components and surrounding material. Induced radioactivity is caused either by direct interaction of the primary beam or by the shower of the secondary particles with matter. Induced radioactivity depends on the type of accelerator, for instance, energy and its irradiation condition including the location of the beam losses, irradiation and decay times, and material elemental composition. Hence, during the dismantling, maintenance or upgrade operations of the particle accelerator, some of the components need to be removed and require radiological characterization prior to their disposal as radioactive waste. Radioactive waste generated at the CERN accelerator complex is temporarily stored at the Radioactive Waste Treatment Centre and Storage (RWTCS) located in the former Intersecting Storage Ring (ISR) tunnel.
A procedure to radiologically characterize LILW waste produced at CERN is developed with accordance to the French National Agency for Radioactive Waste Management (ANDRA). For proper classification and definition of the elimination pathway of the radioactive waste, the radiological characterization needs to be performed. The radiological characterization process consists of a sequence of radiation measurements complemented by analytical calculations. The purpose is to identify the radionuclides present inside the waste package and evaluate their activity concentrations respectively. A significant amount of the radioactive waste collected from the different operations (e.g. dismantling, maintenance) are metallic components, consisting primarily of steel, copper and aluminium. In this paper, we propose a radiological characterization methodology tailored for LILW waste from particle accelerators for disposal after melting. The waste that will be shipped to the melting facility has to consist of stainless steel, black steel or cast iron and galvanized steel. Waste will be packed in containers of 2.7 m 3 or 4 m 3 , or unitary pieces that would fit in a 20-feet container. The waste selection process starts with the so-called pre-selection phase. In this step, one segregates the waste based on the dose rate criteria and verifies which waste could be subjected to further processing. Hence, the waste with the maximum dose at contact between 10 µSv/h and 1 mSv/h is classified as LILW waste candidate. Subsequently, this waste is measured using a non-destructive X-ray fluorescence (XRF) technique in order to determine the elemental composition. Consequently, the waste consisting of stainless steel, cast iron etc. can be grouped and pre-packaged in containers of 2.7 m 3 or 4 m 3 . The LILW waste which is covered by the present study complies with the acceptance criteria of the melting facility, such as: -The dose rate of the unitary items is lower than 2 mSv/h at contact; -The loose surface contamination is < 4 Bq/cm 2 for gamma and beta emitters and < 0. 4 Bq/cm 2 for alpha emitters; -The maximum activity of gamma and beta emitters is 20 kBq/g.
The examples of the LILW waste candidates for melting are shown in Figure 1. Figure 1: Examples of the LILW waste candidates for melting. The apparent density of the waste spans between 0.08 g/cm 3 and 7 g/cm 3 and the masses range from 20 kg to 2700 kg. The maximum dose rate is set to 1 mSv/h at contact due to optimization objectives following the ALARA principle [2] as well the acceptance criteria of the disposal facilities.

Primary waste elimination process
This section presents an overview of the primary waste elimination process developed at CERN for LILW, ferrous, solid, and metallic waste that will be subjected to melting prior to the final disposal. First, the selection step defines an operational method that can estimate the total betagamma specific activities of pre-selected waste items. This method is deployed in order to minimize the number of gamma spectrometry (GS) measurements of the pre-selected items, by further reducing the probability of producing waste packages that do not meet the melting facility acceptance criteria.
After the selection phase, the waste is analyzed by GS prior to its elimination. This step corresponds to the NDA measurements carried out in the GS facility at RWTCS. During the GS analysis, we consider both uniform activity distribution and geometry optimization techniques. We qualify the GS results of LILW waste in order to quantify the impact of assuming uniform activity distribution of the gamma emitters within the waste [3]. For full peak efficiency calculations, we use ISOCS (In Situ Object Counting System) [4] and ISOCS Uncertainty Estimator (IUE) [5] from Mirion Technologies (Canberra). In addition, we use an in-house developed tool Geometry Uncertainty Reduction Utility (GURU) Data Analyzer framework [6] that offers a capability, based on a methodology to identify the best geometry models, to describe the "actual" geometry in terms of activity distribution.
Finally, a validation step is carried out between the average activity values from gamma spectrometry (AVG-GS) and geometry optimization results.

Waste selection Phase
The evaluation of the radionuclide activity concentrations is a crucial step of the radiological characterization. Section 3.1 describes the new operational methodology to predict the activity concentration of the main gamma emitter (Co-60), and consequently the total beta-gamma specific activity by applying the SF approach [7]. This methodology is valid for solid metallic LILW waste generated at CERN under the assumption that Co-60 is the dominant gamma emitter that contributes to the dose rate in the waste item, where the decay time is more than 3 years. The choice of the minimum decay time is dictated to allow the decay of radionuclides other than Co-60. This preliminary prediction of the total beta-gamma activity values is implemented in the pre-packaging phase of the radioactive waste in an operationally efficient manner, taking into account the radiation protection dose optimization objectives following the ALARA principle and the acceptance criteria of the melting facility. The methodology is based on the average dose rate measurements of the ferrous LILW waste generated at CERN. In order to convert the average dose rates of the waste items into Co-60 activities, two approaches are investigated. The first approach is based on the experimental correlation between the ratio of the specific activity of Co-60 and the average dose rate as a function of the apparent density of the waste item. The other approach focuses on accurate geometry modelling of the waste item using a radiation protection code MERCURAD from Mirion Technologies (Canberra).

Measured average dose rate (AVG-DR) and Co-60 activity correlation
This methodology allows the estimation of the total beta-gamma specific activity concentrations of pre-selected waste based on the measured average dose rate and apparent density. In order to establish the correlation between the specific activity and average dose rate at 40 cm, we measure 35 individual representative waste items prior to their conditioning into output waste packages, for a large range of the apparent density values and dose rate levels. All items were measured using GS. The acquisition and analyses are carried out by High Purity Germanium detector (Falcon 5000 HPGe 1 ) in a dedicated area where the background dose rate varies between 0.07 and 0.1 µSv/h (see Figure 2). During the acquisition, the waste-to-detector distance is selected to have a maximum allowed dead time less than 15 % for all measured waste items. We distinguish several shapes for which the acquisition live time varies from 10'000 to 72'000 seconds. The dose rate measurements are carried out using Dose Rate Meter 6150AD 6/H 2 with the range from 0.1 µSv/h to 10 mSv/h and energy range from 60 keV to 1.3 MeV. For waste items, which present a magnetic field, we use the RadEye 3 device from ThermoFisher Scientific that was tested in the presence of the magnetic field strengths up to 300 mT. The dose rates are measured using multiple points around the waste at contact, 10 cm and 40 cm and scanning (only for 6150AD 6/H device), while the apparent density is estimated by taking the ratio of the mass and apparent envelope volume of the waste.  For each AVG-DR measurement distance, we produce a curve of the ratio between the Co-60 specific activity and the AVG-DR at 40 cm as a function of the apparent density as shown in Figure 3. A fit is performed for each data set to produce a penalizing fit function at the 50% confidence level. Figure 3: The ratio of the specific activity of Co-60 and AVG-DR at contact as a function of the apparent density. The data points represent the measurements (GS and dose rate mapping) for hollow (e.g. pipes), ion pumps, containers and other waste items considered as LILW waste candidates.The fit (red line) is ActivityCo-60/Avg Dose rate= 5.07/Apparent density+12.31, R 2 =0.92. The penalizing fit (blue line) is ActivityCo-60/Avg Dose rate= 5.26/Apparent den-sity+17.31, R 2 =1. This method allows for defining a function that correlates the ratio of Co-60 activity to AVG-DR and the apparent density. Considering radiation protection dose optimization objectives and the inherent averaging properties of far dose rate measurements, we recommend implementing the selection criterion methodology that is based on the 40 cm distance. The curves produces for the ratio between the Co-60 specific activity and the AVG-DR at contact and 10 cm can be found in Appendix A.
3.1.2 Computed average dose rate (AVG-DR) and Co-60 activity correlation MERCURAD 4 is a radiation protection code developed by Mirion Technologies (Canberra), dedicated to the calculation of the gamma dose equivalent rate. It is based on the Mercure-6 [8] Kernel (developed by CEA -French Atomic Energy and Alternative Energies Commission). It uses the ray tracing method, with buildup factors. It also uses dose equivalent rate albedos to calculate the dose equivalent rate due to the wall diffusion effect as well as double differential albedos to calculate the dose equivalent rate after reflection of gamma by a wall and attenuation by screens. MERCURAD allows the modelling of complex geometries including hollow objects such as pipes and ion pumps. This functionality turns out to be vital for the purpose of this study to calculate dose rates as close as possible to the measured values. To compute the dose equivalent rate, the MERCURAD sensors are set at 40 cm from the modelled waste items, as presented in Figure 4. MERCURAD allows calculating the dose rate response for a source term corresponding to 1 Bq/g allowing us to convert a measured dose rate into an equivalent specific activity of Co-60 in our case. In the following paragraph, we present the results obtained from the geometry modelling using radiation protection and radiation transport code MERCURAD. The AVG-DR measurements performed in the previous section could be used to estimate a Co-60 activity value for each individual item as described in the methodology above. The results show that the ratio of the estimated Co-60 activities, using MERCURAD to the GS results, is consistent with unity in most of the cases. In some cases, we noticed that the MERCURAD results are within 50% of the expected activity value given by GS. Additional estimations of the Co-60 activities based on MERCURAD and the AVG-DR measurements at contact and 10 cm to the GS results can be found in Appendix B.

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Radiological analysis of waste packages and unitary items
The developed methodology is validated using in-toto GS measurements of both the individual waste items, as well as the waste packages containing the items. The quantification of the gamma emitters (ETM) is performed by GS, under the assumption of homogeneous activity distribution within the item. However, due to the activation mechanisms, some waste can have heterogeneous activation patterns. In this Section, we describe the qualification of GS measurements of LILW waste in order to quantify the impact of assuming the homogenous distribution of activity. The qualification is a process used to assess the capacity of a model to predict physical quantities within a set of assumptions. First, Section 3.2.1 briefly describes the measurement conditions that relate to both the acquisition and analysis parts of the in-toto GS of LILW waste. Subsequently, we present the geometry optimization technique in order to improve the accuracy of the activity values, see Section 3.2.2.
Finally, Section 3.2.3 focuses on the qualification of GS, including the characteristics of the assayed LILW waste, the impact of the various geometries on the efficiency calibrations, and geometry optimization activity results.

Gamma spectrometry setup
GS is a commonly deployed technique at CERN to quantify the residual activity of gamma emitters in various items, ranging from small-volume samples in a laboratory to large items such as unitary blocks or waste containers. GS measurements on LILW items present several challenges during both the acquisition and the analysis steps. The former challenges relate to the high counting rate effects, the long counting time required to meet the Minimum Detectable Activity (MDA) requirements, available physical space, and the necessity to count from multiple faces. The latter challenges are due to the difficulty to model the geometry and combine the multiple counts' results. A significant parameter of the acquisition step is the system dead time. In order to avoid the spectrum distortions, we seek to limit the dead time value up to ∼ 15% nominally. However, the dead time could be higher, as indicated in Figure 6 where the dead time reached 19% due to insufficient space around the waste item. Figure 6: GS setup for in-toto measurement and analysis for ILIW waste package (4 m 3 container) candidate for melting. The measurement distance detector-waste is 1.9 m resulting in a dead time of 19 %. The average dose rate at contact is 98 µSv/h, and the maximum dose rate is 260 µSv/h. Additionally, the acquisition time and the geometry need to be set in such a way to ensure that the MDA values are below the LILW waste declaration thresholds [9,10] for the expected ETM radionuclides.
In order to analyze the output waste package one has to generate the ISOCS reference efficiency calibration curve. The necessary geometry parameters of the reference model implemented in the ISOCS software are shown in Figure 7.

Geometry optimization
When GS measurements are performed on waste items, the knowledge of the geometry model parameters, including dimensions, position with respect to the detector, material composition, 9 This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4487049 P r e p r i n t n o t p e e r r e v i e w e d and activity distribution (hotspots) is often limited, especially for the two last parameters. The uncertainties related to activity distribution are described in [11]. Additionally, [12] focuses on the uncertainties that correspond to dimensions, material composition etc. The ISOCS tool allows the computation of the full energy peak efficiencies for each waste item (or sample) in order to estimate the activity values of the waste without using radioactive source standards at the laboratory. The associated uncertainties of the ISOCS efficiency values take into account only the uncertainties due to the numerical approximations, peak area statistics and emission intensity values. However, performing the GS analysis, the ETM radionuclides are quantified under the assumption of homogeneous distributions of activity within a measured waste. This assumption might lead to underestimating the activity values of the identified ETM. In order to determine the uncertainties of the measured activities, due to waste geometry parameters, such as dimensions and heterogeneous source distribution we use the tool GURU. This tool consists of two modules. One quantifies the geometry model uncertainties and the other reduces them by combining the GS results in order to identify the best estimate model that best describes the "actual" geometry of the waste. By varying the geometry parameters, a set of perturbed efficiency calibration curves is produced. These curves are used to evaluate activity results as a function of the geometry parameters. In order to perform an optimization (i.e. determine the best geometry models), the following constraints should be fulfilled [4]: multi-count consistency is the requirement that multiple GS measurements carried out at different locations should give the same value of the measured activity of the item. Additionally, the calculated activity values for each emission line of a radionuclide should be consistent. Knowing the activity values from each detector count for a reference model, we can correct these activities by the ratio of efficiencies as shown in Equation 1.
A k i (j) is the calculated activity for the radiocuclide with emission j using model i for the face k. Using Equation 1 a set of activities can be calculated for each radionuclide emission, in each model and detector. Then using the line and count consistencies, we match the activities between the different detectors. To this end, we construct a Figure Of Merit (FOM) as follows for each gamma emission j and model i: Where, A k i (j) is the activity of the radionuclide with associated gamma emission j using model i for face k. < A i (j) > is the average over K faces for emission j using model i, which is K . The user needs to select the gamma lines of interest, among the ones identified in all faces of the GS measurement results. Then, one can calculate a Rank (as given in Equation 3) for each gamma emission line and model by summing the sub-ranks (subRank j i ) according to the FOM value. Namely, the sub-rank subRank j i is obtained by ranking the F OM i (j). Hence for all models n, the best model for each gamma emission line is assigned to a sub-rank # 1, the second best to # 2, etc.
Where J is the number of common gamma emission lines formed for each face. The model with the minimum Rank i is considered as the best model.

Validation of AVG-GS and geometry optimization results for waste packages
The determination of the geometry modelling parameters in the GS analysis can be difficult because they are not well known and some geometries are complex to model. The waste may have a heterogeneous activity distribution due to the activation mechanisms, self-attenuation or density variation. This Section demonstrates the application of the developed radiological characterization methodology, giving several examples of waste packages prepared for elimination via melting. It summarizes the estimation of the ETM activities in the waste package and associated uncertainties. The qualification of the GS results is presented in order to quantify the impact of assuming uniform activity distribution of the gamma emitters within the waste.
The main acquisition parameters for the waste packages can be found in Table 1. For each GS acquisition of each face (or count) of the primary waste package, we produce a set of efficiency calibration curves, applying the "Complex Box" ISOCS geometry template. Additionally, for each face, we consider a uniform source distribution in the material matrix. For each face, activity values are determined using Genie 2000 Nuclide Identification with the Interference Correction calculation engine from Mirion Technologies (Canberra). The multicount activity ratios of the reference geometry models are presented in Tables 2-6. Additionally, we present the activity concentration of Co-60 obtained from the operational tool that allows quantifying the specific activities of Co-60 for various unitary waste.
The Co-60 activity concentration of the applied operational methodology for unitary items and GS measurements of the output waste package ranges between a factor of 1.4 and 3. Tables 2-6 present the multi-count activity differences of the reference geometry models respectively. It needs to be noted that in this study the activities of Ti-44 and Sc-44 radionuclides are estimated independently, not taking into account that they are in secular equilibrium Sc-44<Ti-44.       After geometry optimization, the activity ratios should converge to unity, which means that the activity values of two opposite faces are consistent. The GURU framework enables varying the relative source concentrations of the hot spots (referred to as the contrast). The contrast value is estimated as the ratio of the highest and lowest activities between two opposite faces assuming the uniform activity source distribution. The optimization process was performed over two faces at a time. The contrasts parameter varied from 1 to 10, from 1 to 100 or from 1 to 150, which depended on the heterogeneity of the assay waste package. The activity ratios of the two opposite faces from the GS measurements with a uniform activity source distribution (reference models) are shown in Figures 8-12.      Additionally, Co-57 was measured above the MDA value with the uncertainty quoted at 1 σ, however, it is not considered in the optimization process.
It is noted that after the optimization, the activity ratio becomes very close to unity, hence showing the usefulness and effectiveness of the methodology.
The optimization calculations are performed over two opposite faces at a time. We opt for averaging the activity results given for each pair of faces. The activity uncertainty of the average value is calculated as the square root of the quadratic sum of uncertainties corresponding to a single face. In the following Tables 7-11, the average activity values of the reference and optimized models over two and four opposite faces for a given waste package are presented.

Validation of AVG-GS and geometry optimization results for unitary items
In parallel to the validation of the AVG-GS for waste packages, one performs the geometry optimization for unitary items that will not be packaged in the chosen waste packages due to their sizes. The main acquisition parameters for the four unitary pieces are presented in Table  12. Acquisition live time (s) 900 1800 The list of identified radionuclides with the associated activity values of the reference models is presented in Table 13. The optimization process was performed over two faces at a time. The contrasts parameter varies from 1 to 10 and 1 to 50 depending on the heterogeneity of the assay unitary waste item. Figures 13-15 present the activity ratios of the two opposite faces of the gamma spectrometry measurements with a uniform activity source distribution referred to as the reference model and the optimized model.    The optimization process has been performed for unitary items intended for melting. The calculations show that for optimized models the activity ratio of two opposite faces is close to unity.
The following Tables 14-16 combine the average activity values of the reference and optimized models over two, and four opposite faces if applicable for unitary items as presented.

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Validation of AVG-GS results after melting
Section 3.2.5 presents the quantification of the radionuclide activity values before and after melting. Melting of metallic radioactive waste offers several advantages, such as volume reduction and radioactivity homogenization. The primary waste was shipped to the melting facility and transformed into three ingots. Two samples were taken from each ingot, which resulted in total of six samples after melting. The objective of this Section is to compare the activity values of the waste package/unitary items subjected to melting and the samples from the produced ingots in a melting process. Figure  16 shows the melting process including the fusion of the primary waste and the extraction of the samples.

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This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4487049 P r e p r i n t n o t p e e r r e v i e w e d  The activity values of the six samples extracted after melting are given in Table 17.  Table 18 presents the AVG-GS activity values for selected radionuclides before and after melting primary waste. The Co-60 activity values are consistent before and after melting since Co-60 was present in all waste packages and unitary items. Contrary to Co-60, the other radionuclides have not been identified in all waste packages and unitary items. Hence, the corresponding activities averaged over the total mass could deviate from the values after melting. Table 18: Average activity values in Bq/g with uncertainties given at 1 σ of the primary waste before and after melting. The uncertainties do not include geometry parameter uncertainties, such as activity distribution, dimensions, and densities. These uncertainties can be of the order of 50 % [3]. This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4487049 P r e p r i n t n o t p e e r r e v i e w e d

Conclusions
The activity values of the ETM radionuclides are evaluated via a qualified NDA technique, based on gamma spectrometry. The technique presents several challenges related to the accurate determination of the geometry modelling parameters, such as the activity distribution. Hence, the impact of the homogeneous activity distribution assumption within the primary waste (waste package) is investigated using the concept of geometry optimization methodology. The geometry optimization results allow establishing the optimized geometry models. It is achieved by constructing the FOMs that rely on the multi-count and multi-line activity consistencies. After the geometry optimization, the activity values of the opposite faces are consistent using the optimized models. Application of this NDA technique for waste packages and unitary items has shown that multi-count activity ratios of the reference and optimized geometry models range from 0.92 to 1.34. It demonstrates that the uncertainty associated with homogeneous activity distribution in the primary waste leads to consistent results. The activity values can be quantified by computing the average activity for all faces and considering the reference model. The waste packages and unitary items analyzed above are subjected to elimination via melting. The melting process does not allow correlating the samples after melting to waste packages and unitary items. Hence, we compare the AVG activities of all the samples to the averaged values over all primary waste (waste package and unitary items). The results show that the AVG activity values before melting are consistent with the corresponding values after melting, especially for Co-60, which is identified in all primary waste.
Additionally, this paper presents the methodology that allows performing a preliminary quantification of the specific activities of Co-60 for operational waste package production purposes. It is based on the experimental correlation between the ratio of the specific activity of Co-60 and the average dose rate as a function of the apparent density of the waste item. This methodology is valid under the assumption that Co-60 is the dominant gamma dose contributor (KN) in the waste item, where the decay time is more than 3 years. This methodology allows optimizing dose exposure and utilizing resources to guarantee the conformity of the waste packages to the criteria of the melting facility.

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This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4487049 P r e p r i n t n o t p e e r r e v i e w e d Figure 19 presents the activity values for optimized models generated in GURU for opposite faces. The considered contrast values vary from [1][2][3][4][5][6][7][8][9][10] to . The area (purple colour) represents the overlap of pair of faces, providing the "best" optimized models according to the best of our knowledge of the waste package.