2.1. Processing Workflow

The generation of a single-group equivalent cross-section library for the burnup code ORIGEN2 requires a series of processing steps and treatments applied to the evaluated nuclear library. The neutron reaction sublibrary required for the burnup program is obtained by reading, converting, calculating, and organizing the evaluated library using the mainstream nuclear data processing software NJOY. The primary function of the MODER module is the binary conversion of nuclear data, aiming to enhance the processing efficiency of numerical nuclear data files. The source file is transformed into a binary file within the module for internal operations, and it is reverted after processing, facilitating external program and code accessibility.

The overall processing workflow of the Tape9 library is illustrated in Figure 1.

The evaluated library provides cross-section information for multiple primary neutron reactions for each isotope. After consolidation, the corresponding multigroup cross-sections, single-group equivalent cross-sections, and their metadata are written into the respective groups in the library. The library includes cross-section data for six major neutron reactions, and two excited state reactions considered crucial in burnup and source term calculations. When the program reads the actinide (A) cards, there are six neutron reactions with the equivalent cross-section data for the (n, γ), (n, 2n), (n, 3n), (n, f), (n, γ)  ^∗, and (n, 2n)  ^∗ reactions to be considered. In contrast, when the program processes the activation and fission product (FP) fields, the third and fourth parameters are replaced with the equivalent cross-section values for the (n, α) and (n, p) reactions, respectively. The cross-section data for the other neutron reactions remain in the same positions across all types of information cards as they do in the A cards.

In addition to the reaction cross-section data, a comprehensive activated source term library also includes radioactive decay data and fission yield data. Since the ORIGEN code can automatically compress the burnup chain based on yields and half-lives, the burnup sublibrary of the evaluated library directly provides these two sets of data and their metadata, which are processed into the respective nuclide groups.

The PyTape program initially reads the decay data of nuclides contained in the incident neutron sublibrary, organizing it into radioactive decay data sequences in the corresponding format. It then reads in the six reaction cross-section data for isotopes in the same arrangement. At the end of each cross-section card, an identifier controls whether the yield card is read, with the input yield data sharing a data sequence with the corresponding cross-section data.

The current ORIGEN2 program uses the radioactive decay and fission yield library Tape9-B4. However, since this paper aims to study the importance of library iteration based on evaluated data versions for precise burnup and activated source term calculations, the latest authoritative evaluated nuclear library file ENDFB-VIII.0 is selected for processing the Tape9-B80 library. Libraries from other sources can be processed using the same workflow, and the resulting Tape9-B71, Tape9-B70, and Tape9-J33 libraries are verified accordingly.

2.2. Decay and Fission Yield Library Content Design

The radioactive decay library mainly contains information about isotopic decay constants, available energy from decay reactions, natural enrichment in the environment, and products and branching ratios of various decay modes. The decay constants are always recorded in terms of half-life, in seconds (s), and the unit for available energy is megaelectron volts (MeV). It is important to note that, due to the RSIC code’s special handling of extremely short-lived nuclides, marking values below 10⁻⁷ s in the library may cause program faults, and a placeholder of “1.000E-03” is uniformly used. The Tape9-B80 library primarily considers seven decay modes supported by ENDF, as shown in Table 1. Additionally, three physical quantities are further considered in the RSIC computational program’s decay sublibrary:

These three pieces of data come from nuclear data sheets published by the IAEA or some federal regulations publicly available from ORNL and are used only in some special calculations, thus having a lower frequency of usage.

Fission yield data, fundamental to burnup calculations, are usually presented as the measured values of fissionable nuclides at multiple energy points. In the nuclear evaluation library ENDFB-VIII.0, yield data are available for 31 isotopes at four fission energy points: 0.0253 eV, 500 keV, 2 MeV, and 14 MeV. However, not all FPs have yields measured at all four energy points. Most isotopes provide data for two or three energy points, and the 31 isotopes include a total of 41 fission energy points and 11 fusion energy points. Notably, Pu-239 is the only isotope for which fission yield data are provided specifically at 2 MeV. The total number of FPs (counting ground state and excited state nuclei separately) is required not to exceed 2500, with typical counts between 1200 and 1300. Given the large memory requirements for storing burnup chain information, the evaluation process often necessitates selective inclusion of fission yield data. The Tape9-B4 library retains partial fission yield values for Th, U, Pu, Cm, and Cf isotopes. To enhance calculation accuracy without significantly increasing memory usage, the Tape9-B80 library expands the fission yield sublibrary to include 850 FPs, originating from 12 fission reactions of 8 fissile isotopes, recorded as percentages, as shown in Table 2. The yield data in Tape9-B4 mostly originate from binary fission and also provide tertiary fission yields for some important low-mass nuclei. The yield data in Tape9-B80 do not consider yields producing light nuclei, and the total yield for a single fissile isotope is 200% (unit: %), meaning that tertiary fission yields are not included.

2.3. Data Sources and Storage Structure

The PyTape program processes two main types of data: reaction cross-section data, which are consolidated from multigroup cross-sections generated by the GROUPR module, and radioactive decay and fission yield data, which are extracted from the evaluation library by the program itself. Due to the difficulty in preserving complete data information in a numerical library in text format and its poor extensibility, and because binary libraries, though fast in read/write operations, make the data values inaccessible for user viewing and are only suitable for use in intermediate program transfers, the HDF5 hierarchical data format [13] is adopted for storing all the aforementioned data sources. In the Tape9-B80.h5 root group file, groups (named after nuclides) are created to store the corresponding decay, neutron reaction information, etc., in the form of groups or datasets under the group path. Additionally, metadata such as data type, data storage space, compressibility, and custom properties are stored with the corresponding group or dataset. The same method is used to create corresponding Tape9-B71.h5, Tape9-B70.h5, and Tape9-J33.h5 files. This approach facilitates the use of the PyTape program’s submodules for CCC-371 format library read/write operations while preserving the integrity of nuclear data information for easy reference and use in the production of other types of libraries and related data research.

The PyTape program extracts a total of 3818 isotopic nuclear data information entries from the HDF5 based on ENDFB-VIII.0, including all decay data, fission yield information, and neutron reaction cross-section information recognizable by the ORIGEN2 code, along with their consolidated values. Data fields are written according to isotope categories, with nuclides in each field arranged in ascending order based on their six-digit identification numbers. Ultimately, the activation product (AP), A, and FP fields contain 1376, 258, and 1758 isotopic data fields or information cards, respectively. Of these, there are 1290 information cards for unstable nuclides, and 1696 isotopic data fields contain decay sublibrary information.

4.1. Validation of Burnup Benchmark for Different Reactor Types

Considering that decay and yield data are fundamental for burnup calculations to validate the accuracy of the developed library, benchmark calculations for irradiation burnup processes in four different reactor types were conducted. The results obtained from the Tape9-B80 library were then compared with the computational results provided by ORNL.

For traditional PWRs, burnup calculations utilized 3.2% enriched uranium dioxide fuel and assembly hardware. The reactor operated over three cycles, each lasting 1092 days. The core components, along with Zircaloy-4 cladding, 304 stainless steel, 302 stainless steel, INCONEL-718, and NICROBRAZE-50 nickel alloys, underwent alternating irradiation at a constant flux for 293.3 days and 106 days of decay. The irradiation flux in the stainless-steel region was set to 0.011 of the core regions, while other areas received full flux irradiation. The end-of-cycle burnup reached 33,000 MWd/mt. Neutron cross-section libraries of 204, 205, and 206 were employed for structural materials, As, and FPs, respectively(the description of the cross-section sublibrary is shown in Table 3).

For boiling water reactors (BWRs) operating in a four-cycle subcritical mode, the benchmark involved loading 2.75% enriched uranium dioxide fuel. The primary irradiation materials included Zircaloy-4, Zircaloy-2 alloys, 304 and 302 stainless steels, and nickel-based high-temperature deformation alloys. The core’s discharge burnup was 27,500 MWd/mt over a cycle of 1379.8 days, comprising an irradiation scheme alternating between 265.45 days of constant power irradiation and 160 days of decay. The flux in the zirconium cladding and stainless-steel regions was set to half of that in the core. The irradiation subjects were 1000 kg of impurity-containing fuel assemblies and 1 kg of each of the aforementioned ex-core irradiation materials. Structural materials, As, and FPs employed neutron cross-section libraries of 251, 252, and 253, respectively.

Table 4 presents the infinite multiplication factor (Kinf) and its computational deviation calculated by the point burnup code at the end of each cycle [15]. As can be observed, although there is a slight increase in computational deviation over the reactor’s lifespan, the absolute values of the deviations remain within 30 pcm, which is within a reasonable range. This indicates a good numerical agreement, demonstrating the library’s capability for accurate calculations in full-core irradiation decay problems.

To further validate the computational capabilities of the library in advanced reactor designs, benchmark calculations were conducted for an advanced oxide-coated liquid metal fast breeder reactor (LMFBR) and a CANDU reactor. The CANDU reactor model was a benchmark problem with one metric ton of initial heavy metal, using natural-enriched uranium fuel. A fixed-power irradiation of 25.57 MW was implemented in the burnup zone for 293.31 days, achieving a burnup of 7500 MWd/mt. Simultaneously, constant flux irradiation was conducted in the zirconium alloy cladding and lattice grid areas at the core flux level, with the total mass of structural materials being 1 kg. Neutron cross-section libraries 401, 402, and 403 were used for structural materials, As, and FPs, respectively.

The composition of the liquid metal-cooled reactor is more complex. The fuel area was loaded with one metric ton of uranium–plutonium mixed oxide (MOX) fuel, with an enrichment of ~10% in Pu-239. Mixed depleted uranium fuel was used, and uranium or thorium coatings were applied radially and axially to the baskets. The cladding material was 316 stainless steel. A fixed-power irradiation of 123.25 MW was carried out in the fuel assembly and structural material areas for a total of 821.82 days, achieving a burnup of 101.3 GWd/mt. After refueling, constant flux irradiation was performed. Neutron cross-section libraries 311, 312, and 313 were used for structural materials, As, and FPs, respectively. By storing and outputting vectors of the radioactivity intensity of activation and FPs, isotopic concentrations in the reactor, and the release rates of photons and energy during these two benchmark processes, it facilitated the tracking of the transmutation process.

After the completion of the irradiation schemes, the photon emission rates of FPs in the CANDU reactor core components and activated products in cladding materials were compared with the benchmark results provided by ORNL, as shown in Figure 4a. The benchmark comparison results for the photon and energy release rates of core FPs in the liquid metal breeder reactor are shown in Figure 4b. As can be seen from the figures, the developed library achieved good fitting results in both the CANDU reactor core and cladding irradiation calculations and the fuel coating irradiation calculations of the LMFBR. The activation calculations in the Zircaloy-4 alloy cladding and lattice framework of the CANDU reactor showed almost no deviation in each energy group. However, both types of cores showed greater deviations in the high-energy photon region of 4–8 MeV. The calculation results in other energy groups remained well-fitted.

4.2. Impact on Activation Source Term Calculations

To assess the potential impact of the library on practical activation source term calculations, three types of materials commonly encountered in activation and source term calculations were selected: the decay of a single long-lived radionuclide, decay following irradiation of naturally abundant isotopes, and activation of mixed structural materials. The calculation of irradiation and decay processes for these materials was conducted, and the relative deviation in calculations between libraries was evaluated to assess the impact of data iteration on shielding source term analysis and reactor physics design.

Figure 5 presents the calculated radioactivity intensity during the decay processes of Am-242 m and Cf-252 radiation sources. By separately accounting for the total radioactivity intensity and the α-decay radioactivity intensity during the decay process, it was evident that the iteration of the new version of branching data caused a certain deviation in the calculation of the Am-242 m decay process, with almost all of this deviation coming from α-decay. The half-life of Am-242 m is ~141 years, and its main decay modes are isomeric transition (99.54%) and α-decay (0.46%), with the corresponding products being stable Am-242 and Np-238, respectively. Within 300 days, the main product in the system is Pu-238. In the nuclear library, the decay constant of Am-242 m was reduced by about 7.76%, the branching ratio of α-decay decreased by about 8.55%, and the branching ratio of isomeric transition increased by only 0.04%. Pu-238, with a half-life of 87.7 days, undergoes α-decay to form U-234 in a relatively short time, followed by long-term decay of U-234 and its α-decay product Th-230, with consistently small calculation deviations in this process. In contrast, the deviation in the decay process of Cf-252 is relatively small. The α-reaction that generates Cm-248 accounts for 99.99% of the decay process. Since there was no change in the α-decay branching ratio of Cf-252, the ~2% deviation in calculations is attributed to changes in the measured data for its half-life.

Figure 6 presents the discrepancies in photon emission rates calculated for 1 kg of naturally isotopic-abundant metal materials Fe, Pb, and W during a 1500-day constant flux irradiation followed by a 300-day decay period in a fast neutron reactor [16]. The analysis utilizes nuclear libraries 331, 332, and 333 for structural materials, As, and FPs, respectively. It is evident from the figure that there is a significant discrepancy in the calculated photon emission rate of metallic iron, particularly during the decay period immediately following irradiation, where the rate drops sharply, with relative discrepancies reaching ~30%. Such a level of discrepancy can impact the calculations for shielding. For metallic lead and tungsten, the discrepancies in photon emission rates during irradiation are relatively minor, with metallic lead showing less than 1% discrepancy and tungsten displaying a mere 0.8% deviation, which can be almost disregarded in actual shielding and activation calculations. The improved accuracy in photon emission rate calculations for metals like iron and lead during irradiation and decay processes is crucial for analyzing activation issues in advanced solid-state reactors.

The design of advanced reactors increasingly relies on the use of composite materials, where the precision of activation calculations for mixed materials determines the reliability and accuracy of shielding designs.

Samples of antimony-beryllium core blocks, 304 stainless steel for reactor use, low-activation ferritic steel mixtures, and zirconium alloy materials were irradiated under low power conditions for 4380 days, followed by cycles of constant flux irradiation and zero flux decay until saturation. For these materials, isotopes from structural materials, As, and FPs categories utilized neutron cross-section databases 204, 205, and 206, respectively. The distribution of deviations in the radioactivity of selected source terms at each sampling point, as well as their differences based on normalized results, are illustrated in Figure 7a–d, highlighting the activity variation among different source terms. Notably, the irradiation results for the antimony-beryllium core blocks, an essential secondary neutron source component, displayed remarkably consistent deviations. The radioactivity deviation for the Fe-55 source term was around 1.5%, and for the Sb-125 source term, it was ~0.2%, primarily related to corrections in the decay data for antimony and its daughter nuclei, as inferred from the analysis of nuclide half-life deviations discussed earlier. The calculations for the 304 stainless steel and low-activation ferritic steel mixture in the Fe-55, N-59, and Ni-63 source terms showed deviations of about 2%, 5%, and 9%, respectively. Moreover, the steel mixture, having a more complex material composition, exhibited significant deviations in calculations for some low-yield radioactive and excited-state nuclides, such as Mo-93 and Te-125 m, with deviations around 15% and 2%, respectively. The zirconium alloy material demonstrated an overall unstable deviation in radioactivity calculations ranging from 1% to 4%, with larger deviations observed over long-term irradiation and lower deviations during short-term alternating decay periods. The calculation deviation for the Fe-55 source term exhibited a similar pattern.