A total of six advanced reactor concepts have been selected for Generation IV reactor and are being investigated to meet the challenging goals of effective resource utilization and waste minimization. The cross section is one of the most fundamental quantities for the reactor design. The evaluated nuclear data files have been updated over the years with reflecting progress on nuclear modeling, new nuclear experiment measurement, and a lot of feedback from the benchmark analysis. The cross-sections’ data library of neutronics calculation codes is generated by processing the evaluated nuclear data files when it is updated. Therefore, the nuclear data processing code is very important for connecting the evaluated nuclear data file and the reactor analysis and design codes. The motivation for the development of the advanced cross-section process (AXSP) code is to establish a platform to research some new methods of nuclear processing to satisfy the demands on accurate cross sections for the advanced reactor design. For example, in the design of a mixed-spectrum reactor, it is necessary to consider not only the anisotropic scattering in the high-energy region but also the influence of the broad resonances and the upper scattering problems in the low-energy region. The problem of generating a high-precision multigroup cross section cannot be well resolved. Because if we want to better solve the problem of the hybrid spectrum reactor, we need to consider not only the anisotropic scattering in the high-energy region but also the solution of the moderation equation in the all-energy region. There are still many works to be carried out.

Currently, NJOY (Abou Jaoude, 2017), PREPRO (Cullen, 2017), and AMPX (Wiarda et al., 2016) are well-known nuclear data processing codes in the world. There are also some newly developed nuclear data processing codes. For example, RXSP (Jian-kai et al., 2013) (Li and WangKan, 2017) (Liu et al., 2020) (Li, 2012) (Yu, 2015) of Tsinghua University and FRENDY (Tada et al., 2017) of the Japan Atomic Energy Agency (JAEA) have developed to produce an ACE format library for the Monte Carlo code. Ruller (Liu et al., 2016) of the China Institute of Atomic Energy and NECP-Atlas (Zu et al., 2019) of Xi’an Jiao Tong University have been developed to provide a multigroup library. At the same time, EXUS-F of South Korea was developed for a faster reactor multigroup cross-section generation by direct processing of the evaluated nuclear data file.

For the nuclear data processing, the open source nuclear data processing system NJOY is still not perfectly processing the evaluated nuclear data for the advanced nuclear reactor analysis when it is used to calculate the KERMA factors and DPA cross sections (Konno et al., 2016) (Wen et al., 2020) because of some bugs.

Recently, the nuclear data format has been considered to change from the traditional ENDF-6 format to the generalized nuclear data (GND) format (Mattoon et al., 2012) by utilizing the Extensible Markup Language. Since the GND format is completely different from the current ENDF-6 format, which was defined several decades ago, the NJOY code cannot treat such a new format without extensive modification. To solve this problem, several nuclear data processing systems, such as NJOY21 (Conlin, 2015), FUDGE (Beck and Mattoon, 2014), and AMPX-2000, are under development in a few countries.

In this study, the outline of the development, method, and capability of AXSP are described in the Theory and processing method section. In Numerical calculation results section, the verification of each module of AXSP is investigated, and the results of AXSP are compared with those of NJOY 2016. The critical benchmarks from the ICSBEP handbook are applied to demonstrate the accuracy of the multigroup cross section with the Bondarenko method, and ZPR6/7 was used to verify the ACE format library generated by the ACEXS module. The last section is conclusion.

AXSP is developed to solve the problems of the current nuclear data processing systems and satisfy the demands on accurate cross sections (XS) for the advanced reactor. Therefore, modern programming techniques are utilized to make the code more maintainable, modularized, portable, and flexible; it was written in Fortran 2003 by using the object-oriented programming techniques and allocatable memory techniques. Each module has its own class, and the modification of the class does not affect the other classes. The ENDF data class can be easily reused in other modules. The schematic diagram of the AXSP structure is shown in Figure 1. The solid lined modules have already been implemented, while the dotted lined modules are still in development. The GND format is not finalized. Now, the GroupXS module is still based on the Bondarenko method, and on the other hand, the ultrafine group method and hyperfine group method for the fast reactor design will be developed in the future.

The ReconXS module is used to reconstruct resonance cross sections from resonance parameters and to reconstruct cross sections from ENDF nonlinear interpolation schemes by using a traditional inverted-stack method. The BroadXS module generates Doppler-broadened cross sections in the PENDF format from piecewise linear cross sections in the PENDF format from 0 K temperature. To improve the calculation efficiency and maintain the calculation accuracy at the same time, the Gauss–Hermite quadrature has been used in some energy regions, and two points of Gauss–Legendre quadrature are used in other energy ranges (Li, 2012).

The UnresXS module is used to produce effective self-shielded cross sections for resonance reactions in the unresolved energy range. In the unresolved energy range, it is not possible to define precise values for the cross sections of the resonance reactions σ x ( E ) , where x stands for the reaction type, such as total, elastic, fission, or capture. It is only possible to define average values. The average cross sections in the vicinity of E∗ can be written as σ ¯ 0 x ( E ∗ ) = b x ( E ∗ ) + σ ¯ I 0 x 1 − I 0 t (1) and σ ¯ 1 x ( E ∗ ) = b t ( E ∗ ) + σ ¯ I 1 x 1 − I 0 t − I 1 t , (2) where b x ( E ∗ ) is the background cross section for the reaction type x, b t ( E ∗ ) is the background cross section for the total cross section, and I 0 x and I 1 t are the two types of “fluctuation integrals:”. σ ¯ ( E ∗ ) is written as σ ¯ ( E ∗ ) = b t ( E ∗ ) + σ 0 . (3)

The background cross section σ 0 is defined in the input file of AXSP by the user. If we assume that the resonances are widely separated and only the “self” term will be important, the fluctuation integrals become I 0 x = ∑ s A x s , (4) A x s = ( B x s − V 0 x s ) [ 1 − ∑ s ` ≠ s A t s ′ ] , (5) and I 1 t = ∑ s ( D t s − V 1 t s ) [ 1 − ∑ s ` ≠ s A t s ′ ] 2 , (6) where B x s and D t s are the first kinds including the isolated resonance integrals and V 0 x s and V 1 t s are the in-sequence overlap integrals. In the UNRESR module of the NJOY code, the in-sequence overlap corrections V 0 x s and V 1 t s are neglected. This approximation is based on the assumption that resonance repulsion will reduce the overlap between resonances in different sequences as the dominant overlap effect. In the UnresXS module of AXSP, the in-sequence overlap correction V 0 x s was calculated by using the method for computing J, which has been developed by Hang for MC²-2 (Henryson et al., 1976). The improvement of UnresXS comparison with that of UNRESR will be discussed in the Numerical calculation results section.

The unresolved self-shielding data generated by UnresXS are suitable for multigroup methods after processing by GroupXS based on the Bondarenko method. However, the Bondarenko method is not suitable for continuous-energy Monte Carlo codes like MCNP and RMC. Therefore, the PUnresXS module is developed by the ladder-sampling method to generate the probability table for the Monte Carlo code. On the other hand, the PUnresXS module can generate the effective self-shielded cross section which can be used for the multigroup cross-section generation. The disadvantage of PUnresXS is time consumption. To solve this problem, we have optimized the sorting method in the program, which greatly saves the calculation time while ensuring the accuracy. Previous research (Yu, 2015) has shown that the time consumption of the PURR module is mainly related to the sorting algorithm used, and the bubble sort algorithm has been applied in the PURR module. If the bubble sort algorithm was also used in the PUnresXS module of AXSP, the time consumption for the unresolved resonance processing with different codes is shown in Table 1. As shown in Table 1, the time consumption of the PUnresXS module is almost the same as the PURR module of NJOY if the same bubble sort algorithm is used. We also compared the impact of selection sort, quicksort, heap sort, and shell sort on time; the shell sort algorithm was selected and applied in the PUnresXS module because of the better calculation speed. The time consumption with the shell sort algorithm and bubble sort algorithm in PUnresXS for different isotopes is shown in Table 2. As shown in Table 2, for most isotopes, the computation time using the shell sort algorithm is 18% of the computation time of the bubble sort, or less. After using the shell sort algorithm, the calculation time is significantly reduced, and the calculation speed is significantly improved.

Multigroup constants are normally used by computer codes that calculate the distribution of neutrons and/ or photons in space and energy, and these compute various responses to these distributions. The GroupXS module in AXSP was developed to calculate the multigroup constants. The GroupXS module computes not only group average cross sections but also the group-to-group scattering matrix. The average cross sections and group-to-group scattering matrix can be represented as σ ¯ i , x , g = ∫ Δ E g σ x , i ( E ) ϕ 0 ( E ) d E ∫ Δ E g ϕ 0 ( E ) d E , (7) where i, x, and g are the indices for isotopes, reaction type, and multigroup number, respectively. ϕ 0 ( E ) is the neutron spectrum. In the group where the boundary between resolved and unresolved resonance ranges is located, both the resolved and unresolved resonances are self-shielded simultaneously. By dividing the integration interval into the resolved and unresolved resonance intervals, the self-shielding cross section is determined as σ ¯ i , x , g = ∫ Δ E r e s o l v e d σ x , i ( E ) ϕ 0 ( E ) d E + ∫ Δ E u n r e s o l v e d σ x , i ( E ) ϕ 0 ( E ) d E ∫ Δ E r e s o l v e d ϕ 0 ( E ) d E + ∫ Δ E u n r e s o l v e d ϕ 0 ( E ) d E , (8) where the integrals over the resolved resonance interval are evaluated in Eq. 7. When the integrals over the unresolved interval are evaluated, the self-shielding factor generated by the UnresXS or PUnresXS module should be used to be taken into account the self-shielding effects. The GroupXS module calculates the scattering matrix for neutron-induced scattering reactions such as elastic scattering, discrete inelastic scattering, and continuum inelastic scattering. The scattering matrix is also calculated for (n, 2n) and (n, 3n) reactions, including anisotropy by using the ENDF-formatted nuclear data library. The scattering matrix for the l − t h anisotropic scattering can be resented as σ ¯ i , x , g ′ → g l = ∫ Δ E g d E ∫ Δ E g ′ σ i , x ϕ l ( E ′ ) f ( E ′ → E , μ s ) P l ( μ s ) d μ s d E ′ ∫ Δ E g ′ ϕ l ( E ) d E , (9) where f ( E ′ → E , μ s ) is the scattering transfer probability from the incident energy E ′ to the outgoing energy E and the cosine of the scattering angle μ s in the laboratory system. ϕ l ( E ) is the l − t h moment of the neutron flux, and P l ( μ s ) is the l − t h order Legendre polynomial. With a given transfer probability, the element of the scattering transfer matrix can be determined by evaluating the integrals numerically. There are three ways to give the transfer probability, according to the data types given in nuclear data files: the angular distribution in file 4, the angular distribution in file 4 and the energy distribution in file 5, and the energy-angle distribution in file 6.

For the multigroup constant generation, it is important to select the continuum energy neutron flux and flux moment ϕ l ( E ) . In many cases of practical interest, the neutron flux and flux moment ϕ l ( E ) will contain dips corresponding to the absorption resonances of various materials, and these dips will reduce the effect of the corresponding resonance, which is also called self-shielding. If the Bondarenko narrow-resonance weight scheme (MacFarlane, 2012) is used, the flux can be written as ϕ l i ( E ) = C ( E ) [ σ t i ( E ) + σ 0 i ] l + 1 , (10) where σ t i ( E ) is the microscopic total cross section for the isotope i, C(E) is the smooth function of energy, and σ 0 i is a constant background cross section, which represents all the other isotope effects to the flux. However, we know that the Bondarenko method is more suitable for fast spectral reactors, and for thermal reactors, this method will introduce relatively large errors due to the need to consider the broad resonance in the low-energy region. Therefore, in the future, we will use the method of solving the continuous energy neutron transport equation to obtain the energy spectrum so that the generated multigroup cross sections will be more accurate, such as the CENTRM module (Williams and Hollenbach, 2011) in SCALE6.1 and RMET21 (Leszczynski, 2001). The disadvantage of the current version of GroupXS is that it can only handle neutron evaluated data, not yet unable to handle photon evaluated data. Therefore, there still exist some important functions which need to develop in the future, such as treating the thermal neutron cross sections and produce the MATXS format library, and Wims-D and Wims-E format libraries. In the following verification, the MATXS format library was produced by using MATXSR of NJOY.

In this study, a new nuclear process code AXSP was developed, and the basic function of the process-evaluated nuclear data file has been verified by using NJOY2016. The critical benchmarks from the ICSBEP handbook were used to verify the multigroup cross section, and the effective multiplication factor maximum difference between AXSP and NJOY2016 is 14 pcm. The ZPR6/7 benchmark was used to verify the ACE format library generation for the Monte Carlo code, and the k e f f results calculated by the ACEXS module are in good agreement with that of the ACER module, and the difference is only 6 pcm. Therefore, the results of AXSP are in good agreement with that of NJOY2016. Compared with the NJOY program, the precision of the unresolved resonance processing module UnresXS has been significantly improved due to the adoption of a more accurate solution method and the consideration of in-sequence overlap integrals. The improvement is more pronounced when the background cross section is relatively small and the self-shielding effects are strong. The time consumption of PUnresXS has been decreased significantly due to an optimized sorting algorithm. The computation time using the shell sort algorithm is 18% of the computation time of the bubble sort algorithm, or less. After using the shell sort algorithm, the calculation time is significantly reduced, and the calculation speed is significantly improved. In the future, we will use the method of solving the continuous energy neutron transport equation to obtain the energy spectrum in order to obtain more accurate multigroup cross sections, and the module of processing the MATXS format library, and Wims-D and Wims-E format libraries will also be developed (Lim et al., 2018).