JENDL-5 benchmarking for fission reactor applications

ABSTRACT The new version of the Japanese evaluated nuclear data library, JENDL-5, was released in December 2021. This paper demonstrates the validation of JENDL-5 for fission reactor applications. Benchmark calculations are performed with the continuous-energy Monte Carlo codes MVP3 and MCNP6.2 and the deterministic code system MARBLE. The benchmark calculation results indicate that the performance of JENDL-5 for fission reactor applications is better than that of the former library JENDL-4.0.

JENDL-4.0 has been validated using criticality benchmark experiments [11][12][13], post-irradiation examinations (PIE), and so on [11,[14][15][16]; it showed good prediction accuracy for experimental results of light water reactors and fast reactors [11].There have, however, existed several issues.The differences between the calculated results and experimental results (C/E values) were slightly larger in criticalities of plutoniumfueled solution systems and high-temperature gascooled reactors, spectrum indices F64/F49 (reaction rate ratios of 244 Cm fission to 239 Pu fission) of fast reactors [17], dependency of criticality on Gd concentration for uranium fuel systems [18], and so on.
JENDL-5 was newly released in December 2021 [1] after many revisions to JENDL-4.0.The resonance parameters were revised by using the results of the CIELO project [19] and the experimental data measured with ANNRI at J-PARC [20].In addition, the number of nuclides of the neutron reaction data in JENDL-5 has increased to 795, which is close to double of 406 of JENDL-4.0 [2], in order to meet a variety of needs not only for nuclear reactors but for other applications such as accelerators.The validation of JENDL-5 is thus required before extensive use in the fission reactor applications.
The purpose of the present work is to validate JENDL-5 for fission reactor applications.The present paper shows comparison of calculated results with experimental ones for criticality and PIE benchmark tests; it also shows JENDL-4.0 results to clarify the impact of major revisions of JENDL.The calculation results of JENDL-5 were also compared with those of ENDF/B-VII.1 [21] and ENDF/B-VIII.0[22] libraries since they are widely used in the world [4,12,14,16,[23][24][25][26][27].These comparison results provide good information on the prediction accuracy.The majority of the tests were performed with hundreds of criticality experiments contained in the International Criticality Safety Benchmark Evaluation Project (ICSBEP) handbook [28] and the International Reactor Physics Experiment evaluation Project (IRPhEP) handbook [29].Additional calculations, e.g.calculation of measured reaction rate ratios, other selected reactor parameters, and the PIE analysis of the fast system, were also performed.
Neutron transport calculations were performed with a continuous energy Monte Carlo code MVP version 3 (MVP3) [30] and a deterministic code system MARBLE [31].The continuous energy Monte Carlo code MCNP6.2 [32] was also used for the leadvoid reactivity calculation in section 4.3.7.The PIE analysis of the fast system was carried out by using a three-dimensional hexagonal geometry with 70group cross sections by a transport code MINISTRI [33].
This paper is organized as follows.The overview of benchmark tests is described in section 2. Section 3 provides the numerical procedures and calculation conditions for the benchmark calculations.The calculation results of the benchmark tests are shown in section 4. Finally, concluding remarks are summarized in section 5.

Criticality data
The list of the criticality experiments used in these benchmark tests is shown in Table 1.These benchmarks are obtained from the ICSBEP handbook [28].The first three capital letters of the benchmark name mean the fissile material, physical form, and neutron energy range where the majority of the fission occurs.The first capital letter means the fissile material.P is plutonium, H is highly enriched uranium (HEU), I is intermediate enriched uranium (IEU), L is low enriched uranium (LEU), U is 233 U, and M is mixed plutonium-uranium.The second capital letter means the physical form of the fissile material.M is a metal system, C is a compound system, and S is a solution system.The third capital letter means the neutron energy range where the majority of the fission occurs.F is a fast spectra system, I is an intermediate spectra system, L is a thermal spectra system, and M is a mixed spectra system.
The selected experimental number is 111 and the total benchmark case is 770.The thermal and intermediate spectrum reactors are mainly selected.The criticality experiments which are utilized for the validation of other nuclear data libraries, e.g.ENDF/ B-VII.0 [34], ENDF/B-VII.1 [21], and JEFF-3.3[35], were mainly selected.The light water reactor benchmark suite which is compiled by the reactor integral test working group activity of the JENDL committee [18] is also adopted.
We also utilized the criticality experiments of the experimental fast reactor Joyo MK-II [36], the very high temperature reactor critical assembly VHTRC [37], the experimental high temperature gas-cooled reactor HTTR [38], and critical assemblies constructed at the Russian BFS facility [39].

Other neutronic characteristics of fast systems
In addition to the criticalities, JENDL-5 was tested on experimental data of the other neutronic characteristics of fast reactors, such as sodium-void reactivity worths, control rod worths, Doppler reactivity worths, reaction rate distributions, and spectrum indices as well as the validation of JENDL-4.0 [11].The experimental data on these characteristics of ZPPR-9 and ZPPR-10A were taken from the IRPhEP handbook.We also utilized the sodium-void reactivity worth data obtained at BFS and FCA [40] and the SEFOR Doppler benchmark data [41].Furthermore, in the present benchmark, transuranium (TRU) fission rate ratios measured in BFS are used.
At the Comet critical assembly of the National Criticality Experiments Research Center, lead-void reactivity worths were measured systematically in three fast systems with different fuel compositions and lead (Pb): high-enriched uranium (HEU)/Pb, lowenriched uranium (LEU)/Pb and plutonium (Pu)/Pb [42].The Pu/Pb system included weapons-grade Pu plates that had been used in the Zero Power Physics Reactor (ZPPR) of Argonne National Laboratory until the 1990s.While the data in each system is provided in multiple cases with different sizes of voided zone, only the cases with relatively large experimental values were used for this benchmarking.

PIE data of fast systems
In addition to the static characteristics, we utilized the PIE data obtained at the experimental fast reactor Joyo MK-II [43,44] and the 600 MW Dounreay Prototype Fast Reactor (PFR) [45,46] of UK Atomic Energy Authority.
(a) Minor Actinoid Sample Irradiation Tests in Joyo MK-II In the Joyo MK-II core, minor actinoid (MA) irradiation tests were performed from 1994 to 1999.In these tests, MA samples such as 241 Am, 243 Am, and 244 Cm were loaded.Each MA sample includes about 100 mg of MA.While the purity of the 241 Am sample was almost 100%, the 243 Am sample included 241 Am of 12% and the 244 Cm sample included 245 Cm of 3% and 246 Cm of 4%.These samples were placed at the two axial positions (core midplane and+350 mm upper position in the reflector region) for different neutron spectra of the fuel irradiation test subassembly PFB090.Since JENDL-5 was revised for 241 Am, 243 Am, and 244 Cm capture cross section below 1 keV, this study also focuses on the upper reflector position which was sensitive to this energy region.These samples were irradiated for 276 effective full power days (EFPDs) by a neutron fluence of 8.0 × 10 22 n/cm 2 (core midplane) and 2.6 × 10 22 n/cm 2 (upper reflector).After the irradiation, MA isotopic compositions of these samples, except for the 244 Cm sample at the upper reflector position, were quantified by radiochemical analyses [43,44].
(b) Minor Actinoid Sample Irradiation Tests in PFR In the PFR, actinoid sample irradiation tests were performed from 1982 to 1988 [45,46].Small amounts of enriched isotopes such as 235 U, 240 Pu, 241 Pu, 242 Pu, 244 Pu, 241 Am, 243 Am, 244 Cm, 246 Cm, and 248 Cm samples were prepared for the irradiation tests.The purities of the 235 U, 240 Pu, 242 Pu, 241 Am, 243 Am, 244 Cm, 246 Cm, and 248 Cm samples were almost 100%.The purity of the 244 Pu sample was 88%, but impurities were not significant for the present benchmark.Since the 241 Pu sample included 241 Am at 31%, the 244 Cm sample included 246 Cm at 6%, and the 248 Cm sample included 246 Cm at 5%, the measured data for these samples can be utilized for the validation of the corresponding cross sections.All the MA samples were encapsulated and assembled in the fuel pin.The fuel pin had been irradiated for 492 EFPDs by a neutron fluence of 2 × 10 23 n/cm 2 .These conditions were the same as the JENDL-4.0 benchmark [11].Portions of the dissolved samples were transferred to JAERI to determine the compositions of the irradiated samples by radiochemical analyses.

Criticality and reactivity calculations with a continuous energy Monte Carlo code
MVP3 was used to analyze the benchmark experiments in the ICSBEP and IRPhEP handbooks.The input files of the benchmark problems listed in Table 1 were prepared for the validation of JENDL-5.The MVP neutron cross-section library based on JENDL-5 was generated with the combination of nuclear data processing codes FRENDY [47] and LICEM [48].Although most of the neutron reaction data of JENDL-5 are extended in the energy region up to 200 MeV for high energy accelerators, the upper limit energy of the MVP library is 20 MeV.The probability tables were used to consider the self-shielding effect in the unresolved resonance region.The thermal scattering law data of JENDL-5 were also processed with LICEM.
In the criticality calculations, the total number of histories was larger than 20 million and the statistical uncertainties of the criticalilties were less than 0.04%.In the calculations for VHTRC and HTTR, the number of histories for each calculation was set to 60 million.The input files of Refs [37,49] were used for the benchmark problems of VHTRC and HTTR, respectively.
In the reactivity calculations, the number of histories for control rod worths of ZPPR-10A was set to 480 million.The numbers of histories for sodium-void reactivities of ZPPR-9 and BFS were set to 1.1 billion and 4.8 billion, respectively.The sodium-void reactivity worth of FCA employed 1.0 × 10 8 generations of neutrons, with 2.0 × 10 5 histories per generation.The first 50 generations were excluded from the statistics for each case, yielding 1.9995 × 10 13 active histories in each calculation.The calculations for the lead-void reactivity worths at the Comet critical assembly employed 3.1 × 10 3 to 4.2 × 10 3 generations of neutrons, with 5.0 × 10 5 histories per generation.The first 100 to 200 generations were excluded from the statistics for each case, producing 1.50 × 10 9 to 2.05 × 10 9 active histories in each calculation.
In the validation of JENDL-4.0, sodium-void reactivity worths of BFS were calculated by the deterministic procedure, but we applied the Monte Carlo method to them in the present benchmark.In other words, all reactivities shown in the present benchmark of the fast reactor systems are calculated by the Monte Carlo methods.The effective delayed neutron fractions are also calculated by using MVP3 with delayed neutron data given by JENDL-5.

Criticality, reactivity, and reaction rate calculations with a deterministic code system for fast reactor
A deterministic numerical analysis method [8] was also employed to calculate the Doppler reactivity worths, reaction rates, and spectrum indices.The calculation procedure of the deterministic analysis method, which is based on the conventional one for fast reactor analyses in Japan, is basically equivalent to the procedure used for the validation of JENDL-4.0 [11].The details can be found in Ref [50].In addition, a sensitivity analysis method based on the deterministic procedure was used to evaluate the calculation results of JENDL-5.An overview of the sensitivity analysis method will be given later.
The procedure of the deterministic analysis method consists of two-step calculations: homogenization calculation (lattice calculation) and whole core neutron transport calculation.The lattice calculations are performed with the SLAROM-UF code [51] and its library UFLIB.The UFLIB library is composed of a 70-group base library and an ultrafine energy group (about 100,000 groups) library.The former is applied to the whole energy range between 1.0 × 10 −5 eV and 20 MeV, while the latter is used for calculations below 50 keV.These libraries are generated from JENDL-5 by using NJOY2016 [52] and TIMS-1 [53].A simplified onedimensional slab lattice model given in the IRPhEP handbook is used for ZPPR.In calculations for BFS and Monju, a unit lattice, such as a fuel drawer or a fuel subassembly, is also simplified to a onedimensional slab or cylinder.Whole core neutron transport calculations are performed with threedimensional Cartesian or Hexagonal-Z core modeling.Base results are obtained by employing a diffusion code.Calculations with a discrete ordinates transport code are also carried out to obtain correction factors for the transport effect.In these transport calculations, scattering anisotropy is considered by the transport approximation, and the S4 or S8 level symmetric angular quadrature set is used.In order to more accurately treat wide resonances of structural material above 50 keV, additional calculations are performed with a 175-group, and differences between 175-group and 70-group libraries results are also corrected to the base results.
In the sensitivity analysis method, 70-group sensitivity coefficients are calculated based on the generalized perturbation theory in the base calculation which employs the diffusion code.The difference of the calculation results between two nuclear data can be predicted by using the sensitivity coefficients and the differences of nuclear data.The calculation results of JENDL-5 were evaluated by using the calculation results of JENDL-4.0, the sensitivity coefficients based on JENDL-4.0, and the differences of nuclear data between JENDL-4.0 and JENDL-5.

PIE analysis with a deterministic procedure
The MA irradiation test conducted at Joyo MK-II was analyzed by using the deterministic procedure for fast reactors described in the preceding section.Unlike the JENDL-4.0 benchmarking, a base calculation for neutron spectra at the MA sample position was carried out with a three-dimensional hexagonal geometry and 70group cross sections by using the MINISTRI code [10].The base calculation result was corrected for the lattice heterogeneity, spatial mesh size, and ultrafine group effects.One-group cross sections for a burn-up calculation were produced using the corrected neutron spectra.The neutron fluxes of the MA samples were normalized with the fission reaction rate of a 235 U sample adjacent to the MA samples as in the JENDL-4.0 benchmark [11].
As for the calculation of the MA irradiation test at PFR, neutron spectra of the MA sample position were calculated based on composition and geometry data from the literature [54] since the data for the detailed calculation of neutron spectra were not available.Onegroup cross sections were produced via these neutron spectra.The neutron fluxes of the MA samples were normalized with the capture reaction rate of a 235 U sample as in the JENDL-4.0 benchmark [11].The matrix exponential method [55] was used for the burn-up calculation; major heavy nuclides and 137 Cs were considered in this study.The short halflife nuclides such as 242 Am were treated as immediately decaying.The order of the expansion was the order at which the error is less than 0.1% based on the norm of the transition matrix [56].The time step for the burn-up calculation was one step in each operating period.In the burn-up calculation, JENDL-4.0,ORLIBJ33 [57], and Nuclear Chart 2004 [58] were used for the fission yields, branching ratios of decay, and half-lives, respectively.
The isomeric ratio (IR) of 241 Am capture reaction was obtained in an energy-dependent manner by a weighted average at the MA sample positions in this benchmark.The MA sample at the upper reflector position in Joyo MK-II was also treated in this study.
The calculation results were compared in terms of the ratio of production of daughter nuclide to parent nuclide; the ratio between a certain nuclide and its daughter nuclide was suitable for validating the capture cross section of the parent nuclide.For example, an number density ratio of 242m Am to 241 Am could be effectively utilized for the validation of the 241 Am capture cross section.Table 2 presents the relationship between parent and daughter nuclides for the crosssection validation.

Comparison of ICSBEP benchmarks
Table 3 shows the average of C/E-1 values and the chisquare values of the ICSBEP benchmark calculations listed in Table 1.Table 3 shows the calculation results of four libraries, i.e.JENDL-4.0 (J40), ENDF/B-VII.1 (B71) [59], ENDF/B-VIII.0(B80) [22], and JENDL-5 (J5).The chi-square values are calculated as: where N is the number of benchmarks, C i is the calculation value, E i is the experimental value, σ 2 C;i is the calculation uncertainty, and σ 2 E;i is the experimental uncertainty.The chi-square value is preferable to be close to unity.The chi-square value becomes less than or equal to unity if the C/E-1 value is less than or equal to the experimental uncertainty in many cases.The chi-square value becomes larger if the C/E-1 value becomes larger.Note that the chi-squared value becomes higher if the experimental uncertainty is so small even if the C/E-1 value is close to zero.We found that the experimental uncertainty of criticality benchmarks was less than 0.01% which is similar to the statistical uncertainty of the calculation results in some cases.The actual chi-squared value may be smaller since these small experimental uncertainties were not modified in this study.
As shown in Table 3, the chi-square values of JENDL-5 are smaller than or equal to those of JENDL-4.0 without the mixed-oxide (MOX) case.Especially, the chi-squared values of intermediate-enriched uranium (IEU) and Pu cases are largely reduced.The C/E-1 values of the MOX case are small since the chi-squared values of all libraries are less than unity.
The C/E-1 and chi-squared values of JENDL-5 are close to those of ENDF/B-VIII.0.The chi-square value is less than 4.0 in many fissile material experiments.This result indicates that the C/E-1 value is less than or equal to twice of experimental uncertainty in many cases.

Criticality of uranium-fueled light-watermoderated systems
Figure 1 shows the C/E values of the criticality of uranium-fueled light-water-moderated systems selected in Ref. 18.The grey dashed lines in Figure 1 mean the uncertainty of the C/E values.The uncertainty of the C/E value is mainly the experimental uncertainty since the statistical uncertainty of the calculation is 10 times smaller than the experimental uncertainty; it is important to estimate the prediction accuracy.One can consider that the calculation value shows good agreement with the experimental value if the C/E value is located inside the experimental uncertainties.
The C/E values of JENDL-5 are within the uncertainty of the C/E values in many cases.The difference between JENDL-4.0 and JENDL-5 is from −0.407% to −0.009%.Table 4 shows the relative difference of the criticalities (Δk/k) for 'crude' sensitivity analysis: each nuclide is changed from JENDL-5 to JENDL-4.0.'All' in Table 4 means that all nuclides are changed from JENDL-5 to JENDL-4.0.'Total' in Table 4 means the sum of the differences of each nuclide listed in this table.As shown in Table 4, the cause of the difference between JENDL-4.0 and JENDL-5 mainly lies in H in H 2 O, 16 O, 235 U, and 238 U.
In the JENDL-5 evaluation, capture cross sections at the low energy region of 155 Gd and 157 Gd were modified using the measurement results obtained in ANNRI at J-PARC [60].The LEU-COMP-THERM -005 experiment in the ICSBEP benchmark is used to investigate the impact of the modification of 155 Gd and 157 Gd cross sections on the neutronics analysis for the light water reactor.Figure 2 shows the C/E values of criticalities of gadolinium-loaded thermal systems.'J5+Gd155(J40)' and "J5+Gd157(J40) in Figure 2 mean that 155 Gd or 157 Gd is only modified from JENDL-5 to JENDL-4.0.As shown in Figure 2, the effects of 155 Gd and 157 Gd cancel each other.Since 'J5,' 'J5+Gd155(J40),' and 'J5+Gd157(J40)' are inside the uncertainty of the C/E values, it is difficult to estimate which library is better.

Criticality of MOX-fueled light-watermoderated systems
Figure 3 shows the C/E values of the criticality of MOX-fueled light-water-moderated systems selected in Ref. 18.The C/E values of JENDL-5 are within the uncertainty of the C/E values in many cases.The difference between JENDL-4.0 and JENDL-5 is from −0.388% to 0.441%.Table 5 shows the difference in the k-effective values (Δk/k) calculated for the crude sensitivity analysis.'All' in Table 5 means that all nuclides are changed from JENDL-5 to JENDL-4.0.'Total' in Table 5 means the sum of the differences of each nuclide listed in this table.As shown in Table 5, the cause of the difference between JENDL-4.0 and JENDL-5 mainly lies in H in H 2 O, 16 O, 235 U, 238 U, and 239 Pu.
Comparing Tables 4 and 5, the variation of the Δk/k for H in H 2 O of the MOX fuel is larger than that for the uranium fuel.Figure 4 shows the sensitivity of the 1 H scattering cross section in each benchmark case and the inelastic scattering cross section of H in H 2 O.These sensitivities were obtained from the DICE tool in the ICSBEP benchmark [61].Note that the sensitivity analysis results of the DICE tool are based on the ENDF/B library.The difference of the evaluated nuclear data library may be negligible since the nuclear data of 1 H from JENDL-4.0 and that from JENDL-5 are taken from ENDF/B-VII.0 and ENDF/B-VIII.0,respectively.As shown in Figure 4, the difference of the inelastic scattering cross section becomes larger in the range from 1.0 × 10 −2 to 1.0 × 10 +0 eV.The sensitivity of the uranium-fueled light-water-moderated system is similar in this energy region.However, the sensitivity of the MOX-fueled light-water-moderated system depends on the benchmark case.This sensitivity difference affects the Δk/k for H in H 2 O of the MOX fuel.

Criticality of solution systems
Figures 5 and 6 show the C/E values of the low and the high enriched uranium-fueled solution systems, i.e.LST and HST benchmarks in Table 1.The C/E values of JENDL-5 in the low enriched uranium solution system are slightly smaller than those of the other libraries.However, the largest difference is less than 0.5%.As shown in Figure 6, the C/E values become worse for the systems whose the H/U ratio is from 400 to 1,300.These larger differences are also found in the other libraries.
The reason why the C/E values of JENDL-5 in the low enrichment uranium solution system are slightly smaller than those of JENDL-4.0 may be due to the difference in the cross section of H in  4, the sensitivities of the LST systems in the range around 1.0 × 10 −1 eV are different from those of LCT and MCT systems.The differences in the cross section of H in H 2 O may be the cause of the difference in the k-effective values between JENDL-5 and JENDL-4.0.
Figure 7 shows the C/E values of the plutoniumfueled solution system, i.e.PST benchmarks in Table 1.The C/E values of JENDL-5 are smaller than those of JEND-4.0 and the average difference is 0.58%.The average C/E values of JENDL-4.0,ENDF/B-VII.1, ENDF/B-VIII.0,and JENDL-5 are 1.00604, 1.00576, 1.00107, and 1.00020, respectively.These results indicate that the calculation accuracy of JENDL-5 for the plutonium-fueled solution systems is better than that of the other libraries.

Criticality of uraniuum-fueled graphite-moderated systems
The C/E values of the criticality of the VHTRC benchmark are calculated, and the comparisons between the measured and calculated critical control rod positions are performed for HTTR 30 column core at room temperature, in order to reveal the calculation accuracy of JENDL-5 for uranium-fueled graphitemoderated systems.
(a) VHTRC Figure 8 shows the C/E values of the criticality measured at VHTRC for five core temperature points of 25.5°C, 71.2°C, 100.9°C, 150.5°C, and 199.6°C in Ref. 37. In the calculations with ENDF/B-VIII.0 and JENDL-5, the thermal scattering law data of 30%porous graphite was selected since the porosity of the graphite moderator used in VHTRC was approximately 26% [62].It should be noted that and JENDL-5 thermal scattering law data of graphite is the same as ENDF/B-VIII.0.Whereas, the thermal scattering law data for ideal crystalline graphite were used in the calculations with ENDF/B-VII.1 and JENDL-4.0.The C/E values of JENDL-5 are almost within the uncertainty of the C/E values.In addition, JENDL-5 shows a smaller temperature dependence than the other nuclear data libraries.The calculation accuracy of JENDL-5 is generally equivalent to that of JENDL-4.0 in this calculation.The average C/E values of JENDL-4.0,ENDF/B-VII.1, ENDF/B-VIII.0,and JENDL-5 are 0.995 ± 0.003, 0.999 ± 0.003, 1.008 ± 0.003, and 1.004 ± 0.003, respectively.Among the four nuclear data libraries, JENDL-5 showed the second best calculation accuracy in this calculation.(b) HTTR Figure 9 shows the calculation results of the criticalities.In the calculations with ENDF/B-VIII.0 and JENDL-5, the thermal scattering law data of graphite for 30%-porous graphite is selected since the porosity of the graphite moderator used in HTTR is approximately 21% [62].The criticality is calculated at 1 mm intervals at the control rod position, and the point where the criticality is closest to unity is considered to be the calculated critical control rod position.Here, the control rod positions in HTTR are defined as the heights from the bottom of the lowest fuel region to the bottom of the control rod.The lightly colored area between the two dotted lines in the figure represents the measured control rod position with the measurement errors.The solid line in the middle of the area corresponds to the average value, 1775 mm, for the critical control rod position measurement in Ref [63].Based on the results, the calculated critical control rod positions with each nuclear data library are summarized in Table 7.The deviations between the measured critical control rod positions and calculated critical control rod positions with JENDL-4.0,ENDF/ B-VII.1,ENDF/B-VIII.0,and JENDL-5 are +74 , +64 , −8, and 12 mm, respectively.The calculation accuracies with ENDF/B-VIII.0 and JENDL-5 are approximately equal to each other.The calculated  critical control rod position with JENDL-5 is 62 mm lower than that with JENDL-4.0.This is close to the measured value of 1775 mm.These results indicate that the calculation accuracy of JENDL-5 for the uranium-fueled graphitemoderated systems is relatively better than that of the other libraries.

Criticality of small-sized fast systems
Figure 10 shows the C/E values of criticalities of smallsized fast systems.These systems are composed of metallic 235 U, 239 Pu, or 233 U fuel without any reflector materials.The C/E values of JENDL-5 without the Big Ten result are close to or within the uncertainty of the C/E values.Table 8 shows the difference in the k-effective values (Δk/k) for crude sensitivity analysis; each nuclide is changed from JENDL-5 to JENDL-4.0 or ENDF/B-VIII.0.As shown in Table 8, further modifications of 235 U and 238 U may be required to improve the C/E value of the Big Ten result.However, the C/ E-1 value of the Big Ten result of JENDL-5 is less than 0.4%.

Criticality of Middle-and Large-sized Fast Systems
Figure 11 shows the C/E values of criticalities of middle-and large-sized fast systems; the systems are ordered with a small contribution of 239 Pu to the fission reaction on the left side.The Monte Carlo method is employed for all benchmarks except for Monju, in which the sensitivity analysis method is employed.JENDL-5 results agree with the experimental values within the experimental uncertainty except for BFS-62-5 and Joyo MK-II; the deviations are, however, small.Comparing with the JENDL-4.0 results, one can observe that JENDL-5 improves the prediction accuracy of criticalities for the MOX systems whose Pu contribution is relatively large.These results indicate that JENDL-5 maintains or slightly improves the performance of JENDL-4.0.
The sensitivity analysis revealed that the main reason for the larger C/E values of BFS experiments was the revision of the cross section of 235 U fission.Similarly, the main reason for the smaller C/E values of ZPPR-9 and ZPPR-10A was the revision of the cross section of 239 Pu fission.

Sodium-void reactivity worth of ZPPR-9, BFS, and FCA
As with the validation of JENDL-4.0 [11], we utilized three sodium-void reactivity worth data provided in the IRPhEP handbook for ZPPR-9, which are identified as step 3, step 4, and step 5, for the present benchmark.In the IRPhEP handbook, six sodium-void reactivity worth data are provided.These are defined as zone cumulative reactivities, and voided regions are spreading as a void step proceeds.These sodium-void reactivity worths are calculated with MVP3.The sodium-void reactivity worths of BFS are defined as zone-wise reactivities, and the reactivity worths are given for each fuel region: low-enriched uranium, intermediate-enriched uranium, high-enriched uranium, or mixed-oxide region.Note that these calculations are conducted for the most detailed model, in which three-dimensional fuel drawers are exactly treated without any simplifications as well as the validation of JENDL-4.0.As for BFS, new MVP input files were prepared and used in the present benchmark.
Figure 12 shows the C/E values of the sodium-void reactivity worths of ZPPR-9.The error bars attached to the C/E values indicate the statistical uncertainties of the Monte Carlo calculations.There is a slight tendency to overestimate in JENDL-4.0.This tendency has not improved but it has not worsened in JENDL-5. Figure 13 shows the results of the sodium-void reactivity worths of BFS.From this figure, it can be seen that JENDL-5 maintains the performance of JENDL-4.0.
Integral experiments for the validation of 235 U cross sections were conducted at FCA in an intermediate Step 3 Step 4 Step 5 Step 3 Step 4 Step 5 system composed of low and high enriched uranium metals and graphite [40].The sodium-void reactivity worths were measured by voiding sodium plates loaded in the test zone in the center of the core.The data are sensitive in keV energy region of 235 U capture cross section as well as to sodium ones.While the data include the three cases with different sizes of voided zone, only two cases with relatively large experimental values were used for this benchmarking.
The sodium-void reactivity worths of FCA were calculated with MVP3.These calculations were conducted for the most detailed model.Figure 14 shows the C/E values of the sodium-void reactivity worths of FCA.Note that the y-axis range in Figure 14 is larger than that in the other figures.This is because the experimental uncertainties in Figure 14 which are shown by gray dash lines are larger than those in the other figures.The comparison of the experimental uncertainty and the C/ E value is important to estimate the prediction accuracy.While JENDL-4.0 slightly overestimates reactivity worths, JENDL-5 results in good agreement with the experimental values.Supplementarily, this figure gives the calculation results by JENDL-4.0 for only 235 U (or Na) and JENDL-5 for other nuclides.As shown in Figure 14, the improvement by JENDL-5 is due to the re-evaluation of sodium cross sections as well as due to that of 235 U ones.

Control rod worth of ZPPR-10A
The same experimental data of ZPPR-10A in the IRPhEP handbook as the JENDL-4.0 benchmark [11] were used.The handbook provides four cases of benchmark data of control rod worth in ZPPR-10A, whose cases are identified as CR01, CR02, CR03, and CR04.These control rod worths are calculated with MVP3 as well as the JENDL-4.0 benchmark.Figure 15 shows the C/E values.This figure shows that JENDL-5 maintains the performance of JENDL-4.0.

Doppler reactivity worth of ZPPR-9 and SEFOR
As well as the validation of JENDL-4.0, the benchmark data for the Doppler reactivity worths of ZPPR-9 and SEFOR were used.The benchmark data of sample Doppler reactivity worth of ZPPR-9 are taken from the IRPhEP handbook, which provides the Doppler reactivity worths measured at five different temperatures.The SEFOR benchmark data contains wholecore Doppler reactivity worth of two different cores, i.e.Core I and Core II.In these measurements, the core temperature was increased from 678 to 1,366 K in both cores.All these Doppler reactivity worths were calculated using the deterministic procedure as well as the JENDL-4.0 benchmark [11].Figure 16  a relative difference of 5%, and JENDL-5 maintains the performance of JENDL-4.0.

Reaction rate distribution of ZPPR-10A
As with the JENDL-4.0 benchmark [11], the reaction rate spatial distributions of ZPPR-10A were calculated for the following reactions: 239 Pu fission (F49), 235 U fission (F25), 238 U fission (F28), and 238 U capture (C28).The radial distributions along the x-and y-axes were calculated, and then a C/E value for each spatial point was normalized at a C/E value of each reaction rate at the core center position (matrix position 149-45).In this calculation, cell factors provided in the IRPhEP handbook were applied in order to convert drawer-averaged reaction rates to the mapping foil data at the actual irradiating position in drawers.We calculated the cell factors with JENDL-5 and confirmed that the differences from the values provided in the handbook were small and negligible.
Figure 17 shows the C/E values at the most outer drawer in the inner core region (IC) and those at the center drawer in the outer core region (OC) for all the reactions.In this figure, X and Y in parentheses mean the X and Y directions in the core, respectively.Regarding the reaction rate distribution, JENDL-5 maintains the performance of JENDL-4.0.

Spectrum index C28/F49 of ZPPR-10A
The benchmark results of a spectrum index C28/F49 which is the reaction rate ratio of 238 U capture to 239 Pu fission were calculated.This characteristic corresponds to a breeding ratio of fast reactors.The IRPhEP handbook provides benchmark data for spatial-dependent spectrum indices.Figure 18 shows region-and direction-averaged C/E values of the spectrum index; it can be seen that JENDL-5 slightly overestimates compared with JENDL-4.0.The sensitivity analysis revealed that the revisions of both the 239 Pu fission cross section and the 238 U capture cross section contributed to the overestimation but the main contributor was the 239 Pu fission cross section.

Spectrum index F42/F49 and F64/F49 of BFS
In the present benchmark, some of the spectrum indices of TRU measured in BFS were used.The sensitivity analysis method was employed for these calculations.This section shows the benchmark result of a spectrum index F42/F49 which is the reaction rate ratio of 242 Pu fission to 239 Pu fission and that of a spectrum index F64/F49 which is the reaction rate ratio of 244 Cm fission to 239 Pu fission.
Figure 19 shows the C/E values of F42/F49; the BFS systems are ordered with a small contribution of 239 Pu fission reaction to the criticality at the left side.Some of the JENDL-4.0 results do not match with the experimental ones within the experimental uncertainty, and the average of the five C/E values is greater than unity.In contrast, the average of the five C/E values of JENDL-5 is closer to unity than those of JENDL-4.0, although some of those of JENDL-5 are underestimated.These results indicate that JENDL-5 improves the overestimation of JENDL-4.0.Sensitivity analysis revealed that this improvement was due to the revision of the 242 Pu fission cross section.
Figure 20 shows the C/E values of F64/F49.It was known that JENDL-4.0 overestimates this spectrum index [17].This figure shows that JENDL-5 significantly improves the overestimation.The sensitivity analysis revealed that the revision of the 246 Cm fission cross section mainly contributed to the improvement.

Lead-void reactivity worth of fast systems at the comet critical assembly
The lead-void reactivity worths at the Comet critical assembly were calculated with MCNP6.2.These calculations were conducted for the most detailed model.Figure 21 shows the C/E values of lead-void reactivity worths of the three fast systems.The C/E values of JENDL-5 are close to or within the uncertainty for the HEU/Pb and LEU/Pb systems but are still overestimated by more than 20% for the Pu/Pb system.It was reported that the large discrepancy for the Pu/Pb system between JENDL-4.0 and ENDF/B-VIII.0are not due to differences in lead cross sections but due to other nuclides including 239 Pu [42].

PIE analysis of fast systems
The IR of the 241 Am capture reaction strongly affects the atomic number densities of the Am and Cm Am-241 (Am-241 sample) Am-241 capture' indicates the atomic number density ratio of 242m Am to 241 Am, which is sensitive to the 241 Am capture cross section, in the 241 Am sample.Figure 23 shows the C/E values related to capture cross-sections of 241 Am, 243 Am, and 244 Cm; JENDL-5 gives the similar trend as JENDL-4.0 at the core midplane position, whereas the 241 Am, 243 Am, and 244 Cm capture cross section of JENDL-5 affects the results at the upper reflector position.The prediction accuracy of JENDL-5 is however comparable to that of JENDL-4.0. Figure 24 shows the C/E values related to capture cross-sections of 237 Np, 242 Pu, and 241 Am; the results of JENDL-5 are almost identical to those of JENDL-4.0. Figure 25 shows the C/E values related to capture cross-sections of 243 Am, 245 Cm, and 246 Cm; JENDL-5 improves the calculated results by about 14% and 10%.Accordingly, JENDL-5 has produced good calculation results for Joyo MK-II and PFR MA sample irradiation tests.

Conclusions
Benchmark testing for the newly developed Japanese evaluated nuclear data library JENDL-5 has been carried out by using hundreds of criticality experiments contained in the ICSBEP and IRPhEP handbooks and measured at the various experimental facilities in Japan.Benchmark calculations were mainly performed with the continuous-energy Monte Carlo codes MVP3 and MCNP6.2 and the deterministic code system MARBLE.
As results of the benchmark testing of JENDL-5, the following conclusions have been derived.
• The C/E-1 and chi-squared values of JENDL-5 for the criticality of the thermal system are close to those of ENDF/B-VIII.0.• The effects of the modification of 155 Gd and 157 Gd cross section in JENDL-5 cancel each other.
• JENDL-5 maintains or slightly improves the good performance of JENDL-4.0 for the criticality, the sodium-void reactivity worth, the control rod worth, the Doppler reactivity worth, and the reaction rate distribution of middle-and largesized fast systems.

Figure 14 .
Figure 14.C/E values of sodium-void reactivity worth of an intermediate system.K. Tada JENDL-5 Benchmarking for Fission Reactor Applications

Figure 24 .Figure 25 .
Figure 24.C/E values related to capture cross-sections of 237 Np, 242 Pu, and 241 Am for the MA sample irradiation tests in PFR.K. Tada JENDL-5 Benchmarking for Fission Reactor Applications

Table 1 .
Benchmark list for the benchmark test in the ICSBEP handbook for the validation of JENDL-5.

Table 2 .
Parent and daughter nuclide to be analyzed for the validation of capture cross sections.

Table 3 .
Average of C/E-1 values and the chi-square values of the ICSBEP benchmark calculations.

Table 4 .
The δk/k values of uranium-fueled light-water-moderated system when each nuclide is changed from JENDL-5 to JENDL-4.0.

Table 5 .
The δk/k values of MOX-fueled light-water-moderated system when each nuclide is changed from JENDL-5 to JENDL-4.0.
Figure 6.C/E values of criticalities of high enriched uranium-fueled solution systems.K. Tada JENDL-5 Benchmarking for Fission

Table 6 .
The δk/k values of LST20 and LST21 when each nuclide is changed from JENDL-5 to JENDL-4.0.
Figure 7. C/E values of criticalities of low enriched plutonium-fueled solution systems.K. Tada JENDL-5 Benchmarking for Fission Reactor Applications

Table 7 .
The calculated criticality and critical control positions of HTTR.