Monte Carlo burnup analysis of measured nuclide inventories on high-burnup PWR-UO2 and BWR-MOX fuels in the RUBUS program

ABSTRACT To validate the nuclear data in JENDL-4.0 and obtain information to improve their accuracy, the analysis of the measured nuclide inventories of the high-burnup PWR UO2 and BWR MOX fuels in the REBUS program was performed by using MVP-BURN with the nuclear library and burnup chain based on JENDL-4.0, and the ratios of the calculated and measured inventories (C/Es) were compared with the previous results obtained with JENDL-3.2 or JENDL-3.3. As a result, an improvement in the accuracy of the neutron cross-sections and cumulative fission yields (CFYs) in JENDL-4.0 was confirmed for the inventories of 236U, 238Pu, 239Pu, 241Pu, 242Pu, 241Am, 243Cm, 244Cm, 133Cs, 145Nd, 148Sm, 149Sm, 151Sm, and 153Eu of the PWR UO2 fuel and 239Pu, 241Pu, 242Pu, 241Am, 243Am, 243Cm, 244Cm, 246Cm, 134Cs, 144Ce, 145Nd, 147Sm, and 154Eu of the BWR MOX fuel. Based on the C/Es obtained with JENDL-4.0, the directions to improve the neutron cross-sections and CFYs were tentatively proposed. They included the neutron capture cross-sections of 234U, 236U, 237Np, 238Pu, 241Am, 242Cm, 245Cm, 143Nd, 147Pm, 154Eu, and 155Eu, the fission cross-sections of 243Cm and 245Cm, and the CFYs of 144Nd, 147Pm, and 155Eu. GRAPHICAL ABSTRACT


Introduction
The REBUS 1 program was implemented to provide a comprehensive experimental database for the validation of the burnup calculations of light water reactor fuels [1].A unique feature of the program was the direct measurements of the reactivity differences between the fresh and irradiated fuels by using the VENUS light-water moderation critical facility in the Belgian Nuclear Research Center, SCK/CEN.The experiments included the radio-chemical assay of the nuclide inventories in the high-burnup UO 2 and MOX fuel samples that were taken from the 18 × 18 UO 2 fuel assembly irradiated in the GKN II 2 reactor, one of the pressurized water reactors in Germany, and the 9 × 9 MOX fuel assembly irradiated in the Gundremmingen-C reactor, one of the boiling water reactors in Germany.Hereafter, they are referred to as the 'GKN-UO 2 fuel' and 'GUN-MOX fuel,' respectively.The enrichment and burnup of the GKN-UO 2 fuel were 3.80 wt% and 55 GWd/t [2], and the fissile plutonium isotope ( 239 Pu and 241 Pu) content and burnup of the GUN-MOX fuel were 5.52 wt% and 70 GWd/t [3].The experimental data of the REBUS program were compiled in the reports published by the Japan Nuclear Energy Safety Organization [2,4].The experimental data have been analyzed by the organizations that participated in the program to validate the burnup calculation codes used by the organizations.
The measured nuclide inventory data of irradiated fuels are useful to validate the nuclear data involved in the burnup calculations such as neutron cross-sections, fission yields, and decay data.As the validation studies with the Japanese evaluated nuclear data libraries, the author et al. [5]  analyzed the measured nuclide inventories of the GKN-UO 2 fuel with the Pij module in the SRAC2006 code system [6] and the 107-neutron energy group library based on the JENDL-3.2[7].In this analysis, a single fuel cell model (hereafter, it is referred to as the 'cell model.')with a representative fuel rod pitch was used to save the calculation cost.Ando et al. [3] analyzed the measured nuclide inventories of the GUN-MOX fuel with the SRAC2006 code system [6] and the continuous energy Monte Carlo burnup calculation code MVP-BURN [8] with the nuclear library based on JENDL-3.3 [9].They applied an infinite fuel assembly model (hereafter, it is referred to as the 'assembly model.')and a multi-fuel assembly model (hereafter, it is referred to as the 'multiassembly model.')that was a 3 × 3 assembly model with one MOX fuel assembly at the center position surrounded by eight UO 2 fuel assemblies.The multi-assembly model improved the modeling of the burnup condition for MOX fuel assemblies irradiated in the cores partly loaded with MOX fuel assemblies.The author et al. [10] analyzed the GKN-UO 2 and GUN-MOX fuels with CASMO5 [11] coupled with the nuclear library based on JENDL-4.0 by using the assembly and multi-assembly models.
The continuous energy Monte Carlo burnup calculation codes have been used to obtain the precise comparison results between the calculated and measured nuclide inventories for improving the accuracy of the nuclear data.The purpose of the present study is to validate the nuclear data in JENDL-4.0 and obtain information to improve their accuracy by analyzing the measured nuclide inventories of the GKN-UO 2 and GUN-MOX fuels by using MVP-BURN [8] with the nuclear library and the burnup chain based on JENDL-4.0 [12] and comparing the results with the previous results obtained with JENDL-3.2 [7] or JENDL-3.3 [9].Section 2 outlines the nuclide inventory measurements of the GKN-UO 2 and GUN-MOX fuels, Section 3 describes the burnup calculations, Section 4 provides the comparison between the calculated and measured nuclide inventories, and Section 5 mentions the conclusions.

Nuclide inventory measurements of GKN-UO 2 and GUN-MOX fuels
The GKN-UO 2 fuel was taken from the fuel rod M11 in the 18 × 18 UO 2 fuel assembly which was irradiated in the GKN II reactor for four cycles.The fuel rod configuration in the 18 × 18 UO 2 fuel assembly is shown in Figure S1 in the supplemental online material accompanying this manuscript.The height of the fuel sample was between 301.9 cm and 305.0 cm from the bottom end of the effective fuel length which was 390 cm.The GUN-MOX fuel was taken from the fuel rod C7 in the 9 × 9 MOX fuel assembly which was irradiated in the Gundremmingen-C reactor for six cycles.The fuel rod configuration in the 9 × 9 MOX fuel assembly is shown in Figure S2 in the supplemental online material accompanying this manuscript.The height of the fuel sample was between 231.7 cm and 235.3 cm from the bottom end of the effective fuel length which was 371 cm.The main specifications of the fuel assemblies are listed in Table S1 in the supplemental online material accompanying this manuscript.
The measured nuclides are listed in Table 1 [2].The measurements were performed at the hot laboratory in SCK/CEN.The cooling times from the end of irradiation were from 7.1 years to 7.8 years for the GKN-UO 2 fuel and from 4.7 years to 5.5 years for the GUN-MOX fuel.The measurement results and the measurement errors of the GKN-UO 2 fuel in a unit mg/gU-238 were taken from the reference [2].Those of the GUN-MOX fuel were obtained from the results in a unit mg/ g-fuel [2].

GKN UO 2 fuel
The burn-up calculations of the GKN-UO 2 fuel were performed by using MVP-BURN [8] with the JENDL-4.0 [12] base library.A general burnup chain model ChainJ40 (u4cm6fp119bp14T) developed by Okumura et al. [13] based on JENDL-4.0 [12] was used.To be more specific, the nuclear library used in the calculations was based on the partly revised version of JENDL-4.0,JENDL-4.0u1[12,14].In the cell model, the fuel rod pitch of 1.312 cm was the same as in the previous study [5].In addition to the cell model, the assembly model was also adopted to improve the accuracy of modeling the irradiated fuel.The dimensions and atomic number densities of the elements composing the fuel assembly were obtained by referring to Table S1 and the reference [2].Taking into account that the fuel pellets have cracks during irradiation, the fuel pellets were smeared to fill the gaps between the fuel pellets and fuel claddings, and the fuel claddings were kept in the initial condition during irradiation.In the assembly model, the different burnup regions were allocated to all the fuel pellets of the fuel rods in the fuel assembly.However, the same burnup regions were allocated to the fuel pellets of the fuel rods which were located at the symmetry positions in the fuel rod configuration.One burnup region was arranged for the UO 2 fuel pellets and ten radial burnup regions with an equal volume were arranged for the UO 2 -Gd 2 O 3 fuel pellets.
In the cell model, the operating history of the fuel power was taken from the reference [2] that specified it for each operating cycle.In the assembly model, the power history of the assembly-average power was necessary.Since it was not available in the reference [2], the fuel power history of the GKN-UO 2 fuel was used as the assembly-average power for the first trial and it was modified so that the calculated burnup of the GKN-UO 2 fuel was close to the measured fuel burnup of 54.7 GWd/t.The measured fuel burnup was determined by multiplying the conversion factor based on the calculated effective energy release per fission and the atomic percent fission (%FIMA: number of fissions per initial metallic atom in percent) which was provided by the REBUS program organizer who determined the %FIMA by using the measured nuclide inventories of the burnup indicators ( 137 Cs, 144 Ce, and Nd isotopes) and those of heavy nuclides [2].The boron concentrations in the moderator were altered in the early period and the later period in each operating cycle.The representative boron concentration for each period was obtained by averaging the history data [2].The histories of the fuel power, assembly-average power, and boron concentrations are listed in Table S2 in the supplemental online material accompanying this manuscript.The temperature of the fuel pellets was set to be 566°C and that of the moderator was set to be 320°C.They were obtained using operating history data [2] as the average values during the operating period for the axial location of the fuel in the fuel assembly.The temperature of the fuel claddings was set to be the same as that of the moderator.For the temperatures of the fuel pellets and the fuel claddings and moderator that were set to be constant during irradiation, the sensitivity analysis of the calculated isotopic inventories to those temperatures was performed and the results are listed in Table S3 in the supplemental online material accompanying this manuscript.
The burnup calculations were performed with the Predictor-Corrector option [8].The operating histories of the boron concentrations in the moderator, the temperatures of the moderator, and the fuel temperatures were reported every 30 days [2].The burnup steps were set to 30 days for the first cycle and 60 days for the rest of the operating period.As a result, the burnup steps were less than 1.8 GWd/t until the burnable poison burned and less than 3.0 GWd/t after this burnup.In each burnup step, the effective neutron histories of 400,000 with 10,000 neutron histories per batch and ten skip batches were calculated.To estimate the uncertainties in the calculated inventories with the assembly model, five runs were performed with different initial random numbers.The average values and the standard deviations of the calculated nuclide inventories were obtained.The standard errors in the average values were obtained by dividing the standard deviations by the square root of five.
As explained later in Section 4, the calculations targeting the measured burnup of 54.7 GWd/t systematically overestimated the inventories of some of the burnup-indicator Nd isotopes by 1 to 3%.It was considered that the actual number of fissions in the fuel was slightly smaller than those in the calculations.Therefore, an additional calculation with the JENDL-4.0 base library in the assembly model was performed to reproduce the measured inventory of 148 Nd which is commonly used to determine the number of fissions based on the measured inventories of heavy isotopes and 148 Nd [15].The additional calculation also provides the sensitivity of the nuclide inventories to the fuel burnup.

GUN MOX fuel
For the GUN-MOX fuel, the assembly and multiassembly models were adopted as the previous study [3].In the multi-assembly model, the UO 2 fuel assemblies surrounding the MOX assembly were the 9 × 9 − 1 fuel assemblies which were each composed of the eighty irradiated fuel rods with an average fuel enrichment of 3.14 wt% and one water rod.The assembly average burnup of the UO 2 fuel assembly was 19.2 GWd/t, which was decided from the burnup information on the fuel assemblies surrounding the MOX fuel assembly for the six cycles to represent the burnup of the surrounding fuel assemblies [2].
The operating histories of the power of the fuel rod C7 and the in-channel void fractions of the fuel assembly were reported at the time steps of from ten days to twenty days [2].The burnup steps were set to about 30 days for the first cycle and the first half of the second cycle, and about 60 days for the rest of the operating period.As a result, the burnup steps were less than 1.8 GWd/t until the burnable poison burned and less than 3.0 GWd/t after this burn-up.
In the assembly and multi-assembly models, the power history of the assembly-average power was necessary.For the first trial, the fuel power history of the GUN-MOX fuel was used as the assembly-average power and it was modified so that the calculated burnup of the GUN-MOX fuel was close to the measured fuel burnup of 69.90 GWd/t which was reevaluated by Ando et al. [3].The in-channel void fractions were altered in the early period and the later period in each operating cycle.The representative in-channel void fraction for each period was obtained by averaging the history data [2].The histories of the assembly-average power and the in-channel void fraction are listed in Table S2 in the supplemental online material accompanying this manuscript.The temperatures of the fuel claddings and the moderator were set to 268°C [2].The temperature of the moderator was that of the saturated steam and water for the dome pressure 7.06 MPa of the Gundremmingen-C reactor [2].As a nature of the boiling water reactors, the change in the moderator temperature is relatively small and the change in the assembly power during irradiation causes that in the in-channel void fraction.The history of the in-channel void fractions was taken into account in the present burnup calculations as mentioned before.Since the operating history of the fuel pellet temperature was not available, it was set to 520°C [2].For the fuel pellets temperature that was set to be constant during irradiation, the sensitivity of the calculated isotopic inventories to the pellet temperature were performed and the results are listed in Table S3 together with that to the moderator temperature in the supplemental online material accompanying this manuscript.
The effective neutron histories and the skip batches at each burnup step were the same as those of the GKN-UO 2 fuel.In the multi-assembly model calculation, five runs were performed with different initial random numbers to estimate the uncertainties in the calculated inventories.
As explained later in Section 4, the calculations with the JENDL-4.0 base library targeting the measurement value 69.90 GWd/t systematically underestimated the inventories of some of the burnup-indicator Nd isotopes by 1 to 2%.To obtain additional information on the accuracy of the calculated inventories, the calculation with the JENDL-4.0 [12] base library in the multiassembly model was performed to reproduce the measured inventory of 148 Nd.The additional calculation also provides the sensitivity of the nuclide inventories to the fuel burnup.

Comparison between calculated and measured nuclide inventories
The burnups in the calculations are listed with the measured values in Table 2 including those in the calculations targeting the measured 148 Nd inventory.Figures 1, 2 , and 3 show the comparison results of the GKN-UO 2 and GUN-MOX fuels between the calculated and measured inventories for the actinide nuclides, the light fission product nuclides, and heavy fission product nuclides, respectively.The comparison results are shown in (the calculated result/the measured result − 1) (C/E − 1).The figures of the GKN-UO 2 fuel also show the results in the previous study [5] with JENDL-3.2 in the cell model to investigate the differences in the C/E − 1s with the two libraries.The fuel burnup in the previous calculation with JENDL-3.2 was 54.4 GWd/t.It was determined by the gamma-ray measurement and was smaller by 0.6% than the measured burnup (54.7 GWd/t) [5] determined by the isotopic inventory measurement of 148 Nd and the heavy isotopes.The burnup of 54.4 GWd/t was between the measured burnup and the calculated burnup of 54.03 GWd/t for the calculation targeting the measured 148 Nd inventory.The effect of the difference of 0.6% in the burnups on the nuclide inventories was almost half of the effect of the difference between the calculation targeting the measured burnups and that targeting the measured 148 Nd inventory.The effect of the 0.6% difference in the burnups on the nuclear inventory can be estimated by multiplying 0.5 to the differences in the C/E − 1s between the  the multi-assembly model for the GUN-MOX fuel mean those targeting the measured burnups.
The inventories of some of the nuclides are influenced by the neutron energy spectra under which the fuel is irradiated.To help the interpretation of the differences in the C/E − 1s, the neutron energy spectra in 108 energy groups at the beginning of irradiation and the last irradiation cycle were calculated for the GKN-UO 2 and GUN-MOX fuels with MVP3 [14].The calculation conditions were the same as those in MVP-BURN except for the number of neutron histories.For the cell model of the GKN-UO 2 fuel and the assembly model of the GUN-MOX fuel, the effective 4,000,000 neutron histories with 10,000 neutron histories per batch and 100 skip batches were calculated.For the assembly model of GKN-UO 2 fuel and the multi-assembly model of the GUN-MOX fuel, the effective 20,000,000 neutron histories were calculated.
They are illustrated in Figure 4.As seen in the figure of the GKN-UO 2 fuel, the neutron energy spectrum with the assembly model was harder than that with the cell model.For the GUN-MOX fuel, the neutron energy spectrum with the multi-assembly model was softer than that with the assembly model under the influence of the surrounding UO 2 fuel assemblies.
In the following discussion on the comparison of the C/E − 1s of the nuclide inventories, the study on nuclear data sensitivity of the nuclide inventories reported by Oizumi et al. [16] was referred to.They summarized the nuclear-data sensitivity of the nuclide inventories after burnup of the UO 2 and MOX fuels of light water reactors.The analysis method was based on the generalized perturbation theory with JENDL-4.0 [12] and a multi-purpose reactor analysis code MARBLE [17].They focused on the inventories of the 18 actinide nuclides and 35 fission-product.The sensitivities were calculated for the neutron cross-sections, half-lives, and fission yields for the 21 actinide and 104 fissionproduct nuclides.They also presented the important trends in the sensitivities and discussed their physical mechanisms.In the present study, the improving directions of the neutron cross-sections and fission yields in JENDL-4.0 were discussed to make the C/E − 1s of the nuclides close to zero based on the nuclear data sensitivities of the nuclide inventories reported by Oizumi et al. [16].
The neutron cross-sections and fission yields described in the present study were limited to those with relatively large sensitivities.The differences in the thermal neutron crosssections and the resonance integrals of the neutron cross-sections (RI) of the nuclides related to the present study between JENDL4.0 [12], JENDL-3.3 [9], and JENDL-3.2 [7] were investigated.They are listed in Tables S4 and S5 in the supplemental online material accompanying this manuscript.

U-234
In the irradiated UO 2 fuel, a large part of the inventory of 234 U is a residual in the initial content after the elimination by neutron capture, and part of the inventory is produced by α-decay of 238 Pu (T 1/2 : 87.7 y).Here, T 1/2 means a half-life.In the analysis of the GKN-UO 2 , the C/E − 1s with JENDL-4.0 were 10%.It was larger by about 9% than that with JENDL-3.2.The differences in the cross-sections between JENDL-4.0 and JENDL-3.2 were considered to contribute to the different C/E − 1s.They were as follows: the RI of the neutron capture cross-section of 234 U in JENDL-4.0 is smaller by 3.5%, the RI of the neutron capture cross-section of 235  In the irradiated MOX fuel, a large part of the inventory of 234 U is produced by α-decay of 238 Pu.In the analysis of the GUN-MOX fuel, the C/E − 1 of 234 U with JENDL-4.0 was 9%.It was larger by 12% than that with JENDL-3.3.The differences in the neutron cross-sections between JENDL-4.0 and JENDL-3.3 were also examined.As a result, the neutron crosssection of 241 Am was assigned in addition to the neutron cross-sections of 234 U, 237 Np, and 238 Pu since the thermal neutron capture cross-section and RI of 241 Am in JENDL-4.0 are larger by 7% and 9%, respectively.The thermal neutron capture crosssections and RIs of 234 U, 237 Np, and 238 Pu in JENDL-3.3 are the same as those in JENDL-3.2, or the differences are small.The larger neutron capture crosssection of 241 Am increased the inventory of 238 Pu via 241 Am(n, γ) 242m Am(IT, 141 y) 242 Am(β − , 16.02 h) 242 Cm(α, 162.94 d) 238 Pu.
To make the C/E − 1s of 234 U close to zero, the directions improving the neutron cross-sections in JENDL-4.0 were considered based on the nuclear data sensitivities of the nuclide inventories reported by Oizumi et al. [16].They were a larger neutron capture cross-section of 234 U and 238 Pu, a smaller neutron capture cross-section of 238 U and 241 Am, and a larger fission cross-section of 241 Pu.The sensitivity of the inventory of 234 U to the neutron capture crosssection of 238    U was created by the α-decay chain: 242 Cm to 238 Pu to 234 U, and the inventory of 242 Cm was sensitive to the neutron capture cross-section of 238 U [16].

U-235
The inventory of 235 U in the irradiated UO 2 fuel is mainly a residual in the initial content after the elimination by neutron absorption.In the analysis of the GKN-UO 2 fuel, the C/E − 1s of 235 U with JENDL-4.0 were − 1% for the assembly model and − 3% for the cell model.That with JENDL-3.2 was 1%.The difference in the C/E − 1s observed between the assembly and cell models with JENDL-4.0 was due to the difference in the neutron energy spectra in the assembly and cell models at the early irradiation period as shown in Figure 4. Similar differences in the inventories between the assembly and cell models were reported by the authors et al. [5] in the results of the calculations with SRAC2006 [6] and the library based on the JENDL-3.2.
The inventories of 235 U were sensitive to those of fissile plutonium isotopes.Looking at the difference in the C/E − 1s between JENDL-4.0 and JENDL-3.2 for 235 U and fissile plutonium isotopes, the C/E-1s with JENDL-4.0 were smaller than those with JENDL-3.2.This was considered due to the 1%-smaller neutron capture cross-section of 238 U in the thermal and resonance energy regions for JENDL-4.0 than that for JENDL-3.2.It made the neutron energy spectrum with JENDL-4.0 softer than that with JENDL-3.2.It brought a smaller buildup of fissile plutonium isotopes with JENDL-4.0 and a smaller residual of 235 U.The inventories of 235 U were also sensitive to the burnup of the fuel.The calculation targeting 148 Nd inventory resulted in a smaller fuel burnup by 1% than the measured burnup as shown in Table 2, and a positive value of the C/E-1s with JENDL-4.0.
In the analysis of the GUN-MOX fuel, the C/E − 1s of 235 U were 7% with JENDL-4.0 and similar to 6% with JENDL-3.3.The calculation targeting 148 Nd inventory resulted in a larger burnup by 1% than the measured burnup and the C/E − 1s of 4%.
The C/E − 1s obtained in the present study indicated the directions to improve the neutron crosssections in JENDL-4.0:larger fission and neutron capture cross-sections of 235 U and a smaller capture crosssection of 238 U, and a smaller fission cross-section of 239 Pu.

U-236
The main production path of 236 U is the neutron capture of 235 U.In the analysis of the GKN-UO 2 fuel, the C/E − 1 values of 236 U with JENDL-4.0 were − 1% for the assembly and cell models.That with JENDL-3.2 was − 6%.The neutron capture cross-section of 235 U in JENDL-4.0 is larger at the 0.3 eV resonance than that of JENDL-3.2 and the RI is larger by 4.5% while the differences in the thermal fission crosssections and RIs between JENDL-4.0 and JENDL-3.2 are less than 1%.The larger neutron capture crosssection of 235 U in JENDL-4.0 caused the larger C/E − 1 values.
The neutron capture cross-section of 235 U in JENDL-4.0 is close to that in JENDL-3.3.As a result, the difference in the C/E − 1s of 236 U with JENDL-4.0 and JENDL-3.3 was small in the analysis of the GUN-MOX fuel.
The C/E − 1s obtained in the present study indicated the directions to improve the neutron crosssections in JENDL-4.0: a larger neutron capture crosssection of 235 U, a smaller fission cross-section of 235 U, and a smaller neutron capture cross-section of 236 U.

Np-237
In the irradiated UO 2 fuel, the main production path of 237 Np is described by 235 U(n, γ) 236 U(n, γ) 237 U(β − , 6.752 d) 237 Np.In the analysis of the GKN-UO 2 fuel, the C/E − 1s of 237 Np with JENDL-4.0 were 21% for the assembly model and 22% for the cell model.That with JENDL-3.2 was 21% and the differences between JENDL-4.0 and JENDL-3.2 are small.The effect of the larger neutron capture cross-section of 235 U at the 0.3 eV resonance and 236 U at the 5.4 eV resonance in JENDL-4.0 compared with those in JENDL-3.2 increased the inventory of 237 Np and made the C/ E − 1 of 237 Np with JENDL-4.0 larger.However, the effect was almost compensated by the effect that the neutron capture cross-section of 237 Np in JENDL-4.0 is larger than that in JENDL-3.2 and it made the C/E − 1 of 237 Np with JENDL-4.0 smaller.The C/E-1 of the GKN-UO 2 fuel in the analysis with CASMO5 was isolated from those of the fuels other than the GKN-UO 2 fuel [10].The results in the present study were possibly caused by the relatively large systematic error in the measurement result.
In the irradiated MOX fuel, the production path by α-decay of 241 Am is added to the above-mentioned production path.In the analysis of the GUN-MOX fuel, the C/E − 1s of 237 Np with JENDL-4.0 and JENDL-3.3 were also large positive values.Since the radio-chemical assay of both fuels was performed at the same institute, the measurement results of both fuels may have a relatively large systematic error.The differences in the C/E − 1s between JENDL-4.0 and JENDL-3.3 for the GUN-MOX fuel were larger than those for the GKN-UO 2 fuel between JENDL4.0 and JENDL-3.2.It may be related to the difference in the neutron energy spectra in the fuels since the differences in the thermal neutron cross-sections and RIs between JENDL-3.2 and JENDL-3.3 for the influential nuclides are too small to explain the difference in the C/E − 1s between JENDL-4.0 and JENDL-3.3.
While the initial content of 238 Pu in the MOX fuel is reduced by neutron capture, it is added by the main production paths described by 237 Np(n, γ) 238 Np(β − , T 1/2 : 2.099 d) 238 Pu and 242 Cm(α, 162.94 d) 238 Pu.In the analysis of the GUN-MOX fuel, the inventory of 238 Pu at the end of irradiation is 1.65 times the initial content.A considerably large decrease in the thermal neutron capture cross-section (−24%) and RI (−4%) of 238 Pu of JENDL-4.0 compared with that in JENDL-3.3 contributed to the difference in the C/E − 1s same as the GKN-UO 2 fuel.
The C/E − 1s obtained in the present study indicated the directions to improve the neutron crosssections in JENDL-4.0:smaller neutron capture cross-sections of 235 U, 236 U, 237 Np, 239 Pu, 240 Pu, and 241 Am, a larger fission cross-section of 235 U, 239 Pu, and 241 Pu, and a larger neutron capture cross-section of 238 Pu.
In the MOX fuel, the initial content of 239 Pu is reduced by neutron absorption and added by neutron capture of 238 U.In the analysis of the GUN-MOX fuel, the inventory at the end of irradiation was 26% of the initial content.Looking at the difference in the C/E-1s of 239 Pu between JENDL-4.0 and JENDL-3.3, the C/ E-1 for JENDL-4.0 is 4% and smaller than 5% for JENDL-3.3.The differences in the C/E − 1s with JENDL-4.0 and JENDL-3.2 for the GKN-UO 2 fuel and JENDL-3.3 for GUN-MOX fuel were caused by the 1%-smaller neutron capture cross-section of 238 U in JENDL-4.0 in the thermal and resonance energy region as mentioned for 235 U.
The C/E − 1s obtained in the present study indicated the directions to improve the neutron crosssections in JENDL-4.0:smaller neutron capture crosssections of 238 U and 240 Pu, a larger fission and neutron capture cross-section of 239 Pu, and a smaller fission cross-section of 241 Pu.

Pu-240
The main production path of 240 Pu is the neutron capture of 239 Pu.The C/E − 1s of the GKN-UO 2 fuel were negative and the differences in the C/E − 1s between the assembly model with JENDL-4.0, the cell model with JENDL-4.0, and the cell model with JENDL-3.2 were small.
In the analysis of the GUN-MOX fuel, the inventory of 240 Pu was underestimated with JENDL-4.0.The C/E − 1s with JENDL-4.0 indicated the improving directions: larger neutron capture cross-sections of 238 U and 239 Pu, a smaller fission cross-section of 239 Pu, and a smaller neutron capture cross-section of 240 Pu.

Pu-241
The main production path of 241 Pu is the neutron capture of 240 Pu.For the GKN-UO 2 and GUN-MOX fuels, the C/E − 1s of 241 Pu were positive and the C/E − 1s with JENDL-4.0 were slightly smaller than those with JENDL-3.2 and JENDL-3.3.The main cause of the differences in the C/E − 1s between the libraries was the difference in the neutron capture cross-section of 238 U as mentioned for 235 U.The C/E − 1s with JENDL-4.0 indicated the improving directions: smaller neutron capture cross-sections of 238 U, 239 Pu, and 240 Pu, larger fission cross-sections of 239 Pu and 241 Pu, and a larger capture cross-section of 241 Pu.

Pu-242
The main production path of 242 Pu is the neutron capture of 241 Pu.The C/E − 1s in the analysis of the GKN-UO 2 and GUN-MOX fuels were negative or close to zero.The main cause of the differences in the C/E − 1s between JENDL-4.0 and JENDL-3.2 for the GKN-UO 2 was considered to be due to the difference in the neutron capture cross-section of 238 U as mentioned for 235 U.The softer neutron energy spectrum with JENDL-4.0 decreased the elimination of 242 Pu by neutron capture in the resonance energy region.The C/E − 1s with JENDL-4.0 indicated the improving directions: large neutron capture crosssections of 235 U, 239 Pu, 240 Pu, and 241 Pu, smaller fission cross-sections of 235 U, 238 U, 239 Pu, and 241 Pu, and smaller neutron capture cross-sections of 238 U and 242 Pu.

Am-241
Since the measurement of the inventory of 241 Am was performed after 7.3 years for the GKN-UO 2 fuel and 4.7 years for GUN-MOX fuel from the end of irradiation, 84% of the inventory of 241 Am for the GKN-UO 2 fuel and 66% for the GUN-MOX fuel was created by beta decay of 241 Pu after the end of irradiation.Therefore, the inventory of 241 Am is almost the product of the inventory of 241 Pu at the end of irradiation (almost the same as that at the measurement) and (1−e −λt ), where λ is the decay constant of 241 Pu and t is a cooling time (a period between the measurement and the end of irradiation).Therefore, the C/E − 1s of 241 Am was expected to be close to those of 241 Pu.However, the C/E − 1s of 241 Am are considerably larger than those of 241 Pu for both fuels.It may indicate that the measured inventories of 241 Am were unreasonably small compared with the calculated inventories.
Even though the C/E − 1s of 241 Am are considerably larger than those of 241 Pu, the interrelations in the C/E − 1s between the assembly and cell models with JENDL-4.0 and the cell model with JENDL-3.2 for the GKN-UO 2 fuel and those between the multi-assembly models with JENDL-4.0 and JENDL-3.3 were similar to those of 241 Pu.As a result, the C/E − 1s of 241 Am with JENDL-4.0 were smaller than those with JENDL-3.2 and JENDL-3.3 as same as those of 241 Pu.The larger neutron capture cross-section in the thermal and resonance energy regions in JENDL-4.0 than that in JENDL-3.3 also made the C/E − 1s of 241 Am with JENDL-4.0 smaller than that with JENDL-3.3 for the GUN-MOX fuel.

Am-242 m
The main production path of 242m Am is the neutron capture of 241 Am.The thermal and resonance neutron capture cross-sections of 241 Am are noticeably larger in JENDL-4.0 than those in JENDL-3.2 and JENDL-3.3.In addition, the thermal neutron capture crosssection of 242m Am is smaller in JENDL-4.0 than those in JENDL-3.2 and JENDL-3.3.These differences made the C/E − 1s with JENDL-4.0 larger than that with JENDL-3.2 for the GKN-UO 2 fuel and that with JENDL-3.3 for the GUN-MOX fuel.

Am-243
The main production path of 243 Am is described by 242 Pu(n, γ) 243 Pu(β − , 4.956 h) 243 Am.The interrelations of the C/E − 1s of 243 Am with JENDL-4.0 and JENDL-3.2 in the GKN-UO 2 fuel were similar to those of 242 Pu.The RI of the neutron capture cross-section of 243 Am is 2, 040 b in JENDL-4.0.In the analysis of the GUN-MOX fuel, a larger RI of the neutron capture cross-section of 243 Am in JENDL-4.0 compared with that in JENDL-3.3 made the elimination of 243 Am larger and the C/E − 1 with JENDL-4.0 smaller.
The C/E − 1s of 241 Am and 242m Am for both fuels were considerably larger than those of 241 Pu, and those of 243 Am for the GKN-UO 2 fuel were also larger than those of 242 Pu.It was possibly caused by the systematic error in the measurements of americium isotopes.The author et al. reported the theoretical analysis of the measured inventories of the high-burn-up PWR MOX and UO 2 fuels in the MALIBU program and mentioned that Am isotopes were among those for which the differences in the measured results between the three different institutes that participated in the inventory measurements, and the measured results of the institute that performed the measurements of the REBUS program were systematically small than those of the two other institutes [18].

Cm-242
The main production path of 242 Cm is described by 242m Am(IT, 141 y) 242 Am(β − , 16.02 h) 242 Cm.The C/E − 1s of 242 Cm for the GKN-UO 2 fuel were similar to those of 242m Am.They were positive for the GKN-UO 2 fuel and negative for the GUN-MOX fuel.In this study, the signs of the C/E − 1s for the GKN-UO 2 and GUN-MOX fuels were the same for almost all the nuclides.The case of 242 Cm showing the different signs of the C/E − 1s for the GKN-UO 2 and GUN-MOX fuels was one of the scarce cases in the present study.It may be related to the large measurement errors due to the short half-life of 242 Cm (162.94 d).

Cm-243
The main production path of 243 Cm is the neutron capture of 242 Cm.The interrelations of the C/E − 1s of 243 Cm with JENDL-4.0 and that with JENDL-3.2 for the GKN-UO 2 fuel were similar to those of 242 Cm.In addition, the resonance neutron capture cross-section of 242 Cm in JENDL-4.0 is noticeably larger than those in JENDL-3.2 and JENDL-3.3.It made the differences in the C/E − 1s of 243 Cm between JENDL-4.0 and the other libraries larger.The C/E − 1s with JENDL-4.0 indicated the improving direction: smaller neutron capture cross-sections of 238 U, 239 Pu, 240 Pu, 241 Am, and 242 Cm and larger fission cross-sections of 235 U, 239 Pu, 241 Pu, and 243 Cm.

Cm-244
The main production path of 244 Cm is described by 243 Am(n, γ) 244 Am(β − , 10.1 h) 244 Cm.The interrelations of the C/E − 1s of 244 Cm with JENDL-4.0 and that with JENDL-3.2 for the GKN-UO 2 fuel were similar to those of 243 Am.The RI of the neutron capture cross-section of 243 Am is larger by 12% in JENDL-4.0 than that in JENDL-3.2 and by 14% than that in JENDL-3.3.It made the differences in the C/E − 1s of 244 Cm between JENDL-4.0 and the other libraries larger.The C/E − 1s of the GKN-UO 2 fuel targeting the measured 148 Nd inventory resulted in a negative value for JENDL-4.0.The C/E − 1s with JENDL-4.0 indicated the improving directions: larger neutron capture cross-sections of 239 Pu, 241 Pu, 242 Pu, and 243 Am and smaller fission cross-sections of 235 U, 239 Pu, and 241 Pu.

Cm-245
The main production path of 245 Cm is the neutron capture of 244 Cm.The interrelations of the C/E − 1s of Cm with JENDL-4.0 and those with JENDL-3.2 and JENDL-3.3 were similar to those of 244 Cm.The C/E − 1s with JENDL-4.0 indicated the improving direction: smaller neutron capture cross-sections of 239 Pu, 241 Pu, 242 Pu, 243 Am, and 244 Cm and larger fission crosssections of 235 U, 239 Pu, 241 Pu, and 245 Cm.

Cm-246
The analysis of the measured inventory of 246 Cm was performed only for the GUN-MOX fuel.The main production path of 246 Cm is the neutron capture of 245 Cm.The interrelation of the C/E − 1s of 246 Cm between the two libraries was similar to that of 245 Cm.The C/E − 1s with JENDL-4.0 indicated the improving directions: a smaller neutron capture cross-section of 238 U, larger neutron capture crosssections of 239 Pu, 241 Pu, 242 Pu, 243 Am, 244 Cm, and 245 Cm, and smaller fission cross-sections of 235 U, 239 Pu and 241 Pu.

Fission product nuclides
In the following discussion of the C/E − 1s of the fission product (FP) nuclides, the main production paths are described in a simple way to highlight the nuclides that have a relatively large influence on the inventories of the measured FP nuclides.When it is described by 'heavy metallic nuclides (HMs)(n, f) FP nuclide,' or 'the fission of HMs,' they mean that the FP nuclide is directly produced by the fission of HMs and the decay of the FP nuclides in the upstream of the burnup chain.The cumulative fission yields (CFYs) are discussed mainly on the measured FP nuclides.The discussion can be also applied to the CFYs of the FP nuclides in the upstream in the burnup chain model since their independent fission yields are normally negligibly small.Since the CFYs of the fission product nuclides in JENDL-3.3 are the same as those in JENDL-3.2, hereafter, the CFYs of both libraries are referred to as the CFYs of JENDL-3.2.

Mo-95
The main production path of 95 Mo is described by HMs(n, f) 95 Nb(β − , 34.991 d) 95 Mo.The C/E − 1s with JENDL-4.0 are smaller than those with JENDL-3.2 and JENDL-3.3.The CFY of 95 Mo for the thermal fission of 235 U in JENDL-4.0 is the same as that in JENDL-3.2, that for 239 Pu is smaller by 2%, and that for 241 Pu is smaller by 4%.The RI of 95 Nb in JENDL-4.0 is larger by 40% than that in JENDL-3.2 and JENDL-3.3.It made the C/E − 1s of 95 Mo smaller for JENDL-4.0.The RI of 95 Mo in JENDL-4.0 is smaller by 14% than that in JENDL-3.2 and JENDL-3.3, which made the C/E − 1s of 95 Mo larger for JENDL-4.0.Using the sensitivity data reported by Oizumi et al. [16] for the neutron cross-sections and fission yields, the effect of the differences in the above-mentioned neutron cross-sections and fission yields on the C/E − 1s of 95 Mo were preliminarily estimated.It indicated that the C/E − 1s with JENDL-4.0 would be almost the same as that with JENDL-3.2 for the GKN-UO 2 fuel and smaller by 2% than that with JENDL-3.3 for the GUN-MOX fuel.They were not enough to explain the differences in the C/E − 1s between JENDL-4.0 and the other libraries.Further study is necessary to identify the causes.

Tc-99
The main production path of 99 Tc is the fission of HMs.The CFY of 99 Tc is larger by 17% in JENDL-4.0 than that in JENDL-3.2 for the thermal fission of 239 Pu and it is larger by 11% for the thermal fission of 241 Pu.The RI of the neutron capture cross-section of 99 Tc in JENDL-4.0 is larger by 4% than that in JENDL-3.2 and the same as that in JENDL-3.3.Using the sensitivity data reported by Oizumi et al. [16] for the neutron cross-sections and fission yields, the effect of the differences in the abovementioned neutron cross-sections and fission yields on the C/E − 1s of 99 Tc were preliminarily estimated.It indicated that the C/E − 1s with JENDL-4.0 would be larger by 7% the that with JENDL-3.2 for the GKN-UO 2 fuel and larger by 13% than that with JENDL-3.3 for the GUN-MOX fuel.The differences in the C/E − 1s between JENDL-4.0 and the other libraries were small for both fuels and they were inconsistent with the differences in the neutron capture cross-sections and CFYs.Further study is necessary to identify the causes.

Ru-101
The main production path of 101 Ru is the fission of HMs.The C/E − 1s of 101 Ru with JENDL-4.0 were larger than that with JENDL-3.2 for the GKN-UO 2 fuel and that with JENDL-3.3 for the GUN-MOX fuel.The CFY of 101 Ru in JENDL-4.0 is larger by 2% than those in JENDL-3.2 for the thermal fission of 235 U, it is larger by 2% for the thermal fission of 239 Pu, and it is larger by 4% for thermal fission of 241 Pu.The differences in the CFYs were the main reason for the differences in the C/E − 1s.

Rh-103
The main production path of 103 Rh is the fission of HMs.The C/E − 1s of 103 Rh with JENDL-4.0 were larger than that with JENDL-3.2 for the GKN-UO 2 fuel and that with JENDL-3.3 for the GUN-MOX fuel.The CFYs of 103 Rh in JENDL-4.0 are larger by 1% than those in JENDL-3.2 for the thermal fission of 239 Pu and it is larger by 11% for the thermal fission of 241 Pu.The thermal neutron capture cross-section of 103 Rh in JENDL4.0 is smaller by 9% than that in JENDL-3.2 and JENDL-3.3.They were the main reason for the differences in the C/E − 1s.

Pd-105
The main production path of 105 Pd is the fission of HMs.The C/E − 1s of 105 Pd with JENDL-4.0 were larger than that with JENDL-3.2 for the GKN-UO 2 fuel and that with JENDL-3.3 for the GUN-MOX fuel.The CFY of 105 Pd in JENDL-4.0 is larger by 5% than that in JENDL-3.2 for the thermal fission of 239 Pu.It was the main reason for the differences in the C/E − 1s.

Pd-108
The main production path of 108 Pd is the fission of HMs.The CFY of 108 Pd for the thermal fission of 235 U is negligibly small compared with that for 239 Pu.The CFY of 108 Pd for the thermal fission of 239 Pu in JENDLE-4.0 is almost the same as that in JEND-3.2.It made the differences in the C/E − 1s small between JENDL-4.0 and the other libraries.

Ag-109
The main production path of 109 Ag is described by HMs(n, f) 109 Ag and HMs(n, f) 108 Pd(n, γ) 109 Pd(β − , 13.59 h) 109 Ag.The C/E − 1s of 109 Ag with JENDL-4.0 were smaller than that with JENDL-3.2 for the GKN-UO 2 fuel and that with JENDL-3.3 for the GUN-MOX fuel.The CFY of 109 Ag in JENDL-4.0 for the thermal fission of 239 Pu is smaller by 21% than that in JENDL-3.2 and that for 241 Pu is larger by 14%.The CFYs of 108 Pd are explained in Section 4.2.6.The differences in the CFYs were the main reason for the differences in the C/E − 1s.
The C/E − 1s were exceptionally large in the analyses of 99 Tc for the GUN-MOX fuel, 101 Ru for both fuels, 103 Rh for the GKN-UO 2 fuel, 105 Pd for the GKN-UO 2 fuel, 108 Pd for both fuels, and 109 Ag for both fuels.It may be caused by the systematic measurement errors due to the nuclides belonging to the elements that were difficult to completely solve in the standard dissolution procedure and the dissolution of the residue had to be analyzed separately in the radiochemical assay [19].

Cs-133
The main production path of 133 Cs is the fission of HMs.The differences in the CFYs of 133 Cs between JENDL-4.0 and JENDL-3.2 are less than 1% for the thermal fission of 235 U, 239 Pu, and 241 Pu.The RI of the neutron capture cross-section of 133 Cs is larger by 12.6% in JENDL-4.0 than that in JENDL-3.2 and JENDL-3.3.It made the C/E − 1s with JENDL-4.0 smaller than those with JENDL-3.2 and JENDL-3.3.
The C/E − 1 with JENDL-4.0 for the GKN-UO 2 fuel was 5%.That targeting the measured 148 Nd inventory was 4%.Those for the GUN-MOX fuel were close to zero.

Cs-134
The measurement data were available only for the GUN-MOX fuel.The main production path of 134 Cs is described by HMs(n, f) 133 Cs(n,γ) 134 Cs.The CFYs and neutron capture cross-section of 133 Cs are explained in Section 4.2.8.The larger RI of the neutron capture cross-section of 133 Cs in JENDL-4.0 made the C/E − 1 of 134 Cs with JENDL-4.0 larger than that with JENDL-3.3.The C/E − 1s with JENDL-4.0 were close to zero.

Cs-135
The main production path of 135 Cs is described by HMs(n, f) 135 Xe(β − , 9.14 h) 135 Cs.The differences in the CFYs of 135 Cs between JENDL-4.0 and JENDL-3.2 are less than 2% for the thermal fission of 235 U, 239 Pu, and 241 Pu.The thermal neutron capture crosssection of 135 Xe in JENDL-4.0 is larger by 4% than that in JENDL-3.2 and JENDL-3.3, which decreased the C/ E − 1s of 135 Cs for both fuels.For both fuels, the C/E − 1s with JENDL-4.0 were close to zero.

Cs-137
The main production path of 137 Cs is the fission of HMs.The CFY of 137 Cs in JENDL-4.0 for the thermal fission of 235 U is smaller by 1% than that in JENDL-3.2, that for 239 Pu is smaller by 2%, and that for 241 Pu is smaller by 4%.The differences in the CFYs were the main reason for the differences in the C/E − 1s.The C/ E − 1s with JENDL-4.0 were close to zero considering the errors in the C/E − 1s.

Ce-144
The main production path of 144 Ce is the fission of HMs.The differences in the CFYs of 144 Ce between JENDL-4.0 and JENDL-3.2 are less than 1% for the thermal fission of 235 U and 239 Pu.The CFY of 144 Ce in JENDL-4.0 is smaller by 2% than that in JENDL-3.2 for the thermal fission of 241 Pu.The inventory of 144 Ce is reduced by beta-minus decay (T 1/2 : 284.91 d) and the neutron capture of itself.The RI of the neutron capture cross-section of 144 Ce is three times larger in JENDL-4.0 than that in JENDL-3.2 and JENDL-3.3.It made the C/E − 1s in JENDL-4.0 smaller than those in JENDL-3.2 and JENDL-3.3.Taking into account the errors in the C/E − 1s, the C/E − 1s of both fuels with JENDL-4.0 were close to zero.

Nd-142
The main production path of 142 Nd is described by HMs(n, f) 141 Ce(β − , 32.508 d) 141 Pr (n, γ) 142 Pr(β − , 19.12 h) 142 Nd.The differences in the CFYs of 141 Pr between JENDL-4.0 and JENDL-3.2 are less than 1% for the thermal fission of 235 U, 239 Pu, and 241 Pu.The inventory of 142 Nd has a negative sensitivity to the neutron capture cross-section of 238 U.The thermal neutron capture cross-section of 238 U is smaller by 1% in JENDL-4.0 than that in JENDL-3.2 and JENDL-3.3.It increased the C/E − 1s with JENDL-4.0 by 0.7% for the GKN-UO 2 fuel and by 0.3% for the GUN-MOX fuel based on the sensitivity data of Oizumi et al. [16]; however, it was not enough to explain the differences in the C/E − 1s.Further study is necessary to identify the causes.In the analysis of the GKN-UO 2 fuel, the C/E − 1s of 142 Nd was − 6% with JENDL-4.0 and different from the other Nd isotopes.A possible reason was a systematic measurement error caused by the contamination of 142 Ce due to the incomplete element separation of neodymium from cerium in the radio-chemical assay.

Nd-143
The main production path of 143 Nd is the fission of HMs.The differences in the CFYs of 143 Nd between JENDL4.0 and JENDL3.2 for the thermal fission of 235 U and 239 Pu are less than 1%.For the thermal fission of 241 Pu, the CFY of 143 Nd in JENDL-4.0 is smaller by 3% than that in JENDL-3.2.The smaller CFY for the thermal fission of 241 Pu made the C/E − 1 smaller than that in JENDL-3.3 for the GUN-MOX fuel.The C/E − 1 of 143 Nd was 1% for the GUN-MOX fuel with JENDL-4.0 and it was slightly different from those of the other Nd isotopes such as 145 Nd, 146 Nd, 148 Nd, and 150 Nd whose C/E − 1s were negative.The C/E − 1s with JENDL-4.0 in the present study indicated the improving directions: a larger neutron capture cross-section of 143 Nd and a smaller CFY of 143 Nd than those in JENDL-4.0.

Nd-144
The main production paths of 144 Nd are described by HMs(n, f) 144 Nd and HMs(n, f) 143 Nd(n, γ) 144 Nd.The differences in the CFYs of 144

Nd-145
The main production path of 145 Nd is the fission of HMs.The differences in the CFYs of 145 Nd for the thermal fission of 235 U and 239 Pu are less than 1%.The CFY of 145 Nd in JENDL-4.0 is smaller by 2% than that in JENDL-3.2 for the thermal fission of 241 Pu.The smaller CFY for 241 Pu made the C/E − 1 smaller than that in JENDL-3.3 for the GUN-MOX fuel.The neutron capture cross-section of 145 Nd in the thermal and resonance energy regions is larger for JENDL-4.0 than that for JENDL-3.2 and JENDL-3.3.It made C/E − 1s with JENDL-4.0 smaller than those with JENDL-3.2 and JENDL-3.3.The C/E-1s with JENDL-4.0 were 1% for the GKN-UO 2 fuel and − 1% for the GUN-MOX fuel.They were similar to those of 146 Nd, 148 Nd, and 150 Nd.

Nd-146
The main production paths of 146 Nd are described by HMs(n, f) 146 Nd and HMs(n, f) 145 Nd(n, γ) 146 Nd.The differences in the CFYs of 145 Nd between the three libraries are explained in Section 4.2.16.The differences in the CFYs of 146 Nd between JENDL4.0 and JENDL3.2 for the thermal fission of 235 U and 239 Pu are less than 0.5%.The CFY of 146 Nd in JENDL-4.0 is smaller by 3% than that in JENDL-3.2 for the thermal fission of 241 Pu.The neutron capture cross-section of 145 Nd in the thermal and resonance energy regions is larger for JENDL-4.0 than that for JENDL-3.2 and JENDL-3.3.While the effect of the difference in the neutron capture cross-section of 145 Nd made the C/E − 1s with JENDL-4.0 larger than those with the other libraries, it was compensated by the smaller CFYs of 145 Nd and 146 Nd for 241 Pu in the C/E − 1s of the GUN-MOX fuel.The C/E-1s with JENDL-4.0 were 2% for the GKN-UO 2 fuel and − 1% for the GUN-MOX fuel.They were similar to those of 145 Nd, 148 Nd, and 150 Nd.

Nd-148
The main production path of 148 Nd is the fission of HMs.The differences in the CFYs of 148 Nd for the thermal fission of 235 U and 239 Pu are less than 1%.The CFY of 148 Nd in JENDL-4.0 is smaller by 3% than that in JENDL-3.2 for the thermal fission of 241 Pu.The smaller CFY for 241 Pu made the C/E − 1 smaller than that in JENDL-3.3 for the GUN-MOX fuel.The C/ E-1s with JENDL-4.0 were 1% for the GKN-UO 2 fuel and − 1% for the GUN-MOX fuel.They were similar to those of 145 Nd, 146 Nd, and 150 Nd.

Nd-150
The main production path of 150 Nd is the fission of HMs.The CFY of 150 Nd for the thermal fission of 235 U in JENDL-4.0 is larger by 1%, that of 239 Pu is almost the same, and that of 241 Pu is smaller by 3% than those in JENDL-3.2.The C/E-1s of the GKN-UO 2 fuel and the GUN-MOX fuel were almost caused directions: a larger CFY of 151 Sm and 152 Sm and a smaller neutron capture cross-section of 152 Sm.

Eu-151
The measurement data were available only for the GUN-MOX fuel.The main production path of 151 Eu is described by 151 Sm(β − , 90 y) 151 Eu.The CFY of 151 Sm is explained in Section 4.2.24.The C/E − 1s were almost the same as those of 151 Sm.

Eu-153
The main production paths of153 Eu are described by HMs(n, f) 153 Eu and 152 Sm(n, γ) 153 Sm(β − , 1.9285 d) 153 Eu.The CFY of 153 Eu for the thermal fission of 235 U in JENDL-4.0 is smaller by 2%, that for 239 Pu is smaller by 1%, and that for 241 Pu is smaller by 1% than those in JENDL-3.2.The RI of the neutron capture cross-section of 152 Sm is larger by 8% in JENDL-4.0 than that in JENDL-3.2 and JENDL-3.3.It made the C/E − 1s with JENDL-4.0 larger and almost compensated the effects of the smaller CFYs of 153 Eu, 152 Sm, and 151 Sm for JENDL4.0.The C/E − 1s of the GKN-UO 2 fuel with JENDL-4.0 ranged from 1% to 2%.The C/E − 1 of the GUN-MOX fuel with JENDL4.0 was close to zero.

Eu-154
The main production path of 154 Eu is described by 153 Eu(n, γ) 154 Eu.The CFY of 153 Eu is explained in Section 4.2.27.The neutron capture cross-section of 154 Eu is prominently large in the thermal energy region and is smaller by 27% in JENDL-4.0 compared with JENDL-3.2 and JENDL-3.3.It was the main reason that the C/E − 1s of154 Eu were larger with JENDL-4.0 for both fuels.The C/E − 1s with JENDL-4.0 in the present study indicated the improving directions: smaller CFYs of 151 Sm, 152 Sm, and 153 Eu, a larger neutron capture crosssection of 154 Eu, and smaller neutron capture crosssections of 152 Sm and 153 Eu.

Eu-155
The main production paths of 155 Eu are described by HMs(n, f) 155 Eu, and 154 Eu(n,γ) 155 Eu.The CFYs of 155 Eu in JENDL-4.0 are almost the same as those in JENDL-3.2 for the thermal fission of 235 U, 239 Pu, and 241 Pu.While the inventories of 154 Eu with JENDL-4.0 were larger than those with JENDL-3.2 and JENDL-3.3 as shown in Section 4.2.28, the production of 155 Eu by neutron capture of 154 Eu was reduced due to the smaller neutron capture cross-section of 154 Eu in JENDL-4.0 and the differences in the inventories of 155 Eu between JENDL-4.0 and the other libraries were small.The C/E − 1s with JENDL-4.0 in the present study indicated the improving directions: larger CFYs of 151 Sm, 152 Sm,

Gd-155
The main production path of 155 Gd is described by 155 Eu(β − , 4.753 y) 155 Gd.The cooling times to the measurement were 7.3 years for the GKN-UO 2 and 4.7 years for GUN-MOX fuel and most of the inventory was produced by beta-minus decay of 155 Eu during the cooling time.The trend in the C/E − 1s of 155 Gd was almost the same as that of 155 Eu for the GKN-UO 2 fuel.The C/E − 1 values with JENDL-4.0 in the present study indicated the improving directions: a larger CFY of 151 Sm, 152 Sm, 153 Eu, and 155 Eu, a smaller neutron capture cross-section of 155 Eu, and larger neutron capture cross-sections of 152 Sm, 153 Eu, and 154 Eu.

Feedback to nuclear data in JENDL
The improving directions of the nuclear data in JENDL-4.0 are summarized in Table 3.It is shown in a plus sign for increasing the nuclear data and a minus sign for decreasing the nuclear data.The neutron cross-sections investigated in the present study were the neutron-energy-one-group cross-sections which were obtained by weighting the microscopic cross-sections by the energydependent neutron fluxes through the irradiation histories.The cumulative fission yields were those obtained by weighting the cumulative fission yields of the HMs by the partial contributions of the HMs to the total fissions through the irradiation histories.
The effect of the nuclear data revised from JENDL-4.0 [12] to JENDL-5.0 [20] on the C/E − 1s was evaluated by using the information in Table 3.In JENDL-5, the thermal neutron capture cross-section of 235 U is larger by 0.7%.than that in JENDL-4.0.While it will improve the C/E − 1s of 235 U, 236 U, and 242 Pu, it will worsen the C/E − 1s of 238 Pu.The thermal fission cross-section of 235 U is larger by 0.3%.While it will improve the C/E − 1s of 235 U, 238 Pu, and 243 Cm, it will worsen the C/E − 1s of 236 U and 242 Pu.The thermal neutron capture cross-section of 237 Np is smaller by 2.4%, which will improve the C/E − 1s of 238 Pu.The thermal neutron capture cross-section of 238 Pu is larger by 22%, which will improve the C/E − 1s of 234 U and 238 Pu.The peak and width of the first resonance neutron capture cross-section of 242 Pu are larger.While it will improve the C/E − 1s of 244 Cm and 246 Cm, it will worsen the C/E − 1s of 242 Pu and 245 Cm.The thermal neutron capture cross-section of 243 Am is smaller by 0.5%.While it will improve the C/E − 1s of 245 Cm, it will worsen the C/E − 1s

Figure 1 .
Figure 1.The comparison between the calculated and measured inventories of the actinide nuclides for the GKN-UO 2 (top) and GUN-MOX fuels (bottom).The results with JENDL-3.2 and JENDL-3.3 were taken from the references [5] and [3], respectively.

Figure 2 .
Figure 2. The comparison between the calculated and measured inventories of the light-mass fission product nuclides for the GKN-UO 2 (top) and GUN-MOX fuels (bottom).The results with JENDL-3.2 and JENDL-3.3 were taken from the references [5] and [3], respectively.

Figure 3 .
Figure3.The comparison between the calculated and measured inventories of the heavy-mass fission product nuclides for the GKN-UO 2 (top) and GUN-MOX fuels (bottom).The results with JENDL-3.2 and JENDL-3.3 were taken from the references[5] and[3], respectively.

Figure 4 .
Figure 4.The neutron energy spectra in 108 energy groups at the beginning of irradiation and cycle 4 for the GKN-UO 2 fuel (top) and the beginning of irradiation and cycle 6 for GUN-MOX fuel (bottom). 234 Nd for the thermal fission of 235 U and 239 Pu are less than 1%.The CFY of 144 Nd in JENDL-4.0 is smaller by 2% than that in JENDL-3.2 for the thermal fission of 241 Pu.The CFYs of 143 Nd are explained in Section 4.2.14.The smaller CFYs of 143 Nd and 144 Nd for 241 Pu made the C/E − 1 smaller than that in JENDL-3.3 for the GUN-MOX fuel.The C/E − 1s of 144 Nd were zero for the GKN-UO 2 fuel and − 4% for the GUN-MOX fuel with JENDL-4.0 and different from the other Nd isotopes such as 145 Nd, 146 Nd, 148 Nd, and 150 Nd.The C/E − 1s with JENDL-4.0 in the present study indicated the improving directions: a larger CFYs of 143 Nd and 144 Nd and a larger neutron capture cross-section of 143 Nd than those in JENDL-4.0.
aThe standard errors of the average calculated burnups.bTheratio of the calculated burnup to the measured burnup.cThecalculationtargeting the measured148Nd inventory.
U was large for the UO 2 fuel since part of