Issue 
EPJ Nuclear Sci. Technol.
Volume 5, 2019



Article Number  24  
Number of page(s)  19  
DOI  https://doi.org/10.1051/epjn/2019056  
Published online  23 December 2019 
https://doi.org/10.1051/epjn/2019056
Regular Article
Feedback from experimental isotopic compositions of used nuclear fuels on neutron cross sections and cumulative fission yields of the JEFF3.1.1 library by using integral data assimilation
^{1}
CEA, DEN Cadarache, 13108 Saint Paul les Durance, France
^{2}
Orano Cycle, BU Recyclage, Paris, France
^{*} email: axel.rizzo@cea.fr
Received:
17
April
2019
Received in final form:
11
October
2019
Accepted:
21
November
2019
Published online: 23 December 2019
Comparisons of calculated and experimental isotopic compositions of used nuclear fuels can provide valuable information on the quality of nuclear data involved in neutronic calculations. The experimental database used in the present study − containing more than a thousand isotopic ratio measurements for UOX and MOX fuels with burnup ranging from 10 GWd/t up to 85 GWd/t − allowed to investigate 45 isotopic ratios covering a large number of actinides (U, Np, Pu, Am and Cm) and fission products (Nd, Cs, Sm, Eu, Gd, Ru, Ce, Tc, Mo, Ag and Rh). The Integral Data Assimilation procedure implemented in the CONRAD code was used to provide nuclear data trends with realistic uncertainties for Pressurized Water Reactors (PWRs) applications. Results confirm the quality of the ^{235}U, ^{239}Pu and ^{241}Pu neutron capture cross sections available in the JEFF3.1.1 library; slight increases of +1.2 ± 2.4%, +0.5 ± 2.2% and +1.2 ± 4.2% are respectively suggested, these all being within the limits of the quoted uncertainties. Additional trends on the capture cross sections were also obtained for other actinides (^{236}U, ^{238}Pu, ^{240}Pu, ^{242}Pu, ^{241}Am, ^{243}Am, ^{245}Cm) and fission products (^{103}Rh, ^{153}Eu, ^{154}Eu) as well as for the ^{238}U(n,2n) and ^{237}Np(n,2n) reactions. Meaningful trends for the cumulative fission yields of ^{144}Ce, ^{133}Cs, ^{137}Cs and ^{106}Ru for the ^{235}U(n_{th},f) and ^{239}Pu(n_{th},f) reactions are also reported.
© A. Rizzo et al., published by EDP Sciences, 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1 Introduction
Numerous studies report comparisons of calculated (C) and experimental (E) isotopic compositions of used fuels for nuclear data validation purposes. In this work, we have used an experimental database that mainly contains proprietary data obtained from French PWRs fleet. Our database contains 1370 isotopic ratio measurements for UOX and MOX fuels with burnup ranging from 10 GWd/t up to 85 GWd/t. It allows to investigate 45 isotopic ratios for a large number of actinides (U, Np, Pu, Am and Cm) and fission products (Nd, Cs, Sm, Eu, Gd, Ru, Ce, Tc, Mo, Ag and Rh).
Interpretations of postirradiation experiments (PIEs) of samples irradiated in nuclear power reactors can be performed with the deterministic calculation package DARWIN2.3 [1], which is a calculation tool designed for fuel cycle applications. It solves the Boltzmann and Bateman equations to compute fuel cycle parameters at any irradiation and cooling time. A flow chart of the DARWIN2.3 package for PWR calculations is presented in Figure 1 [1]. DARWIN2.3 includes the APOLLO2 deterministic transport code [2], which provides neutron data to the PEPIN2 depletion solver [3], namely selfshielded crosssections libraries and multigroup neutron fluxes.
Stateoftheart calculatedtoexperimental (C/E1) ratios obtained with the JEFF3.1.1 library [4] are summarized in reference [1]. The objectives of the present study are to include most of these C/E1 ratios in the Integral Data Assimilation procedure of the CONRAD code [5,6] and to provide valuable trends on the nuclear data compiled in the JEFF3.1.1 library. Guidelines to achieve these objectives and strategies to take into account uncertainties coming from experiments, nuclear data and numerical biases are discussed in references [7–9]. The originality of our approach lies in the use of the AGS code method [10] to generate covariances between the C/E1 ratios and of the marginalization procedure [11] to propagate uncertainties of “nuisance” parameters. Final results indicate that reliable trends can be obtained for the capture cross sections of some important actinides (^{235}U, ^{236}U, ^{238}Pu, ^{239}Pu, ^{240}Pu, ^{241}Pu, ^{242}Pu, ^{241}Am, ^{243}Am, ^{245}Cm) and fission products (^{103}Rh, ^{153}Eu, ^{154}Eu) as well as for both ^{238}U(n,2n) and ^{237}Np(n,2n) reactions. Meaningful trends can also be obtained for the cumulative fission yields of ^{144}Ce, ^{133}Cs, ^{137}Cs and ^{106}Ru.
The integral data assimilation procedure is presented in Section 2, alongside free and nuisance parameters. Trends obtained on nuclear data are presented in Section 3 and discussed in Section 4.
Fig. 1 Flow chart of the DARWIN2.3 package for PWR calculations. 
2 Integral Data Assimilation procedure
The Integral Data Assimilation procedure implemented in the CONRAD code [5,6] is based on a twostep calculation scheme. The first step is a leastsquare fitting procedure, namely the analytic resolution of a standard generalized leastsquare equation [12], that consists in adjusting model parameters (i.e. nuclear data) on a given set of integral values. The second step is a marginalization procedure designed to propagate nuisance parameter uncertainties after the fitting procedure.
2.1 Governing equations
For a correct use of the Integral Data Assimilation procedure of the CONRAD code, two types of model parameters have to be defined, namely observable and nuisance parameters. The observable parameters are free variables whose values are adjusted during the fitting procedure. The nuisance parameters are fixed model parameters with known uncertainties. Nuisance parameter uncertainties are taken into account via the marginalization technique [11]. The algorithm consists in building a “full” covariance matrix Σ between the observable and nuisance parameters as follows [13]:(1)where(2)and(3)with x being the set of adjusted parameters, M _{ x } being the posterior covariance matrix associated to x, θ being the set of nuisance parameters and M _{ θ } the corresponding covariance matrix. Matrices G _{ x } and G _{ θ } contain the partial derivatives of the calculated values with respect to the observable and nuisance parameters:(4) (5)
2.2 Used nuclear fuel data and uncertainties
Integral values included in the fitting procedure are C/E1 ratios obtained from the interpretation of PIEs with the DARWIN2.3 package [1] using the JEFF3.1.1 library. Table 1 gives the nuclides for which C/E1 values are available in the DARWIN2.3 validation suite, as well as the number and the type of fuel rod samples extracted per reactor. Examples of average 〈C/E〉1 ratios at 40 GWd/t are given in Figure 2. This burnup is representative of the burnup of PWR assemblies at discharge. More information can be found in references [1,14]. According to data reported in Figure 2, the concentrations of the major actinides ^{235}U, ^{239}Pu and ^{241}Pu at 40 GWd/t are accurately calculated for UOX fuels with the JEFF3.1.1 library. The mean 〈C/E〉1 ratios are −0.4 ± 3.7%, 0.0 ± 0.8% and −0.8 ± 1.8%, respectively. Average results obtained for MOX fuels remain consistent within the quoted uncertainties, except for the ^{241}Pu/^{238}U ratio. For both types of fuel, the largest C/E–1 ratios are obtained for the curium isotopes. These discrepancies, reaching about −50% for ^{247}Cm in UOX fuels, or discrepancies observed between UOX and MOX fuels, can be explained by using the Integral Data Assimilation procedure of the CONRAD code. The calculatedtoexperimental ratios considered in this work share the same sources of systematic uncertainties (parameters p _{1} to p _{4} detailed in the next paragraph). Therefore, the AGS code method [10] has been used to estimate the covariance matrix M _{ C/E−1} between the C/E1 values. The originality of the AGS code method is to combine uncorrelated and correlated uncertainties as follows:(6)in which D is a n × n diagonal matrix containing the variances of the uncorrelated uncertainties and S is a n × m rectangular matrix containing the correlated contributions for each of the j ∈ ⟦1, m⟧ sources of uncertainty. No correlation between the experimental isotopic ratios was provided alongside the results of the chemical analyses. Therefore, the covariance matrix D is a diagonal matrix that only contains the experimental uncertainties coming from the measurement process.(7)in which var (C _{ i }/E _{ i } − 1) represents the uncertainty associated with the ith experiment. For the Smatrix, four sources of systematic uncertainties are considered:(8)with:(9)
Parameters p _{1} and p _{2} are related to the fuel and moderator temperatures, respectively. Their contributions Δ_{1,i } and Δ_{2,i } are calculated with DARWIN2.3 from direct perturbations of the parameters, by considering an uncertainty of ±50 °C for the fuel temperature and ±2 °C for the moderator temperature at 1σ. Parameters p _{3} and p _{4} are numerical schemerelated uncertainties, depending on the use of DARWIN2.3. The former corresponds to the differences that could be obtained between deterministic and MonteCarlo calculation schemes. It was estimated from pincell depletion calculations performed with the deterministic code APOLLO2 and the MonteCarlo code TRIPOLI4 [15], with the same filiation chain. The latter corresponds to the differences due to resonant upscattering effects [16] on fuel inventory calculations. Examples of differences obtained on the calculated isotopic ratios for a UOX fuel (3.7 wt.% ^{235}U) at 40 GWd/t are given in Figure 3. Most of the obtained differences lie below 1%. The comparison of the deterministic and MonteCarlo calculations schemes indicates that the differences are significant for the curium isotopes and nonnegligible for ^{137}Cs. Among the fission products, ^{137}Cs seems to be an isolated case needing more extensive studies. As expected, in the case of the upscattering effect, nonnegligible increases of the concentration of all the actinides are observed. The final correlation matrix between the C/E1 values reconstructed with the AGS code method (Eq. (6)) is shown in Figure 4. An interesting feature is the correlations between the UOX and MOX fuel data that introduces constraints on the variations of the observable parameters during the fitting procedure.
Experimental database used for the validation of the DARWIN2.3 package (grey colour means that a portion or all the samples were analysed, white colour means that no experimental values are available).
Fig. 2 Average calculatedtoexperimental values (〈C/E〉1) obtained for UOX and MOX fuels with the DARWIN2.3 package at 40 GWd/t using the JEFF3.1.1 library. 
Fig. 3 Differences obtained on the isotopic concentrations (normalized to ^{238}U concentration) on a pincell geometry for a 3.7% ^{235}Uenriched UOX fuel at 40 GWd/t between i) in blue: APOLLO2 (AP2) and TRIPOLI4 depletion calculations (T4), ii) in red: two APOLLO2 depletion calculations, with (AP2UPS) and without (AP2) resonant upscattering effects. Error bars represent the statistical uncertainty provided by the TRIPOLI4 calculations. 
Fig. 4 Correlation matrix between calculatedtoexperimental isotopic ratios used for the assimilation procedure. 
2.3 Observable parameters
Isotopic ratios depend on a wide number of nuclear data. Therefore, the CYRUS tool [17] was used, coupled with PEPIN2 depletion solver, to establish an exhaustive list of nuclear data involved in the buildup of actinides and fission products.
The selected set of observable parameters that will be adjusted with the CONRAD code is given in Table 2. It was chosen not to adjust fission cross sections, because it would imply modifying the burnup of the analysed samples. This is incompatible with the fact that the burnup is a fixed parameter for each sample with a known uncertainty of about ±2% (see next section). It was also decided not to fit the decay constants; in our study, decay constants of interest are well known, with quoted uncertainties lesser than 0.6% (see Tab. 3). Eventually, it was chosen not to fit some nuclear data (e.g. fission yields on samarium isotopes, or samarium cross sections) because the number of free parameters was too important with respect to the number of constraints, thus leading to an underdetermined system.
Parameter y_{c} (X,A) indicates the thermal cumulative fission yield of nuclide X for actinide A. For reducing the number of free parameters, the (n,γ) and (n,2n) cross sections are effective cross sections which are averaged over the neutron flux φ(E):(10)
Prior uncertainties for neutron cross sections come from the COMACV2.0 covariance matrix database [18,19], developed at CEA Cadarache. For fission yields, they come from the JEFF3.1.1 library.
Fitted parameters, relative prior uncertainty and origin of the uncertainty.
Marginalized parameters and associated relative uncertainty (Unc.)
2.4 Nuisance parameters
Nuisance parameters are fixed parameters whose uncertainties are propagated via the marginalization procedure of the CONRAD code (Sect. 2.1). The list of the nuisance parameters introduced in the CONRAD calculation is given in Table 3. It gathers all nuclear data involved in the buildup of nuclides considered, determined with the CYRUS tool, except the ones fitted (see previous section). The cross section uncertainties come from the COMACV2.0 database. Uncertainties for the decay data (periods, isomeric ratios and branching ratios) and fission yields are directly taken from the JEFF3.1.1 library.
Nuisance parameters are not only the nuclear data involved in the buildup of actinides and fission products, but also experimental parameters such as the burnup scaling parameter. The relative uncertainty associated to the latter parameter is close to ±2%.
3 Nuclear data adjustment trends and uncertainties
Nuclear data adjustment trends provided by the Integral Data Assimilation of our used nuclear fuel database are reported in Table 4. Results are listed by ascending order of adjustment coefficient. In particular, those obtained for the europium capture cross sections and cumulative fission yield of ^{137}Cs confirm the results previously reported in references [8,9].
Table 4 also compares the relative uncertainties obtained before and after the marginalization of the nuisance parameters (Sect. 2.4). For most of the posterior values, the fitting uncertainties are lower than 1%. The marginalization provides more realistic uncertainties that allow discussing the quality of some cumulative fission yields and cross sections recommended in the JEFF3.1.1 library and hence the content of the covariance database COMACV2.0.
3.1 Cumulative fission yields
Adjustment trends on a few number of cumulative fission yields were extracted from the Integral Data Assimilation of our used nuclear fuel data. This work provide information on the cumulative fission yields of ^{106}Ru, ^{144}Ce, ^{133}Cs and ^{137}Cs for both ^{235}U(n,f) and ^{239}Pu(n,f) reactions with relative uncertainties ranging from 1.3% to 5.7%. These trends can be directly applied to the cumulative fission yields recommended in the JEFF3.1.1 library. For ^{235}U, adjustment trends reported in Table 4 provide the following results:
y _{ c }(^{144}Ce,^{235}U) = 0.0524 ± 0.0018 (3.4%),
y _{ c }(^{133}Cs,^{235}U) = 0.0701± 0.0014 (2.0%),
y _{ c }(^{137}Cs,^{235}U) = 0.0669 ± 0.0013 (1.9%).
For ^{239}Pu, the following results are obtained:
y _{ c }(^{144}Ce,^{239}Pu) = 0.0345 ± 0.0005 (1.3%),
y _{ c }(^{133}Cs,^{239}Pu) = 0.0690 ± 0.0021 (3.1%),
y _{ c }(^{137}Cs,^{239}Pu) = 0.0654 ± 0.0021 (3.1%),
y _{ c }(^{106}Ru,^{239}Pu) = 0.0457 ± 0.0026 (5.7%).
Comparisons with evaluated values and data available in the literature are reported in Section 4.
3.2 Neutron cross sections
Results obtained for the (n,γ) and (n,2n) reactions can be divided in three groups.

The first group concerns the reactions for which the adjustment trends remain within the uncertainties obtained after marginalization. This can be observed for six actinides and two fission products: ^{235}U(n,γ), ^{236}U(n,γ), ^{239}Pu(n,γ), ^{241}Pu(n,γ), ^{244}Cm(n,γ), ^{246}Cm(n,γ), ^{133}Cs(n,γ) and ^{99}Tc(n,γ). The case of technetium should be considered with caution because of the large uncertainty obtained (±7.8%). This first group refers to reactions that are correctly described in JEFF3.1.1 or for which minor corrections are expected.

The second group concerns the reactions for which the adjustment trends are higher than the uncertainty obtained after marginalization, while remaining lower than 5%. This is the case of three actinides: ^{238}U(n,2n), ^{240}Pu(n,γ) and ^{242}Pu(n,γ).

The third group concerns the reactions for which the adjustment trends are higher than the uncertainty obtained after marginalization and also higher than 5%. Six actinides and three fission products fulfil these conditions: ^{237}Np(n,2n), ^{241}Am(n,γ), ^{243}Am(n,γ), ^{242}Cm(n,γ), ^{245}Cm(n,γ), ^{247}Cm(n,γ), ^{153}Eu(n,γ), ^{154}Eu(n,γ) and ^{103}Rh(n,γ). Results obtained for the ^{247}Cm(n,γ) and ^{237}Np(n,2n) reactions only indicate that such reactions are poorly known. Our used nuclear fuel data cannot provide accurate information to improve them. This latest group provides key information on reactions that have to be corrected in priority for improving significantly the DARWIN2.3 calculations for fuel cycle applications. However, adjustment trends reported in Table 4 need to be interpreted by examining the evolution with the burnup of the posterior calculatedtoexperimental ratios provided by CONRAD at the end of the Integral Data Assimilation procedure. ^{241}Am and ^{243}Am are discussed below.
Figures 5 and 6 show the prior and posterior C/E1 values for the ratio ^{241}Am/^{238}U in UOX and MOX fuels respectively, from 20 GWd/t to 85 GWd/t. The review of the posterior results reveals a slight improvement in average for UOX fuels, while the average C/E discrepancy is slightly degraded for MOX fuels. This result might be explained by the nonnegligible dispersion of the calculatedtoexperimental values, especially for MOX fuels. Final uncertainties in Table 4 do not reflect the potential inconsistencies between the used nuclear fuel data.
The production chain of ^{244}Cm (Fig. 7) shows that the impact of ^{243}Am capture cross section can be quantified on the calculatedtoexperimental ratios of ^{244}Cm/^{238}U. The prior and posterior C/E1 values for UOX and MOX fuels are reported in Figures 8 and 9. The posterior values are closer to zero in average. However, a dependence of the results with the burnup can be observed. Below approximately 30 GWd/t, the ^{244}Cm/^{238}U ratio is still underestimated. This could be explained by the low amount of ^{244}Cm in the fuel at low burnup, suggesting that the experimental values at low burnup should be considered with caution. Hence, when considering only high burnup data on Figures 8 and 9, for which the ^{244}Cm content becomes more significant, one can observe a slight overestimation of the ^{244}Cm/^{238}U isotopic ratio. This indicates that the increase of the ^{243}Am capture cross section suggested in Table 4 is overcompensating the initial C/E1 values. In that case, the obtained adjustment trend of +9.4 ± 2.2% should be considered as an upper limit.
Fig. 5 Evolution of the calculatedtoexperimental discrepancies before and after integral data assimilation for the ^{241}Am/^{238}U isotopic ratio in UOX fuels. 
Fig. 6 Evolution of the calculatedtoexperimental discrepancies before and after integral data assimilation for the ^{241}Am/^{238}U isotopic ratio in MOX fuels. 
Fig. 7 Production chain of ^{244}Cm. 
Fig. 8 Evolution of the calculatedtoexperimental discrepancies before and after integral data assimilation for the ^{244}Cm/^{238}U isotopic ratio in UOX fuels. 
Fig. 9 Evolution of the calculatedtoexperimental discrepancies before and after integral data assimilation for the ^{244}Cm/^{238}U isotopic ratio in MOX fuels. 
3.3 Feedback on the COMACV2.0 library
Results reported in Table 4 can be used to assess the quality of the COMACV2.0 database: the mean posterior values obtained in this work should presumably remain within the limit of the prior uncertainties provided by COMACV2.0, otherwise the latter is underestimated. On the contrary, a prior uncertainty value which is significantly larger than the posterior trend may indicate that the prior uncertainty is overestimated.
When comparing the posterior values with the prior uncertainties, it seems indeed that the prior uncertainties for the capture cross sections of ^{133}Cs, ^{236}U, ^{242}Pu, ^{244}Cm and ^{246}Cm are overestimated. As an example, the COMACV2.0 library provides a relative uncertainty for the ^{242}Pu(n,γ) reaction which is close to 12%, while the present study suggests a slight increase of the capture cross section of +3.8 ± 2.8%. On the other hand, the COMACV2.0 database seems to underestimate the uncertainties of the ^{103}Rh(n,γ), ^{241}Am(n,γ) and ^{243}Am(n,γ) reactions. This feedback constitutes guidelines for the improvement of the COMACV2.0 database.
4 Discussions of the results
Results provided by the Integral Data Assimilation procedure and presented in Section 3 were obtained using the JEFF3.1.1 library. Since its official release in 2009, numerous validation studies were conducted on this library; furthermore new experimental data and evaluated nuclear data files are now available in the literature. This section compares results obtained in the present work with those reported in the literature and the international libraries in order to draw some recommendations for improving the JEFF library.
4.1 Comparison with results reported in the literature
Some examples of results available in the nuclear data literature for actinides and fission products are highlighted in Tables 5 and 6. We have selected some works that provide nuclear data adjustment trends which are associated to the JEFF3.1.1 library.
From an integral point of view, many oscillations and activation experiments were carried out in the MINERVE reactor of CEA Cadarache in order to obtain an insight on nuclear data adjustment trends for a large amount of isotopes. OSMOSE [20,21], CERES [22], BUC [23] and MAESTRO [24–26] are programs specifically dedicated to actinides, MOX fuels, fission products and structural materials respectively. PIEs of samples irradiated in thermal spectra (such as the ICARE and SHERWOOD programs carried out in the MELUSINE reactor of CEA Grenoble [27]) and in fast spectra (such as the PROFIL program carried out in the PHENIX reactor of CEA Marcoule [28]) provide integral information similar to used nuclear fuel data, namely isotopic ratios. One must pay attention that the reported C/E1 values are not adjustment trends on nuclear data. This means that adjustment trends obtained in the present work should compensate the C/E1 values reported in Tables 5 and 6 (i.e. having opposed signs).
From a microscopic point of view, three timeofflight experiments carried out in the past years for ^{242}Pu [29], ^{243}Am [30] and ^{153}Eu [31] at the n_TOF and RPI facilities were considered. Resonance parameters extracted from these data provide useful information on the capture resonance integral. For the fission yields, results obtained at the ILL with the Lohengrin spectrometer [32–34] are listed.
From the evaluation point of view, it was chosen to focus on the case of ^{103}Rh, for which a new evaluation has been recently performed at IRSN (Institut de Radioprotection et de Sûreté Nucléaire) with the SAMMY code [35].
In addition to the abovementioned works, several studies were conducted based on the analyses of integral experiments. Two recent Integral Data Assimilation studies were performed on actinides with the RDN code using criticalitysafety benchmarks in association to used nuclear fuel data [36], and integral data provided by the CERES program [22]. Posterior results are reported in Table 5. Finally, a nuclear data trend for the ^{154}Eu(n,γ) reaction has been also obtained from the analysis of used nuclear fuel data [37]. Results are reported in Table 6.
A detailed review of the results listed in Table 5 and 6 leads to three major conclusions.

For the cumulative fission yields, trends suggested by our Integral Data Analysis are fully consistent with the ILL results. The agreement between the values remains within the limit of the reported uncertainties, which represents an encouraging result. An exhaustive comparison with a wider number of cumulative fission yields measured in various places could provide good indications about the robustness of our work.

For the capture cross sections of the fission products, most of the reported results are also consistent, excepted those related to the ^{103}Rh(n,γ) reaction. The large inconsistencies between the BUC and MAESTRO experiments carried out in the MINERVE reactor justify the replacement of the ^{103}Rh evaluation by a new evaluated nuclear data file, such as the one produced at IRSN [35].

The last conclusion concerns the actinides for which the numerous inconsistencies observed between the reported integral data can lead to erroneous conclusions. For some reactions, this confused situation can be clarified with microscopic data, such as recent timeofflight experiments carried out in the RPI and n_TOF facilities. Examples given in Table 5 and 6 for the ^{242}Pu(n,γ), ^{243}Am(n,γ) and ^{153}Eu(n,γ) reactions provide capture resonance integrals in favor of our Integral Data Assimilation results.
This comparative study indicates that our work provides consistent results for some actinides, fission products and cumulative fission yields; the present set of nuclear data adjustment trends represents a reliable guideline for improving the JEFF library.
Comparison of our Integral Data Assimilation results for actinides with results reported in the literature. No data is available for ^{246}Cm(n,γ), ^{242}Cm(n,γ), ^{237}Np(n,2n) and ^{246}Cm(n,γ).
Comparison of our Integral Data Assimilation results for fission products with results reported in the literature. I_{0} and σ_{0} refers to the capture resonance integral and the thermal capture cross section, respectively.
4.2 Recommended evaluated nuclear data files and resonance parameters
The nuclear data adjustment trends suggested by our Integral Data Assimilation procedure can be used to propose cross section evaluations that could improve calculations related to the fuel cycle. Table 7 gives a list of recommended Evaluated Nuclear Data files or resonance parameters. We only consider capture reactions for which meaningful adjustment trends were obtained. Cumulative fission yields are not discussed because the evaluation process is more complex than the one for cross sections, since it generally relies on an experimental database containing a large number of independent and cumulative fission yield measurements. Adjustment trends obtained on fission yields can nevertheless be used for the validation of the next fission yield evaluation releases.
Two types of recommendations can be distinguished. The first one consists in proposing existing Evaluated Nuclear Data files whose resonance parameters and neutron cross sections fulfil the nuclear data adjustment trends suggested by our study. This is the case for the ^{236}U, ^{238}U, ^{241}Am and ^{154}Eu nuclides. The proposed evaluations come from new or old versions of the JEFF library or from the Japanese library JENDL4.0. Justifications of these choices are given in Table 7. One can precise that the recommended evaluation for ^{154}Eu capture crosssection relies on a work carried out in [40], which aims at assessing the impact of different nuclear data evaluations on Europium isotopes buildup with the DARWIN package. This study showed that best results are obtained using JEFF3.0 for ^{154}Eu capture cross section, which exhibits changes on the first resonance parameters that induce a higher thermal capture crosssection compared to JEFF3.1.1. The second type of recommendations consists in selecting resonance parameters which are not yet available in an official neutron library. Parameters could be retrieved from recent publications [29–31] for ^{242}Pu, ^{243}Am, and ^{153}Eu, and introduced in an Evaluated Nuclear Data file for further validation studies, or they could come from recent resonance analyses for ^{240}Pu and ^{103}Rh. The latter are usually preliminary works that provide encouraging results.
Evaluated nuclear data files and new resonance parameters in agreement with the nuclear data adjustment trends provided by our Integral Data Assimilation study.
5 Conclusions
In this paper, comparisons of calculated and experimental isotopic compositions of used nuclear fuels are carried out to provide information on the accuracy of nuclear data from the JEFF3.1.1 library for fuel cycle applications. The method applied relies on both a fitting algorithm and a marginalization procedure implemented in the CONRAD code.
Final results confirm the accuracy of ^{235}U, ^{239}Pu and ^{241}Pu neutron capture cross sections available in the JEFF3.1.1 library. Slight increases of +1.2 ± 2.4%, +0.5 ± 2.2% and +1.2 ± 4.2% are respectively suggested, these all remaining within the limit of the quoted uncertainties. Results indicate the good quality of ^{236}U, ^{244}Cm, ^{246}Cm and ^{133}Cs capture cross sections as well, since the adjustment trends obtained remain within the quoted uncertainties. Our study also suggest to slightly increase ^{238}U(n,2n), ^{240}Pu(n,γ) and ^{242}Pu(n,γ), adjustment trends obtained being lower than +5%. Adjustment trends greater than +5% are obtained for ^{237}Np(n,2n), ^{241}Am(n,γ), ^{243}Am(n,γ), ^{242}Cm(n,γ), ^{245}Cm(n,γ), ^{247}Cm(n,γ), ^{153}Eu(n,γ), ^{154}Eu(n,γ) and ^{103}Rh(n,γ).
Meaningful adjustment trends for the cumulative fission yields of ^{144}Ce, ^{133}Cs, ^{137}Cs and ^{106}Ru for the ^{235}U(n_{th},f) and ^{239}Pu(n_{th},f) reactions, ranging from −8% to +9% approximately, are also reported.
Comparisons with data from the literature show a good agreement of the adjustment trends obtained on cumulative fission yields with experiments recently conducted at the ILL facility, and show a global agreement of the adjustment trends obtained on neutron cross sections with integral and microscopic experiments carried out in the past. Based on these results, several cross section evaluation are recommended to improve fuel cycle calculations: these evaluations may come from other international libraries or be based on resonance parameters recently measured at timeofflight facilities. The evaluations recommended in this paper represent a valuable feedback of the fuel cycle applications that can be used for the improvement of the future JEFF library releases and more generally for the improvement of nuclear data.
Acknowledgments
Authors would like to thank Orano for its support and Luiz Leal for providing resourceful information on the ^{103}Rh evaluation. Special acknowledgements go to colleagues from CEA for their valuable help during this work, especially David Bernard, Coralie Carmouze, Vanessa Vallet and Pascal Archier.
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Cite this article as: Axel Rizzo, Claire VaglioGaudard, Gilles Noguere, Romain Eschbach, Gabriele Grassi, JulieFiona Martin, Feedback from experimental isotopic compositions of used nuclear fuels on neutron cross sections and cumulative fission yields of the JEFF3.1.1 library by using integral data assimilation, EPJ Nuclear Sci. Technol. 5, 24 (2019)
All Tables
Experimental database used for the validation of the DARWIN2.3 package (grey colour means that a portion or all the samples were analysed, white colour means that no experimental values are available).
Comparison of our Integral Data Assimilation results for actinides with results reported in the literature. No data is available for ^{246}Cm(n,γ), ^{242}Cm(n,γ), ^{237}Np(n,2n) and ^{246}Cm(n,γ).
Comparison of our Integral Data Assimilation results for fission products with results reported in the literature. I_{0} and σ_{0} refers to the capture resonance integral and the thermal capture cross section, respectively.
Evaluated nuclear data files and new resonance parameters in agreement with the nuclear data adjustment trends provided by our Integral Data Assimilation study.
All Figures
Fig. 1 Flow chart of the DARWIN2.3 package for PWR calculations. 

In the text 
Fig. 2 Average calculatedtoexperimental values (〈C/E〉1) obtained for UOX and MOX fuels with the DARWIN2.3 package at 40 GWd/t using the JEFF3.1.1 library. 

In the text 
Fig. 3 Differences obtained on the isotopic concentrations (normalized to ^{238}U concentration) on a pincell geometry for a 3.7% ^{235}Uenriched UOX fuel at 40 GWd/t between i) in blue: APOLLO2 (AP2) and TRIPOLI4 depletion calculations (T4), ii) in red: two APOLLO2 depletion calculations, with (AP2UPS) and without (AP2) resonant upscattering effects. Error bars represent the statistical uncertainty provided by the TRIPOLI4 calculations. 

In the text 
Fig. 4 Correlation matrix between calculatedtoexperimental isotopic ratios used for the assimilation procedure. 

In the text 
Fig. 5 Evolution of the calculatedtoexperimental discrepancies before and after integral data assimilation for the ^{241}Am/^{238}U isotopic ratio in UOX fuels. 

In the text 
Fig. 6 Evolution of the calculatedtoexperimental discrepancies before and after integral data assimilation for the ^{241}Am/^{238}U isotopic ratio in MOX fuels. 

In the text 
Fig. 7 Production chain of ^{244}Cm. 

In the text 
Fig. 8 Evolution of the calculatedtoexperimental discrepancies before and after integral data assimilation for the ^{244}Cm/^{238}U isotopic ratio in UOX fuels. 

In the text 
Fig. 9 Evolution of the calculatedtoexperimental discrepancies before and after integral data assimilation for the ^{244}Cm/^{238}U isotopic ratio in MOX fuels. 

In the text 
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