Retroactive Generation of Covariance Matrix of Nuclear Model Parameters Using Marginalization Techniques

Covariance of resonance parameters ascribed to systematic uncertainties in experiments

In resonance analyses, experimental uncertainties affect the accuracy of resonance parameters. The resonance analysis code REFIT can consider the statistical uncertainty of the experimental data when evaluating the resonance parameter uncertainty. However, since the systematic uncertainties are not independent at each measured energy, they must be treated differently from the statistical uncertainty. In the present study, we developed a new method to incorporate the systematic uncertainty coming from sample thickness into the uncertainty of resonance parameters. We applied this method to transmission of natural zinc measured at ANNRI of MLF in J-PARC and derived the systematic uncertainty of resonance parameters. We found that some of resonance parameters have larger systematic uncertainties than the statistical ones.

Marginalization methods for the production of conservative covariance on nuclear data

The production of evaluated nuclear data consists not only in the determination of best estimate values for the quantities of interest but also on the estimation of the related uncertainties and correlations. When nuclear data are evaluated with underlying nuclear reaction models, model parameters are expected to synthesize all the information that is extracted from the experimental data they are adjusted on. When dealing with models with a small number of parameters compared to the number of experimental data points – e.g. in resonant cross section analysis – one sometimes faces excessively small evaluated uncertainty compared for instance with model/experimental data agreement. To solve this issue, an attempt was to propagate the uncertainty coming from experimental parameters involved in the data reduction process on the nuclear physics model parameters. It pushed experimentalists to separately supply random (statistical) and systematic uncertainties. It also pushed evaluators to include or mimic the data reduction process in the evaluation. In this way experimental parameters – also called nuisance parameters – could be used to increase evaluated parameter uncertainty through marginalization techniques. Two of these methods: Matrix and Bayesian marginalizations – respectively called sometimes Analytical and Monte-Carlo Marginalizations – that are currently used for evaluation will be discussed here and some limitations highlighted. A third alternative method, also based on a Bayesian approach but using the spectral decomposition of the correlation matrix, is also presented on a toy model, and on a a simple case of resonant cross section analysis.

CONRAD – a code for nuclear data modeling and evaluation

The CONRAD code is an object-oriented software tool developed at CEA since 2005. It aims at providing nuclear reaction model calculations, data assimilation procedures based on Bayesian inference and a proper framework to treat all uncertainties involved in the nuclear data evaluation process: experimental uncertainties (statistical and systematic) as well as model parameter uncertainties. This paper will present the status of CONRAD-V1 developments concerning the theoretical and evaluation aspects. Each development is illustrated with examples and calculations were validated by comparison with existing codes (SAMMY, REFIT, ECIS, TALYS) or by comparison with experiment. At the end of this paper, a general perspective for CONRAD (concerning the evaluation and theoretical modules) and actual developments will be presented.

Feedback from experimental isotopic compositions of used nuclear fuels on neutron cross sections and cumulative fission yields of the JEFF-3.1.1 library by using integral data assimilation

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 235U, 239Pu and 241Pu neutron capture cross sections available in the JEFF-3.1.1 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 (236U, 238Pu, 240Pu, 242Pu, 241Am, 243Am, 245Cm) and fission products (103Rh, 153Eu, 154Eu) as well as for the 238U(n,2n) and 237Np(n,2n) reactions. Meaningful trends for the cumulative fission yields of 144Ce, 133Cs, 137Cs and 106Ru for the 235U(nth,f) and 239Pu(nth,f) reactions are also reported.

Generation of the 1H in H2O neutron thermal scattering law covariance matrix of the CAB model

The thermal scattering law (TSL) of 1H in H2O describes the interaction of the neutron with the hydrogen bound to light water. No recommended procedure exists for computing covariances of TSLs available in the international evaluated nuclear data libraries. This work presents an analytic methodology to produce such a covariance matrix-associated to the water model developed at the Atomic Center of Bariloche (Centro Atomico Bariloche, CAB, Argentina). This model is called as CAB model, it calculates the TSL of hydrogen bound to light water from molecular dynamic simulations. The performance of the obtained covariance matrix has been quantified on integral calculations at “cold” reactor conditions between 20 and 80∘ C. For UOX fuel, the uncertainty on the calculated reactivity ranges from ±71 to ±155 pcm. For MOX fuel, it ranges from ±110 to ±203 pcm.

Nuclear data adjustment based on the interpretation of post-irradiation experiments with the DARWIN2.3 package

DARWIN2.3 is the French reference package dedicated to fuel cycle applications, computing fuel inventory as well as decay heat, neutron emissions, α, β and γ spectra. The DARWIN2.3 package fuel inventory calculation was experimentally validated with Post-Irradiation Experiments (PIEs), mainly consisting in irradiated fuel pellets analysis. This paper presents a method to assimilate these integral trends for improving nuclear data. In this study, the method is applied to 137Cs/238U concentration ratio. Results suggest an increase of the JEFF-3.1.1 235U cumulated thermal fission yield in 137Cs by (+3.8 ± 2.1)%, from 6.221E-02 to 6.460E-02 ± 2.1%.