Impact of H in H2O thermal scattering data on criticality calculation: uncertainty and adjustment

In this paper, the impact of the thermal scattering data for H in H20 is estimated on criticality benchmarks, based on the variations of the CAB model parameters. The Total Monte Carlo method for uncertainty propagation is applied for 63 keff criticality cases, sensitive to H in H20. It is found that their impact is of a few tenth of pcm, up to 300 pcm maximum, and showing highly non-linear distributions. In a second step, an adjustment is proposed for these thermal scattering data, leading to a better agreement between calculated and experimental keff values, following an increase of scattering contribution. This work falls into the global approach of combining advanced theoretical modelling of nuclear data, followed by possible adjustment in order to improve the performances of a nuclear data library.

Using effective temperature as a measure of the thermal scattering law uncertainties to UOX fuel calculations from room temperature to 80°C

The effective temperature Teff is an important physical quantity in neutronic calculations. It can be introduced in a Free Gas Model to approximate crystal lattice effects in the Doppler broadening of the neutron cross sections. In the last decade, a few research works proposed analytical or Monte-Carlo perturbation schemes for estimating uncertainties in neutronic calculations due to thermal scattering laws. However, the relationship between the reported results with Teff was not discussed. The present work aims to show how the effective temperature can measure the impact of the thermal scattering law uncertainties on neutronic calculations. The discussions are illustrated with Monte-Carlo calculations performed with the TRIPOLI-4® code on the MISTRAL-1 benchmark carried out in the EOLE facility of CEA Cadarache (France) from room temperature to 354 K (80°C). The uncertainty analysis is focused on the impact of the thermal scattering laws of H2O and UO2 on the neutron multiplication factor keff for UOX fuel moderated by water. When using the H2O and UO2 candidate files for the JEFF-4 library, the variation range of Teff leads to a keff uncertainty of 2.3 pcm/K, on average. In the temperature range investigated in this work, Teff uncertainties of ±20 K for H2O and ±10 K for UO2 give uncertainties on the multiplication factor that remains close to ±50 pcm. Such a low uncertainty confirms the improved accuracy achieved on the modelisation of the latest thermal scattering laws of interest for light water reactors. In the future evaluated nuclear data libraries, uncertainty budget analysis associated with the low neutron energy scattering process will be a marginal contribution compared to the capture process.

Temperature-dependent dynamic structure factors for liquid water inferred from inelastic neutron scattering measurements

Temperature-dependent dynamic structure factors S(Q, ω) for liquid water have been calculated using a composite model, which is based on the decoupling approximation of the mean square displacement of the water molecules into diffusion and solid-like vibrational parts. The solid-like vibrational part S_vib(Q, ω) is calculated with the phonon expansion method established in the framework of the incoherent Gaussian approximation. The diffusion part S_diff(Q, ω) relies on the Egelstaff-Schofield translational diffusion model corrected for jump diffusions and rotational diffusions with the Singwi-Sjölander random model and Sears expansion, respectively. Systematics of the model parameters as a function of temperature were deduced from quasi-elastic neutron scattering data analysis reported in the literature and from molecular dynamics (MD) simulations relying on the TIP4P/2005f model. The resulting S(Q, ω) values are confronted by means of Monte Carlo simulations to inelastic neutron scattering data measured with IN4, IN5, and IN6 time-of-flight spectrometers of the Institut Laue-Langevin (ILL) (Grenoble, France). A modest range of temperatures (283-494 K) has been investigated with neutron wavelengths corresponding to incident neutron energies ranging from 0.57 to 67.6 meV. The neutron-weighted multiphonon spectra deduced from the ILL data indicate a slight overestimation by the MD simulations of the frequency shift and broadening of the librational band. The descriptive power of the composite model was suited for improving the comparison to experiments via Bayesian updating of prior model parameters inferred from MD simulations. The reported posterior temperature-dependent densities of state of hydrogen in H₂O would represent valuable insights for studying the collective coupling interactions in the water molecule between the inter- and intramolecular degrees of freedom.

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.