Bayesian updating for data adjustments and multi-level uncertainty propagation within Total Monte Carlo

Abstract

In this work, a method is proposed for combining differential and integral benchmark experimental data within a Bayesian framework for nuclear data adjustments and multi-level uncertainty propagation using the Total Monte Carlo method. First, input parameters to basic nuclear physics models implemented within the state of the art nuclear reactions code, TALYS, were sampled from uniform distributions and randomly varied to produce a large set of random nuclear data files. Next, a probabilistic data assimilation was carried out by computing the likelihood function for each random nuclear data file based first on only differential experimental data (1st update) and then on integral benchmark data (2nd update). The individual likelihood functions from the two updates were then combined into a global likelihood function which was used for the selection of the final 'best' file. The proposed method has been applied for the adjustment of 208 Pb in the fast neutron energy region below 20 MeV. The 'best' file from the adjustments was compared with available experimental data from the EXFOR database as well as evaluations from the major nuclear data libraries and found to compare favourably.

In search of the best nuclear data file for proton induced reactions: Varying both models and their parameters

“…Similar to Ref. [7], experiments that were observed to be inconsistent with other experimental sets and deviate from the trend of our model calculations as well as other evaluations (when available), were not considered. Also, for the cases where the only experimental data available for a particular energy range has no uncertainties reported, we assume a 10% uncertainty for that experimental set.…”

“…In Ref. [7], a weighted χ 2 where channel weights proportional to the average channel cross section, was presented. The idea was to assign channels with large average cross sections higher weights and those with lower relatively smaller average cross sections, lower weights.…”

“…Further, similar to Refs. [7,8], the experimental data points were assumed to be uncorrelated. The reason being that, experimental correlations especially for proton induced reactions were not readily available.…”

Windowed multipole representation of R-matrix cross sections

“…One such algorithm is the Rayleigh-quotient method, used by Brune to find alternative parameters in [54]. Alternatively, it is sometimes more computationally advantageous to first find the radioactive poles {p j } directly by solving the channel determinant problem, det R −1 L (z) z=pj = 0, or the corresponding level determinant one, det A −1 (z) z=pj = 0, and to second solve the associated eigenvalue problem (which is now linear), or even to directly evaluate the residues at the found poles by contour integrals (83) and (84). Such methods tailored to find all the roots of the radioactive problem where introduced in [29], in section 5 of [36], or in equations ( 200) and (204) of [55].…”

“…And yet, these parameters distributions are our best way of balancing all the different uncertainties from disjointed experiments with the underlying Rmatrix theory which unifies our understanding of nuclear interactions physics. Significant work has been carried out to infer parameter distributions that accurately reproduce our uncer-tainty of nuclear cross sections [55,[78][79][80][81][82][83][84][85]. Assuming R-matrix cross section uncertainty is well represented by the resonance parameters multivariate normal distribution N (Γ, Var (Γ)) documented in standard nuclear data libraries (file 32 in ENDF/B-VIII.0 [14]), there are two ways of translating this into cross section distributions: 1) first-order sensitivity propagation, or; 2) stochastic cross sections.…”