Performing Bayesian Analyses With AZURE2 Using BRICK: An Application to the 7Be System

Abstract

Phenomenological R-matrix has been a standard framework for the evaluation of resolved resonance cross section data in nuclear physics for many years. It is a powerful method for comparing different types of experimental nuclear data and combining the results of many different experimental measurements in order to gain a better estimation of the true underlying cross sections. Yet a practical challenge has always been the estimation of the uncertainty on both the cross sections at the energies of interest and the fit parameters, which can take the form of standard level parameters. Frequentist (χ2-based) estimation has been the norm. In this work, a Markov Chain Monte Carlo sampler, emcee, has been implemented for the R-matrix code AZURE2, creating the Bayesian R-matrix Inference Code Kit (BRICK). Bayesian uncertainty estimation has then been carried out for a simultaneous R-matrix fit of the 3He (α,γ)7Be and 3He (α,α)3He reactions in order to gain further insight into the fitting of capture and scattering data. Both data sets constrain the values of the bound state α-particle asymptotic normalization coefficients in 7Be. The analysis highlights the need for low-energy scattering data with well-documented uncertainty information and shows how misleading results can be obtained in its absence.

Improved S factor of the C12(p,γ)N13Skowronski, Masha, Piatti et al. 2023Phys. Rev. C4000View full textAdd to dashboardCite

“…For the studies that do not report any systematic uncertainty, a value of 20% was considered. The present results are included with the error budget aforementioned and The minimization and the error estimation was handled through the bayesian approach using the BRICK framework [41]. Only uninformative priors were used apart from the ANC, which distribution was assumed to be gaussian.…”

“…Additionally, the normalization factors were treated as free parameters with prior distributions defined as gaussians peaked at 1 and sigma given by their systematic error. Apart from the systematic and statistical errors, the energy calibration error was included as well in the fitting procedure [41].…”