A consistent, Bayesian, approach to the cross section probability distribution in the unresolved resonance region

Abstract

The cross sections of neutron-induced reactions can be divided into three energy ranges: the resolved resonance region (RRR), the unresolved resonance region (URR), and the fast region. In general, the cross sections in the URR show significant fluctuations that cannot be predicted and cannot be experimentally resolved, thus, it is commonly assumed that the cross section at a specific energy is given by a probability distribution function (PDF) over a range of values that can span several orders of magnitude. The current methodology used to describe such behavior is to construct the PDF by stochastically generating resonance ladders and numerically measuring the PDF. The resonance ladders are sampled using known resonance statistical properties and average resonance widths and spacings extrapolated from the RRR. Although this is a standard and widely used technique, it is computationally very expensive, therefore, an alternative, analytical, approach would be preferable due to the considerable speed up of the computational time in real life applications. Moreover, the current methodology does not take into account existing experimental data, such for total and capture cross sections, that are available for many nuclei. Finally, this approach was developed to be used in reactor-scale applications and it is not suited for use in single-event applications. In this work we will rethink the entire approach to the PDF construction using a Bayesian mindset. This will allow us to provide a different definition of the PDF that allows a much faster calculation of the higher-temperature PDFs and a proper combination of theoretical and experimental PDFs following the probability theory. We will also show that our definition is well suited for single-event applications and we will make an explicit connection between our method and the standard approach. We do this by showing that the central limit theorem applies and our method leads to the same PDF obtained with the standard methodology, for a large number of events per history.