Neutron multiplicity counting distribution reconstruction from moments using Meixner polynomial expansion and N-forked branching approximations

TL;DR

This paper introduces two novel methods for reconstructing neutron multiplicity distributions from moments, utilizing Meixner polynomial expansion and N-forked branching approximations, to improve nuclear parameter inference.

Contribution

It presents two new approaches for distribution reconstruction from moments, expanding the toolkit for neutron count analysis in nuclear physics.

Findings

Demonstrates effectiveness of Meixner polynomial expansion in distribution reconstruction.

Shows N-forked branching approximation improves correlation modeling.

Provides a comparative analysis of the two methods.

Abstract

Methods used to infer nuclear parameters from neutron count statistics fall into two categories depending on whether they use moments or count number probabilities. As probabilities are in general more difficult to calculate, we are interested here in the reconstruction of distributions from their first moments. For this, we explore two approaches. The first one relies on a generalization of the 2-forked branching correlation (quadratic) approximation used in the PMZBB and Poisson radical distributions, the second one is based on the expansion of the distribution on a basis of Meixner discrete orthogonal polynomials.