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

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.