Analytical and Numerical Modelling of the Detection Statistics of Emission from a Fissile Sample with Absorption

This paper investigates an analytical derivation of the distribution of the number of neutrons and photons emitted by a multiplying sample. The relationship between the statistics of the generated and detected neutrons and photons is also described. The analytical model described in this paper accounts for absorption, thus extending the model presented in previous studies. By using this new, improved model, one can investigate the relative feasibilities of measuring neutrons or gamma photons for the analysis of a specific fissile sample. In fact, larger mass will lead to larger self-shielding for gamma photons, whereas for neutrons a larger mass will lead to increased multiplicities due to an increased probability to induce fission for each neutron, with absorption playing a minor role. The results suggest that although photons have a larger initial (source) multiplication, neutrons might be more favourable to measure in the case of large samples because of the increasing self-shielding effect for gamma photons.