The detection statistics of neutrons and photons emitted from a fissile sample

The purpose of this paper is to present new analytical derivations to describe the statistical properties of the emission and detection of neutrons and photons generated in and emitted from fissile samples, with absorption included. The results of the analytical approach are compared with and validated by corresponding Monte Carlo simulations. The joint detection probability of the generated and detected neutrons and photons are also described. The analytical model described in this paper accounts for absorption and detection, thus extending the model presented in previous studies. By using this new, more realistic model, one can investigate the relative feasibilities of measuring neutrons, gamma photons or combinations thereof, for the analysis of a specific fissile sample. It is seen that, in contrast to the case of neutrons, for an increasing mass the absorption in the sample decreases the probability of multiple photon emissions. Hence we confirm previous observations 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.