Fissile mass determination by the active neutron correlation technique with the generalised Poisson parameters or its factorial moments

An analytical model is derived for a process with a fissile sample irradiated periodically by a pulsed neutron source in a neutron moderator assembly. The generated induced fission neutrons are detected in a specialised thermal neutron detector assembly, dimensioned for a short thermal neutron lifetime 1/λ. This known lifetime is much shorter than the thermal neutron lifetime 1/Λ of the moderator assembly. Neutrons arriving in the detector assembly are registered in periodically opened observation intervals of duration τ. This is repeated after each pulse of the neutron generator. The probability distribution of these signals is treated as a generalised inhomogeneous Poisson distribution. It is characterised by the parameter Γj(t) for the detection of j, j=1,2,3,…, neutrons in the thermal neutron detector assembly during the observation interval [t−τ, t] after time t−τ≥s0 following each source pulse at time s=0. The normalised factorial moment m ( μ ) * ( t ) of Γj(t) with order μ is proportional to the number of events, where all μ signals are correlated i.e., from a common fission event. Γj(t) and m ( μ ) * ( t ) x are expressed as a function of the probability distribution bx(t), for x=0,1,2,3,…, and as a function of its normalised factorial moments m(μ)(t), for μ=0,1,2,3,…, respectively. Both Γj(t) and m ( μ ) * ( t ) depend each on a component decreasing exponentially with the argument Λt for all j and μ values, due to induced fission events. These also have a component independent of t, due to spontaneous fission and background events. This relationship is used to discriminate between induced fission and stationary events. It serves to determine the fissile mass GF, the detection probability εF for slowed down fission neutrons, the mass GS of spontaneous fission neutron emitters, the detection probability εS for slowed down spontaneous fission neutrons and neutrons from (α, n) reactions. A solution for two thermal neutron lifetimes 1/Λi, i=1,2 of the moderator assembly is given. It is valid for fissile material embedded in a waste matrix affecting the lifetime 1/Λ of the neutron moderator assembly.