The Number Distribution and Factorial Moments of Neutrons and Gamma Photons Generated in a Multiplying Sample

An analytical derivation of the full probability distribution was demonstrated for the number of neutrons and gamma photons generated in a fissile sample with internal multiplication. The formulae for the probability distribution P(n) are derived in a recursive manner, and the results are compared with Monte Carlo calculations. We calculate the probability distribution up to values of n where P(n) becomes negligible. By introducing modified factorial moments of the number of neutrons and gamma photons generated in fission, the resulting probability distribution is formally equivalent with the expressions for factorial moments of the total number of neutrons and photons generated in the sample. These calculations are in very good agreement with Monte Carlo simulations. The results show that with increasing sample mass, the probability distributions change by acquiring a tail for higher n values.