The number distribution of neutrons and gamma photons generated in a multiplying sample

We demonstrate an analytical derivation of the full probability distribution for the number of neutrons and 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. Comparisons with Monte Carlo calculations show very good agreement. The results show that with increasing mass the probability distributions change by acquiring a tail for higher n values.