Influence of the quadratic approximation on the moments of the neutron and count distributions in a multiplying system

The determination of the neutron and count distributions in a multiplying system is generally performed utilizing the quadratic approximation for the probability generating function of the neutrons emitted per fission. The validity of this approximation, when used for moments calculation, is investigated in this paper. Rigorous and approximate expression for the third and fourth factorial moments of both distributions are obtained and compared. In agreement with the interpretation based on the model with sampled particles, the results show that the quadratic approximation may be applied for obtaining the moments of the counting distribution without any efficiency limitations, as well as for obtaining the moments of the neutron distribution. (author)