Fluctuations of the Number of Neutrons in a Pile

Statistical fluctuations in the number of neutrons in a pile which is just under critical and contains distributed neutron sources such as spontaneous fissions, $\ensuremath{\alpha}\ensuremath{-}n$ reactions, etc., are considered for the following two cases: (a) The delayed neutrons are taken into account, but the pile is assumed to be operating at a steady power, and (b), the power at which the pile operates is assumed to change periodically, but the delayed neutrons are neglected.For both cases the expression for the standard deviation of the number of neutrons is derived, and in case (a) the expression for the coefficient of correlation between the number of neutrons and the number of excited nuclei of each particular type, which lead to the formation of the delayed neutrons, is also given.The method used throughout the calculations is that of the probability generating function.For the case of a steadily operating pile, the effect of a finite resolving time of the recording instrument upon the observed value of the standard deviation of the number of neutrons is also determined through a study of the spectrum of the fluctuations.