Abstract
The distribution of neutron counts in a subcritical multiplying system with an external source has been investigated in the framework of the Kolmogorov equations (KE), introducing some generalizations. The backward KE, without delayed neutrons, has been solved for the probability generating function ( pgf) in the case of many counting intervals and suitably differentiated for the determination of joint probabilities and moments. Attempts have been made to solve the backward KE taking into account the delayed neutrons and a recurrent relation has been obtained for the pgf. However, this solution is too complicated to lend itself to further manipulations. All the above calculations adopt the usual simplified fission model. Without any such assumption the backward and the forward KE with delayed neutrons have been solved for the first two moments in case of a single counting interval, thus obtaining the most general expression for the reduced variance. This formula, in the frame of the simplified fission model, reduces to a much simpler expression, which is shown to be practically equivalent to the generally used one. Finally, the backward KE with delayed neutrons and the simplified fission model assumption has been solved for the mean value, variance and covariance of neutron counts in the case of time dependent sources.
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