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A Discussion of a model (related to one used earlier in RM-2288, Invariant Imbedding and Wave Propagation in Stochastic Media) to investigate the probability distribution of the total number of neutrons produced by an initial trigger neutron. Emphasis is given to the case in which the length of the fissionable body is exactly critical. The model is a simplified one that examines only one-dimensional motion of the neutrons in a nuclear chain reaction. The results of this work may be suggestive to nuclear physicists and weapon designers in studies of critical size or of situations in which a stray neutron may excite a chain reaction.

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