A study of the neutron population in a nuclear reactor as a branching process. New results are presented on the extinction probability of a supercritical reactor near the critical dimension, extending results of T. E. Harris. In this special context, parts of the theory of branching processes are given. The results apply to spheres, to infinite slabs, and to rods, with the assumptions that the neutron energy is constant and that the collision- fission process is isotropic. Homogeneity is also assumed, although similar results can be obtained in nonhomogeneous cases of restricted types. Thus, a new computational method is determined for estimating the critical dimension and the steady-state flux for the reactors considered. This replaces the eigenvalue problem of transport theory by a nonlinear functional equation that can be solved by iteration.
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