A method is presented for computing the multiplication factor of single region systems which contain fissile material and which may be specified by one, two or three coordinates. The systems are assumed to be unreflected, homogeneous assemblies which have no re-entrant surfaces. The method follows the successive scattered neutron collisions which take place in a system and computes for each interaction the product of the probability of a fission collision and the average number of secondaries per fission. The sum of these products, in the limit as the number of collisions become infinite, is the multiplication factor of the system. The initial energy distribution of the neutron-source density needed to start the calculations, is specified in a sixteen energy-group format. The initial spatial neutron distribution is assumed to be uniform and to remain unchanged as a result of collisions. The source-density amplitudes for each successive collision is taken as the probability of a scattering interaction multiplied by the source-density amplitude for the previous collision. The source-density energy distribution is recomputed after each collision using multigroup methods. Critical sizes are found by obtaining the multiplication factor as a function of the system dimensions and graphically determining the dimensions which make the factor equal unity. The critical dimensions of several plutonium metal and enriched-uranium metal systems are computed and, when possible, the calculated dimensions are compared with experimental values. The computed dimensions are from 2·1 to 5·6 per cent higher than the measured values. This discrepancy is due primarily to the assumption of a uniformly distributed source density. © 1970.
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