Abstract
Since neutrons at certain energies colliding with fissile nuclei may cause them to undergo Fission reaction by splitting them, new neutrons are produced at high energies but certain amount of fissile material is required for a sustainable chain reaction by these high energetic neutrons. It is required to determine the amount of mass necessary for a Fission chain reaction since the procedure is completely random for neutrons to strike target nuclei. It is known that the critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction in any system. It is obvious that the critical mass of a fissionable material depends upon its nuclear properties, such as its fission cross-section, its density, its shape, its enrichment, its purity, etc. In this study, the Monte Carlo Method is studied to calculate the critical mass for three basic geometries. The survival fraction value is determined for the criticality condition for geometries and is compared, respectively. All calculations are also repeated for sphere with a reflector. Analytical and numerical results are compared. A conclusion is presented.
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