Reactor Theory (Nuclear Parameters)DOE-HDBK-1019/2-93NEUTRON LIFE CYCLETABLE 1Average Number of Neutrons Liberated in FissionFissile NucleusThermal NeutronsFast NeutronsnhnhUranium-2332.492.292.582.40Uranium-2352.422.072.512.35Plutonium-2392.932.153.042.90In the case where the fuel contains several fissionable materials, it is necessary to account foreach material. In the case of a reactor core containing both uranium-235 and uranium-238, thereproduction factor would be calculated as shown below.(3-2)h NU235sU235fnU235NU235sU235aNU238sU238aExample:Calculate the reproduction factor for a reactor that uses 10% enriched uranium fuel. Themicroscopic absorption cross section for uranium-235 is 694 barns. The cross sectionfor uranium-238 is 2.71 barns. The microscopic fission cross section for uranium-235 is582 barns. The atom density of uranium-235 is 4.83 x 1021atoms/cm3. The atom densityof uranium-238 is 4.35 x 1022 atoms/cm3. n is 2.42.Solution:Use Equation (3-2) to calculate the reproduction factor.h NU235sU235fnU235NU235sU235aNU238sU238a4.83 x 1021atomscm3582 x 1024cm22.424.83 x 1021atomscm3694 x 1024cm24.35 x 1022atomscm32.71 x 1024cm21.96Rev. 0NP-03Page 7
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