It is known the fission neutrons are of importance in any chain-reacting system. It can be seen there is a limit value about η = 2.08. As a result of the ratios of the microscopic cross-sections, η increases strongly in the region of low enrichment fuels. Where e is the atomic degree of enrichment e = N 5/(N 5+N 8), the reproduction factor is determined by the nuclear fuel composition and strongly depends on the neutron flux spectrum in the core, for natural uranium in the thermal reactor, η = 1.34. Reproduction factor as a function of the uranium enrichment This equation can also be written in terms of uranium enrichment: In which ν is the average neutrons production of 235U, N 5 and N 8 are the atomic number densities of the isotopes 235U and 238U (when using other uranium isotopes or plutonium, the equation is modified trivially). In the case of fresh uranium fuel, we consider only one fissile isotope, 235U, and the numerical value of η is given by the following equation: This factor is determined by the probability that fission reaction will occur times the average number of neutrons produced per one fission reaction. Source: JANIS (Java-based Nuclear Data Information Software) The JEFF-3.1.1 Nuclear Data Library The ratio depends strongly on the incident neutron energy. The capture-to-fission ratio may be used as an indicator of “quality” of fissile isotopes. Of thermal neutrons absorbed in the fuel. The reproduction factor, η, is the ratio of the number of fast neutrons produced by thermal fission to the number The neutron reproduction factor determines the number of neutrons created in the new generation. The neutrons finish one generation, and a new generation of neutrons may be created. Each fissionable nuclei have a different fission probability, and microscopic cross-sections determine these probabilities. About 85% of all absorption reactions result in fission. If we consider the thermal neutron and the nucleus of 235U, then about 15% of all absorption reactions result in radiative capture of a neutron. All these isotopes have to be included in the calculations of the reproduction factor.Īnother fact is that not all the absorption reactions that occur in the fuel result in fission. The major consequence of increasing fuel burnup is that the content of the plutonium increases (especially 239Pu, 240Pu, and 241Pu). The isotope of 236U and also trace amounts of 232U appears. In power reactors, the fuel significantly changes its isotopic content as the fuel burnup increases. In the fresh uranium fuel, only three fissionable isotopes must be included in the calculations – 235U, 238U, 234U. But the nuclear fuel is an isotopically rich material even in this case, in which we consider only the fissionable nuclei in the fuel. The thermal utilization factor gives the fraction of the thermal neutrons absorbed in the nuclear fuel in all isotopes of the nuclear fuel. The reproduction factor, η, is defined as the ratio of the number of fast neutrons produced by thermal fission to the number of thermal neutrons absorbed in the fuel.
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