The thermal utilization factor gives the fraction of the thermal neutrons that are absorbed in the nuclear fuel, in all isotopes of the nuclear fuel. But the nuclear fuel is isotopically rich material even in this case, in which we consider only the fissionable nuclei of in the fuel. In the fresh uranium fuel, there are only three fissionable isotopes that have to be included in the calculations – 235U, 238U, 234U. In the power reactors, the fuel significantly changes its isotopical content as the fuel burnup increases. The isotope of 236U and also trace amounts of 232U appears. The major consequence of increasing fuel burnup is that the content of the plutonium increases (especially 239Pu, 240Pu and 241Pu). All these isotopes have to be included in the calculations of the reproduction factor.
Another fact is that not all the absorption reactions that occur in the fuel results 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 neutron. About 85% of all absorption reactions result in fission. Each of fissionable nuclei have different fission probability and these probabilities are determined by microscopic cross-sections.
It is obvious at this point the neutrons finish one generation and new generation of neutrons may be created. The number of neutrons created in the new generation is determined by the neutron reproduction factor. 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. The reproduction factor is shown below.