Reactor Theory (Nuclear Parameters)DOE-HDBK-1019/2-93NEUTRON LIFE CYCLEFastFissionFactor,()The first process that the neutrons of one generation may undergo is fast fission. Fast fissionis fission caused by neutrons that are in the fast energy range. Fast fission results in the netincrease in the fast neutron population of the reactor core. The cross section for fast fission inuranium-235 or uranium-238 is small; therefore, only a small number of fast neutrons causefission. The fast neutron population in one generation is therefore increased by a factor calledthe fast fission factor. The fast fission factor() is defined as the ratio of the net number of fastneutrons produced by all fissions to the number of fast neutrons produced by thermal fissions.The mathematical expression of this ratio is shown below.number of fast neutrons produced by all fissionsnumber of fast neutrons produced by thermal fissionsIn order for a neutron to be absorbed by a fuel nucleus as a fast neutron, it must pass closeenough to a fuel nucleus while it is a fast neutron. The value of will be affected by thearrangement and concentrations of the fuel and the moderator. The value of is essentially 1.00for a homogenous reactor where the fuel atoms are surrounded by moderator atoms. However,in a heterogeneous reactor, all the fuel atoms are packed closely together in elements such aspins, rods, or pellets. Neutrons emitted from the fission of one fuel atom have a very goodchance of passing near another fuel atom before slowing down significantly. The arrangementof the core elements results in a value of about 1.03 for in most heterogeneous reactors. Thevalue of is not significantly affected by variables such as temperature, pressure, enrichment,or neutron poison concentrations. Poisons are non-fuel materials that easily absorb neutrons andwill be discussed in more detail later.ResonanceEscapeProbability,(p)After increasing in number as a result of some fast fissions, the neutrons continue to diffusethrough the reactor. As the neutrons move they collide with nuclei of fuel and non-fuel materialand moderator in the reactor losing part of their energy in each collision and slowing down.While they are slowing down through the resonance region of uranium-238, which extends fromabout 6 eV to 200 eV, there is a chance that some neutrons will be captured. The probabilitythat a neutron will not be absorbed by a resonance peak is called the resonance escapeprobability. The resonance escape probability (p) is defined as the ratio of the number ofneutrons that reach thermal energies to the number of fast neutrons that start to slow down. Thisratio is shown below.p number of neutrons that reach thermal energynumber of fast neutrons that start to slow downRev. 0NP-03Page 3

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