NEUTRON LIFE CYCLEDOE-HDBK-1019/2-93Reactor Theory (Nuclear Parameters)InfiniteMultiplicationFactor,kNot all of the neutrons produced by fission will have the opportunity to cause new fissionsbecause some neutrons will be absorbed by non-fissionable material. Some will be absorbedparasitically in fissionable material and will not cause fission, and others will leak out of thereactor. For the maintenance of a self-sustaining chain reaction, however, it is not necessarythat every neutron produced in fission initiate another fission. The minimum condition is foreach nucleus undergoing fission to produce, on the average, at least one neutron that causesfission of another nucleus. This condition is conveniently expressed in terms of a multiplicationfactor. The number of neutrons absorbed or leaking out of the reactor will determine the value of thismultiplication factor, and will also determine whether a new generation of neutrons is larger,smaller, or the same size as the preceding generation. Any reactor of a finite size will haveneutrons leak out of it. Generally, the larger the reactor, the lower the fraction of neutronleakage. For simplicity, we will first consider a reactor that is infinitely large, and thereforehas no neutron leakage. A measure of the increase or decrease in neutron flux in an infinitereactor is the infinite multiplication factor, k. The infinite multiplication factoris the ratio ofthe neutrons produced by fission in one generation to the number of neutrons lost throughabsorption in the preceding generation. This can be expressed mathematically as shown below.k_{}neutron production from fission in one generationneutron absorption in the preceding generationFourFactorFormulaA group of fast neutrons produced by fission can enter into several reactions. Some of thesereactions reduce the size of the neutron group while other reactions allow the group to increasein size or produce a second generation. There are four factors that are completely independentof the size and shape of the reactor that give the inherent multiplication ability of the fuel andmoderator materials without regard to leakage. This four factor formulaaccurately represents theinfinite multiplication factor as shown in the equation below.k= p f hwhere:= fast fission factorp = resonance escape probabilityf = thermal utilization factorh = reproduction factorEach of these four factors, which are explained in the following subsections, represents a process thatadds to or subtracts from the initial neutron group produced in a generation by fission.NP-03Rev. 0Page 2