NEUTRON LIFE CYCLEDOE-HDBK-1019/2-93Reactor Theory (Nuclear Parameters)As temperature varies, each absorption and fission microscopic cross section varies according tothe 1/v relationship (see Module 2). Since both the numerator and the denominator changeequally, the net change in h is zero. Therefore, h changes only as uranium-235 enrichmentchanges. h increases with enrichment because there is less uranium-238 in the reactor makingit more likely that a neutron absorbed in the fuel will be absorbed by uranium-235 and causefission.To determine the reproduction factor for a single nuclide rather than for a mixture, thecalculation may be further simplified to the one shown below.h ^{sf n}saEffectiveMultiplicationFactorThe infinite multiplication factor can fully represent only a reactor that is infinitely large,because it assumes that no neutrons leak out of the reactor. To completely describe the neutronlife cycle in a real, finite reactor, it is necessary to account for neutrons that leak out. Themultiplication factor that takes leakage into account is the effective multiplication factor (k_{eff}),which is defined as the ratio of the neutrons produced by fission in one generation to the numberof neutrons lost through absorption and leakage in the preceding generation. The effective multiplication factor may be expressed mathematically as shown below.k_{eff }neutron production from fission in one generationneutron absorption in thepreceding generationneutron leakage in thepreceding generationSo, the value of k_{eff} for a self-sustaining chain reaction of fissions, where the neutron populationis neither increasing nor decreasing, is one. The condition where the neutron chain reaction isself-sustaining and the neutron population is neither increasing nor decreasing is referred to asthe criticalcondition and can be expressed by the simple equation k_{eff}= 1 .If the neutron production is greater than the absorption and leakage, the reactor is calledsupercritical. In a supercriticalreactor, k_{eff} is greater than one, and the neutron flux increaseseach generation. If, on the other hand, the neutron production is less than the absorption andleakage, the reactor is called subcritical. In a subcritical reactor, k_{eff} is less than one, and theflux decreases each generation. NP-03Rev. 0Page 8

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