REACTION RATES - h1019v1

Nuclear Cross Section and Neutron Flux Summary

Nuclear Physics and Reactor Theory Volume 1 of 2
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1 ) REACTION RATES DOE-HDBK-1019/1-93 Reactor Theory (Neutron Characteristics) NP-02 Page 18 Rev. 0 REACTION RATES It is possible to determine the rate at which a nuclear reaction will take place based on the neutron flux, cross section for the interaction, and atom density of the target. This relationship illustrates how a change in one of these items affects the reaction rate. EO 2.10 Given the neutron flux and macroscopic cross section, CALCULATE the reaction rate. EO 2.11 DESCRIBE the relationship between neutron flux and reactor power. Reaction Rates If the total path length of all the neutrons in a cubic centimeter in a second is known, (neutron flux (1 )), and if the probability of having an interaction per centimeter path length is also known (macroscopic cross section (* )), multiply them together to get the number of interactions taking place in that cubic centimeter in one second. This value is known as the reaction rate and is denoted by the symbol R. The reaction rate can be calculated by the equation shown below. R = 1 * (2-6) where: R = reaction rate (reactions/sec) 1 = neutron flux (neutrons/cm -sec) 2 * = macroscopic cross section (cm ) -1 Substituting the fact that * = N ) into Equation (2-6) yields the equation below. where: ) = microscopic cross section (cm )² N = atom density (atoms/cm )³

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