1)REACTION RATESDOE-HDBK-1019/1-93Reactor Theory (Neutron Characteristics)NP-02Page 18Rev. 0REACTION RATESIt is possible to determine the rate at which a nuclear reaction will take placebased on the neutron flux, cross section for the interaction, and atom density of thetarget. This relationship illustrates how a change in one of these items affects thereaction rate. EO 2.10Given the neutron flux and macroscopic cross section,CALCULATE the reaction rate.EO 2.11DESCRIBE the relationship between neutron flux and reactorpower.ReactionRatesIf the total path length of all the neutrons in a cubic centimeter in a second is known, (neutronflux (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 takingplace in that cubic centimeter in one second. This value is known as the reaction rate and isdenoted 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 )-1Substituting the fact that * = N ) into Equation (2-6) yields the equation below.where:)=microscopic cross section (cm )^{2}N =atom density (atoms/cm )^{3}