NDOE-HDBK-1019/1-93NUCLEAR CROSS SECTIONS AND NEUTRON FLUXReactor Theory (Neutron Characteristics)NP-02Page 8Rev. 0Whether a neutron will interact with a certain volume of material depends not only on themicroscopic cross section of the individual nuclei but also on the number of nuclei within thatvolume. Therefore, it is necessary to define another kind of cross section known as themacroscopic cross section ( ). The macroscopic cross section is the probability of a givenreaction occurring per unit travel of the neutron. is related to the microscopic cross section( ) by the relationship shown below.(2-2)where:=macroscopic cross section (cm )-1N =atom density of material (atoms/cm )^{3}=microscopic cross-section (cm )^{2}The difference between the microscopic and macroscopic cross sections is extremely importantand is restated for clarity. The microscopic cross section ( ) represents the effective target areathat a single nucleus presents to a bombarding particle. The units are given in barns or cm .^{2}The macroscopic cross section ( ) represents the effective target area that is presented by all ofthe nuclei contained in 1 cm of the material. The units are given as 1/cm or cm .3-1A neutron interacts with an atom of the material it enters in two basic ways. It will eitherinteract through a scattering interaction or through an absorption reaction. The probability ofa neutron being absorbed by a particular atom is the microscopic cross section for absorption,. The probability of a neutron scattering off of a particular nucleus is the microscopic crossasection for scattering, . The sum of the microscopic cross section for absorption and thesmicroscopic cross section for scattering is the total microscopic cross section, . T= + TasBoth the absorption and the scattering microscopic cross sections can be further divided. Forinstance, the scattering cross section is the sum of the elastic scattering cross section () andsethe inelastic scattering cross section ().si= + ssesiThe microscopic absorption cross section () includes all reactions except scattering. However,afor most purposes it is sufficient to merely separate it into two categories, fission () andfcapture (). Radiative capture of neutrons was described in the Neutron Interactions chaptercof Module 1.= + afc