DOE-HDBK-1019/1-93Reactor Theory (Neutron Characteristics)NUCLEAR CROSS SECTIONS AND NEUTRON FLUXRev. 0Page 17NP-02Nuclear Cross Section and Neutron Flux SummaryAtom density (N) is the number of atoms of a given type per unit volume ofmaterial.Microscopic cross section () ) is the probability of a given reaction occurringbetween a neutron and a nucleus. Microscopic cross sections are measured in units of barns, where 1 barn = 10^{-24}cm .^{2}Macroscopic cross section (* ) is the probability of a given reaction occurring perunit length of travel of the neutron. The units for macroscopic cross section arecm .-1The mean free path () is the average distance that a neutron travels in a materialbetween interactions. Neutron flux (1 ) is the total path length traveled by all neutrons in one cubiccentimeter of material during one second.The macroscopic cross section for a material can be calculated using the equationbelow.*= N )The absorption cross section for a material usually has three distinct regions. Atlow neutron energies (<1 eV) the cross section is inversely proportional to theneutron velocity. Resonance absorption occurs when the sum of the kinetic energy of the neutronand its binding energy is equal to an allowed nuclear energy level of the nucleus.Resonance peaks exist at intermediate energy levels. For higher neutron energies,the absorption cross section steadily decreases as the neutron energy increases.The mean free path equals 1/* .The macroscopic cross section for a mixture of materials can be calculated usingthe equation below.*= N ) + N ) + N ) + ....... N )1 1 2 2 3 3 n nSelf-shielding is where the local neutron flux is depressed within a material due toneutron absorption near the surface of the material.