Mean Free Path

( DOE-HDBK-1019/1-93 NUCLEAR CROSS SECTIONS AND NEUTRON FLUX Reactor Theory (Neutron Characteristics) NP-02 Page 10 Rev. 0 Assuming that uranium-236 has a nuclear quantum energy level at 6.8 MeV above its ground state, calculate the kinetic energy a neutron must possess to undergo resonant absorption in uranium-235 at this resonance energy level. BE = [Mass( U) + Mass(neutron) - Mass( U)] x 931 MeV/amu 235 236 BE = (235.043925 + 1.008665 - 236.045563) x 931 MeV/amu BE = (0.007025 amu) x 931 MeV/amu = 6.54 MeV 6.8 MeV - 6.54 MeV = 0.26 MeV The difference between the binding energy and the quantum energy level equals the amount of kinetic energy the neutron must possess. The typical heavy nucleus will have many closely- spaced resonances starting in the low energy (eV) range. This is because heavy nuclei are complex and have more possible configurations and corresponding energy states. Light nuclei, being less complex, have fewer possible energy states and fewer resonances that are sparsely distributed at higher energy levels. For higher neutron energies, the absorption cross section steadily decreases as the energy of the neutron increases. This is called the "fast neutron region." In this region the absorption cross sections are usually less than 10 barns. With the exception of hydrogen, for which the value is fairly large, the elastic scattering cross sections are generally small, for example, 5 barns to 10 barns. This is close to the magnitude of the actual geometric cross sectional area expected for atomic nuclei. In potential scattering, the cross section is essentially constant and independent of neutron energy. Resonance elastic scattering and inelastic scattering exhibit resonance peaks similar to those associated with absorption cross sections. The resonances occur at lower energies for heavy nuclei than for light nuclei. In general, the variations in scattering cross sections are very small when compared to the variations that occur in absorption cross sections. Mean Free Path If a neutron has a certain probability of undergoing a particular interaction in one centimeter of travel, then the inverse of this value describes how far the neutron will travel (in the average case) before undergoing an interaction. This average distance traveled by a neutron before interaction is known as the mean free path for that interaction and is represented by the symbol . The relationship between the mean free path ( ) and the macroscopic cross section (* ) is shown below. (2-3)