(DOE-HDBK-1019/1-93NUCLEAR CROSS SECTIONS AND NEUTRON FLUXReactor Theory (Neutron Characteristics)NP-02Page 10Rev. 0Assuming that uranium-236 has a nuclear quantum energy level at 6.8 MeV above its groundstate, calculate the kinetic energy a neutron must possess to undergo resonant absorption inuranium-235 at this resonance energy level.BE = [Mass( U) + Mass(neutron) - Mass( U)] x 931 MeV/amu235 236BE = (235.043925 + 1.008665 - 236.045563) x 931 MeV/amuBE = (0.007025 amu) x 931 MeV/amu = 6.54 MeV6.8 MeV - 6.54 MeV = 0.26 MeVThe difference between the binding energy and the quantum energy level equals the amount ofkinetic 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 arecomplex and have more possible configurations and corresponding energy states. Light nuclei,being less complex, have fewer possible energy states and fewer resonances that are sparselydistributed at higher energy levels.For higher neutron energies, the absorption cross section steadily decreases as the energy of theneutron increases. This is called the "fast neutron region." In this region the absorption crosssections are usually less than 10 barns.With the exception of hydrogen, for which the value is fairly large, the elastic scattering crosssections are generally small, for example, 5 barns to 10 barns. This is close to the magnitudeof 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 elasticscattering and inelastic scattering exhibit resonance peaks similar to those associated withabsorption cross sections. The resonances occur at lower energies for heavy nuclei than for lightnuclei. In general, the variations in scattering cross sections are very small when compared tothe variations that occur in absorption cross sections.MeanFreePathIf a neutron has a certain probability of undergoing a particular interaction in one centimeter oftravel, then the inverse of this value describes how far the neutron will travel (in the averagecase) before undergoing an interaction. This average distance traveled by a neutron beforeinteraction is known as the mean free pathfor that interaction and is represented by the symbol. The relationship between the mean free path () and the macroscopic cross section (* ) isshown below.(2-3)