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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)
