Page 255 - Dynamics and Control of Nuclear Reactors

256 APPENDIX C Basic reactor physics

U-235 ¼ 0:714%
U-238 ¼ 99:28%

C.3 Reaction rates and nuclear power generation
In this section, some of the interactions between neutrons and atomic nuclei, are
reviewed. Since neutrons have no electrical charge, they can enter into nuclear
reactions even when their velocities are low. A brief review of neutron cross sections,
neutron flux, reaction rates, and power generation follows in this section.
In a nuclear reactor, the issue is the fate of fission neutrons. Fission neutrons
result in new fissions, non-fission neutron captures, and neutron leakage. The aver-
age energy of fission neutrons is around 2MeV. These fast neutrons interact with
the core materials (structure, fuel, moderator, etc.) by absorption and scattering
reactions. Collisions resulting in scattering will slow down the neutrons.
Neutron cross sections are the basic data used for determining nuclear reaction
rates. The microscopic cross section is represented by the symbol, σ. Microscopic
cross sections are basically target areas for incident neutrons. The units for
2
2
cross sections are cm . Typical values for cross sections are 10 22 to 10 26 cm .
To simplify specification of cross section values, a new unit, called the barn is
2
used. A barn is defined as 10 24 cm . Early workers, apparently a jocular bunch, said
that, to a neutron, a target with area, 10 24 square centimeters, is as big as a ‘barn
door’.
Reactions of importance in nuclear reactors are fission, capture, absorption
(fission + capture), elastic scattering and inelastic scattering. Cross sections are
energy dependent. Fission and capture cross sections decrease with increasing
neutron energy. For many isotopes these cross sections vary as the reciprocal of
the neuron velocity at low energies (1/v or as the reciprocal of the square root of
the neutron energy). Isotopes that follow the 1/v law are called 1/v absorbers.
The total microscopic cross section, σ T , available for interaction between a
neutron and a target nucleus is
σ T ¼ σ a + σ s (C.2)

σ a ¼microscopic absorption cross section
σ s ¼microscopic scattering cross section.
These may be further classified as

ð
σ a ¼ σ f + σ c fission + captureÞ
σ s ¼ σ se + σ si elastic + inelasticð Þ
For a given concentration of target nuclei, the number of collisions in a given time
interval is proportional to the distance traveled by the neutrons in the volume.
Some important relationships follow:
2
• Neutron flux: ϕ¼nv (number of neutrons/cm -s)