NEUTRON LIFE CYCLE
DOE-HDBK-1019/2-93
Reactor Theory (Nuclear Parameters)
The value of the resonance escape probability is determined largely by the fuel-moderator
arrangement and the amount of enrichment of uranium-235 (if any is used). To undergo
resonance absorption, a neutron must pass close enough to a uranium-238 nucleus to be absorbed
while slowing down. In a homogeneous reactor the neutron does its slowing down in the region
of the fuel nuclei, and this condition is easily met. This means that a neutron has a high
probability of being absorbed by uranium-238 while slowing down; therefore, its escape
probability is lower. In a heterogeneous reactor, however, the neutron slows down in the
moderator where there are no atoms of uranium-238 present. Therefore, it has a low probability
of undergoing resonance absorption, and its escape probability is higher.
The value of the resonance escape probability is not significantly affected by pressure or poison
concentration.
In water moderated, low uranium-235 enrichment reactors, raising the
temperature of the fuel will raise the resonance absorption in uranium-238 due to the doppler
effect (an apparent broadening of the normally narrow resonance peaks due to thermal motion
of nuclei). The increase in resonance absorption lowers the resonance escape probability, and
the fuel temperature coefficient for resonance escape is negative (explained in detail later). The
temperature coefficient of resonance escape probability for the moderator temperature is also
negative. As water temperature increases, water density decreases. The decrease in water density
allows more resonance energy neutrons to enter the fuel and be absorbed. The value of the
resonance escape probability is always slightly less than one (normally 0.95 to 0.99).
The product of the fast fission factor and the resonance escape probability ( p) is the ratio of
the number of fast neutrons that survive slowing down (thermalization) compared to the number
of fast neutrons originally starting the generation.
Thermal Utilization Factor, (f)
Once thermalized, the neutrons continue to diffuse throughout the reactor and are subject to
absorption by other materials in the reactor as well as the fuel. The thermal utilization factor
describes how effectively thermal neutrons are absorbed by the fuel, or how well they are
utilized within the reactor. The thermal utilization factor (f) is defined as the ratio of the
number of thermal neutrons absorbed in the fuel to the number of thermal neutrons absorbed in
any reactor material. This ratio is shown below.
f
number of thermal neutrons absorbed in the fuel
number of thermal neutrons absorbed in all reactor materials
The thermal utilization factor will always be less than one because some of the thermal neutrons
absorbed within the reactor will be absorbed by atoms of non-fuel materials.
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