Reactor Theory (Nuclear Parameters)
DOE-HDBK-1019/2-93
NEUTRON LIFE CYCLE
Fast Fission Factor, (
)
The first process that the neutrons of one generation may undergo is fast fission. Fast fission
is fission caused by neutrons that are in the fast energy range. Fast fission results in the net
increase in the fast neutron population of the reactor core. The cross section for fast fission in
uranium-235 or uranium-238 is small; therefore, only a small number of fast neutrons cause
fission. The fast neutron population in one generation is therefore increased by a factor called
the fast fission factor. The fast fission factor ( ) is defined as the ratio of the net number of fast
neutrons produced by all fissions to the number of fast neutrons produced by thermal fissions.
The mathematical expression of this ratio is shown below.
number of fast neutrons produced by all fissions
number of fast neutrons produced by thermal fissions
In order for a neutron to be absorbed by a fuel nucleus as a fast neutron, it must pass close
enough to a fuel nucleus while it is a fast neutron. The value of will be affected by the
arrangement and concentrations of the fuel and the moderator. The value of is essentially 1.00
for a homogenous reactor where the fuel atoms are surrounded by moderator atoms. However,
in a heterogeneous reactor, all the fuel atoms are packed closely together in elements such as
pins, rods, or pellets. Neutrons emitted from the fission of one fuel atom have a very good
chance of passing near another fuel atom before slowing down significantly. The arrangement
of the core elements results in a value of about 1.03 for in most heterogeneous reactors. The
value of is not significantly affected by variables such as temperature, pressure, enrichment,
or neutron poison concentrations. Poisons are non-fuel materials that easily absorb neutrons and
will be discussed in more detail later.
Resonance Escape Probability, (p)
After increasing in number as a result of some fast fissions, the neutrons continue to diffuse
through the reactor. As the neutrons move they collide with nuclei of fuel and non-fuel material
and moderator in the reactor losing part of their energy in each collision and slowing down.
While they are slowing down through the resonance region of uranium-238, which extends from
about 6 eV to 200 eV, there is a chance that some neutrons will be captured. The probability
that a neutron will not be absorbed by a resonance peak is called the resonance escape
probability. The resonance escape probability (p) is defined as the ratio of the number of
neutrons that reach thermal energies to the number of fast neutrons that start to slow down. This
ratio is shown below.
p
number of neutrons that reach thermal energy
number of fast neutrons that start to slow down
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