REACTIVITY COEFFICIENTS
DOE-HDBK-1019/2-93 Reactor Theory (Nuclear Parameters)
Moderator Effects
As discussed in the previous module, a moderator possesses specific desirable characteristics.
(a) large neutron scattering cross section
(b) low neutron absorption cross section
(c) large neutron energy loss per collision
With the exception of the Liquid Metal Fast Breeder Reactor (LMFBR), the remaining major
reactor types that are currently employed use moderating materials to reduce fission neutron
energies to the thermal range. Light moderators (composed of light nuclei) are found to be more
effective than heavy moderators because the light moderator removes more energy per collision
than a heavy moderator. Therefore, the neutrons reach thermal energy more rapidly and they are
less likely to be lost through resonance absorption.
As discussed in a previous module, the ability of a given material to slow down neutrons is
referred to as the macroscopic slowing down power (MSDP) and is defined as the product of
the logarithmic energy decrement per collision (x) times the macroscopic scattering cross section
for neutrons as follows.
MS DP x Ss
Macroscopic slowing down power indicates how rapidly slowing down occurs in the material
in question, but it does not completely define the effectiveness of the material as a moderator.
An element such as boron has a high logarithmic energy decrement and a good slowing down
power, but is a poor moderator. It is a poor moderator because of its high probability of
absorbing neutrons, and may be accounted for by dividing the macroscopic slowing down power
by the macroscopic absorption cross section. This relationship is called the moderating ratio
(MR).
MR
x Ss
Sa
The moderating ratio is merely the ratio of slowing down power to the macroscopic absorption
cross section. The higher the moderating ratio, the more effectively the material performs as a
moderator.
Another ratio, the moderator-to-fuel ratio (Nm/Nu), is very important in the discussion of
moderators. As the reactor designer increases the amount of moderator in the core (that is,
Nm/Nu increases), neutron leakage decreases. Neutron absorption in the moderator (Sma ) increases
and causes a decrease in the thermal utilization factor. Having insufficient moderator in the core
(that is, Nm/Nu decreases) causes an increase in slowing down time and results in a greater loss
of neutrons by resonance absorption. This also causes an increase in neutron leakage. The
effects of varying the moderator-to-fuel ratio on the thermal utilization factor and the resonance
probability are shown in Figure 2.
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