ln Ei
ln Ef
ln
Ei
Ef
2
A
2
3
NEUTRON MODERATION
DOE-HDBK-1019/1-93
Reactor Theory (Neutron Characteristics)
NP-02
Page 24
Rev. 0
The ideal moderating material (moderator) should have the following nuclear properties.
large scattering cross section
small absorption cross section
large energy loss per collision
A convenient measure of energy loss per collision is the logarithmic energy decrement. The
average logarithmic energy decrement is the average decrease per collision in the logarithm of
the neutron energy. This quantity is represented by the symbol (Greek letter xi).
(2-8)
where:
= average logarithmic energy decrement
E
= average initial neutron energy
i
E
= average final neutron energy
f
The symbol is commonly called the average logarithmic energy decrement because of the fact
that a neutron loses, on the average, a fixed fraction of its energy per scattering collision. Since
the fraction of energy retained by a neutron in a single elastic collision is a constant for a given
material, is also a constant. Because it is a constant for each type of material and does not
depend upon the initial neutron energy, is a convenient quantity for assessing the moderating
ability of a material.
The values for the lighter nuclei are tabulated in a variety of sources. The following commonly
used approximation may be used when a tabulated value is not available.
This approximation is relatively accurate for mass numbers (A) greater than 10, but for some low
values of A it may be in error by over three percent.
