ln E_{i}ln E_{f}lnE_{i}E_{f}2A23NEUTRON MODERATIONDOE-HDBK-1019/1-93Reactor Theory (Neutron Characteristics)NP-02Page 24Rev. 0The ideal moderating material (moderator) should have the following nuclear properties.large scattering cross sectionsmall absorption cross sectionlarge energy loss per collisionA convenient measure of energy loss per collision is the logarithmic energy decrement. Theaverage logarithmic energy decrementis the average decrease per collision in the logarithm ofthe neutron energy. This quantity is represented by the symbol (Greek letter xi).(2-8)where:= average logarithmic energy decrementE = average initial neutron energyiE = average final neutron energyfThe symbol is commonly called the average logarithmic energy decrement because of the factthat a neutron loses, on the average, a fixed fraction of its energy per scattering collision. Sincethe fraction of energy retained by a neutron in a single elastic collision is a constant for a givenmaterial, is also a constant. Because it is a constant for each type of material and does notdepend upon the initial neutron energy, is a convenient quantity for assessing the moderatingability of a material.The values for the lighter nuclei are tabulated in a variety of sources. The following commonlyused 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 lowvalues of A it may be in error by over three percent.