Editing Neutron moderator (section)

===Materials===
Some nuclei have larger [[Neutron cross section#Absorption cross section|absorption cross sections]] than others, which removes free neutrons from the [[flux]]. Therefore, a further criterion for an efficient moderator is one for which this parameter is small. The ''moderating efficiency'' gives the ratio of the [[Nuclear cross section#Macroscopic cross section|macroscopic cross sections]] of scattering, <math>\Sigma_s</math>, weighted by <math>\xi</math> divided by that of absorption, <math>\Sigma_a</math>: i.e., <math>\frac{\xi\Sigma_s}{\Sigma_a}</math>.<ref name="Weston" /> For a compound moderator composed of more than one element, such as light or heavy water, it is necessary to take into account the moderating and absorbing effect of both the hydrogen isotope and oxygen atom to calculate <math>\xi</math>. To bring a neutron from the fission energy of <math>E_0</math> 2 MeV to an <math>E</math> of 1 eV takes an expected <math>n</math> of 16 and 29 collisions for H<sub>2</sub>O and D<sub>2</sub>O, respectively. Therefore, neutrons are more rapidly moderated by light water, as H has a far higher <math>\Sigma_s</math>. However, it also has a far higher <math>\Sigma_a</math>, so that the moderating efficiency is nearly 80 times higher for heavy water than for light water.<ref name="Weston" />

''The ideal moderator is of low mass, high scattering cross section, and low absorption cross section''.
{| class="table" 
 !
 ![[Hydrogen]]
 ![[Deuterium]]
 ![[Beryllium]]
 ![[Carbon]]
 ![[Oxygen]]
 ![[Uranium]]
 |-
 |Mass of nuclei [[atomic mass unit|u]]
 |1
 |2
 |9
 |12
 |16
 |238
 |-
 |Energy decrement <math>\xi</math>
 |1
 |0.7261
 |0.2078
 |0.1589
 |0.1209
 |0.0084
 |-
 |Number of Collisions
 |18
 |25
 |86
 |114
 |150
 |2172
 |}