In nuclear engineering, a neutron moderator is a medium that reduces the speed of fast neutrons, ideally without capturing any, leaving them as thermal neutrons with only minimal (thermal) kinetic energy. These thermal neutrons are immensely more susceptible than fast neutrons to propagate a nuclear chain reaction of uranium-235 or other fissile isotope by colliding with their atomic nucleus. Water (sometimes called "light water" in this context) is the most commonly used moderator (roughly 75% of the world's reactors). Solid graphite (20% of reactors) and heavy water (5% of reactors) are the main alternatives. Beryllium has also been used in some experimental types, and hydrocarbons have been suggested as another possibility.
Moderation Neutrons are normally bound into an atomic nucleus and do not exist free for long in nature. The unbound neutron has a half-life of 10 minutes and 11 seconds. The release of neutrons from the nucleus requires exceeding the binding energy of the neutron, which is typically 7-9 MeV for most isotopes. Neutron sources generate free neutrons by a variety of nuclear reactions, including nuclear fission and nuclear fusion. Whatever the source of neutrons, they are released with energies of several MeV. According to the equipartition theorem, the average kinetic energy, E ¯ {\displaystyle {\bar {E}}} , can be related to temperature, T {\displaystyle T} , via:
E ¯ = 1 2 m n ⟨ v 2 ⟩ = 3 2 k B T {\displaystyle {\bar {E}}={\frac {1}{2}}m_{\text{n}}\langle v^{2}\rangle ={\frac {3}{2}}k_{\text{B}}T} , where m n {\displaystyle m_{\text{n}}} is the neutron mass, ⟨ v 2 ⟩ {\displaystyle \langle v^{2}\rangle } is the average squared neutron speed, and k B {\displaystyle k_{\text{B}}} is the Boltzmann constant. The characteristic neutron temperature of several-MeV neutrons is several tens of billions kelvin. Moderation is the process of the reduction of the initial high speed (high kinetic energy) of the free neutron. Since energy is conserved, this reduction of the neutron speed takes place by transfer of energy to a material called a moderator. The probability of scattering of a neutron from a nucleus is given by the scattering cross section. The first few collisions with the moderator may be of sufficiently high energy to excite the nucleus of the moderator. Such a collision is inelastic, since some of the kinetic energy is transformed to potential energy by exciting some of the internal degrees of freedom of the nucleus to form an excited state. As the energy of the neutron is lowered, the collisions become predominantly elastic, i.e., the total kinetic energy and momentum of the system (that of the neutron and the nucleus) is conserved. Given the mathematics of elastic collisions, as neutrons are very light compared to most nuclei, the most efficient way of removing kinetic energy from the neutron is by choosing a moderating nucleus that has near identical mass.
A collision of a neutron which has mass of 1 with a 1H nucleus (a proton) could result in the neutron losing virtually all of its energy in a single head-on collision. More generally, it is necessary to take into account both glancing and head-on collisions. The mean logarithmic reduction of neutron energy per collision, ξ {\displaystyle \xi } , depends only on the atomic mass, A {\displaystyle A} , of the nucleus and is given by:
ξ = ln E 0 E = 1 − ( A − 1 ) 2 2 A ln ( A + 1 A − 1 ) {\displaystyle \xi =\ln {\frac {E_{0}}{E}}=1-{\frac {(A-1)^{2}}{2A}}\ln \left({\frac {A+1}{A-1}}\right)} . This can be reasonably approximated to the very simple form ξ ≃ 2 A + 2 / 3 {\displaystyle \xi \simeq {\frac {2}{A+2/3}}} . From this one can deduce n {\displaystyle n} , the expected number of collisions of the neutron with nuclei of a given type that is required to reduce the kinetic energy of a neutron from E 0 {\displaystyle E_{0}} to E 1 {\displaystyle E_{1}}
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