Neutron Moderator - Moderation

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 just under 15 minutes. 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.

Since the kinetic energy, can be related to temperature via:

the characteristic neutron temperature of a several-MeV neutron is several tens of millions of degrees Celsius.

Moderation is the process of the reduction of the initial high kinetic energy of the free neutron. Since energy is conserved, this reduction of the neutron kinetic energy takes place by transfer of energy to a material known as a moderator. It is also known as neutron slowing down, since along with the reduction of energy comes a reduction in speed.

The probability of scattering of a neutron from a nucleus is given by the scattering cross section. The first couple of 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, depends only on the atomic mass, of the nucleus and is given by:

.

This can be reasonably approximated to the very simple form . From this one can deduce, 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 to :.