Elastic collisions to slow neutrons

"fast" neutrons are less likely to be absorbed by a nucleus than "thermal" neutrons.

Fast neutrons (produced by fission) are neutrons with very high kinetic energy these neutrons are traveling so fast that they are unlikely to be absorbed by a nucleus. Thermal neutrons (those with kinetic energy about that of particles at room temperature) have a very high absorption rate and are more likely to produce fission events.

Within a nuclear reactor the best way to sustain a stable chain reaction is by quickly reducing the kinetic energy of the neutrons produced by fission so they can be used to drive further fission.

Types and quality of moderators.

Their are several materials that are used as moderators in nuclear reactors we will be comparing two.

The two types we are looking at are water (which mostly uses the two hydrogen atoms to moderate the neutrons) and carbon.

Due to the similar masses the proton that is a hydrogen nucleus can remove >99% of the energy of a neutron with each collision.

In perfectly (or close to perfect) elastic collisions both momentum and kinetic energy are conserved. If we look at the neutron from the moderating nuclei's frame of reference this means that the ratio of the initial speed and final speed of the neutron is proportional to the mass difference between the neutron and the moderating nucleus.

so for carbon the neutron only loses 1/12 of its speed (~8%) which to take a 1 MeV neutron to 1 eV would take nearly 166 collisions. The hydrogen in water takes almost all of the energy (due to not being perfectly elastic) thus it only takes a couple of collisions to reduce the speed.