If a slow neutron is absorbed by a ²³⁵U nucleus, the nucleus may undergo fission, splitting into two fission fragments and releasing two or three fast neutrons. These neutrons may in turn be absorbed by other ²³⁵U nuclei and cause further fissions, each releasing additional neutrons. In an idealised case in which each fission causes two further fissions, four nuclei undergo fission in the second generation, eight in the third, and so on. By the 30th generation, more than one billion nuclei would undergo fission. This rapidly multiplying process is known as a fission chain reaction.

Natural uranium contains about 0.7% ²³⁵U, while conventional light water reactor fuel is typically enriched to several percent ²³⁵U. 

Chain Reaction Conditions

A self-sustaining chain reaction can occur only if, on average, at least one neutron from each fission causes another fission. In practice, many neutrons are lost by leakage from the core or by absorption without causing fission. Several conditions therefore influence whether a chain reaction can be sustained.

Schematic diagram of a fission chain reaction.

Critical mass

If there is too little fissile material, or if its concentration and geometrical arrangement are unsuitable, too many neutrons escape or are absorbed without causing further fission. The minimum amount of fissile material required to sustain a chain reaction under specified conditions is known as the critical mass. Its value depends not only on the material itself, but also on its concentration, geometry and surrounding materials.

Absorber

Many atomic nuclei can absorb neutrons without undergoing fission. Neutrons lost in this way can no longer propagate the chain reaction. If too many neutrons are absorbed, a self-sustaining chain reaction cannot be maintained. Isotopes of boron and cadmium are strong neutron absorbers and are therefore widely used to control nuclear reactors. ²³⁸U can also absorb neutrons, particularly through radiative capture.

Moderator

Fast neutrons can cause fission in ²³⁵U, but the probability of fission is much greater for slow, or thermal, neutrons. In thermal reactors, a moderator is therefore used to slow down the fast neutrons produced by fission and increase the probability that they will cause further fissions.

The effective neutron multiplication factor (k_eff) describes the change in the neutron population from one generation to the next. When k_eff = 1, the chain reaction is self-sustaining and the reactor is critical; when k_eff < 1 it is subcritical, and when k_eff > 1 it is supercritical.

The Discovery of Chain Reactions

In 1934, Enrico Fermi and his colleagues bombarded uranium and other elements with neutrons and observed the formation of unexpected radioactive products. The nature of the process remained unclear until December 1938, when Otto Hahn and Fritz Strassmann identified barium among the products of neutron-bombarded uranium. Lise Meitner and Otto Frisch subsequently explained that the uranium nucleus had split into lighter nuclei, releasing a large amount of energy, and Frisch named the process nuclear fission. The possibility of a nuclear chain reaction had already been proposed by Leó Szilárd in 1933. Once it was established that additional neutrons are released during uranium fission, the possibility of a self-sustaining fission chain reaction became clear. In 1942, a team led by Fermi achieved the world’s first controlled, self-sustaining nuclear chain reaction in Chicago Pile-1.

The discovery of nuclear fission was a crucial step towards the development of nuclear power. The scientists associated with the discovery and early research into nuclear fission are commemorated on German, Italian and American postage stamps.

Fermi and his colleagues discovered in 1934 that slowing neutrons down could greatly increase the probability of certain neutron-induced nuclear reactions. They experimented with hydrogen-rich materials such as paraffin and water, laying important foundations for the later development of neutron moderators.