Fission arises because nuclei of atomic number 92 and higher are so large and rich in protons that they are unstable if set into vibration of large amplitude, from which one of the modes of decay is division into two smaller nuclei and two to four free neutrons. Vibration of an amplitude sufficient to cause this fission can be induced in a heavy nucleus by the absorption of a suitably energetic neutron. In the case of heavy nuclei with an odd number of neutrons to start with—such as uranium-233 (U-233), U-235, plutonium-239 (Pu-239), and Pu-241—the absorption of a neutron with the very low energy associated with thermal motion at room temperature is sufficient to induce fission. For heavy nuclei with an even number of neutrons to start with, fission can only be induced if the absorbed neutron carries an energy of a million electron volts (MeV) or more.
Depending on the number of neutrons released per fission, the energy distribution arrived at by the neutrons, the densities of heavy nuclei in the vicinity and their probabilities of fissioning as a function of the energy of an incident neutron, and the probabilities of nonproductive absorption of neutrons or their escape from the vicinity (which depend on the geometry and composition of the materials at hand), it may happen that, for each and every nuclei that fissions, exactly one of the resulting neutrons induces yet another fission. This situation corresponds to a chain reaction that is just "critical," in which the fission rate and thus the rate of nuclear-energy release do not change with time. (This would be the case, for example, in a nuclear reactor operating at constant power level.) If the circumstances are such, on the other hand, that the neutrons released by each fission succeed in inducing more than one additional fission, the chain reaction is "supercritical," and the fission rate and rate of nuclear-energy release grow with time; this growth can be gradual, as in a nuclear reactor during the startup phase, when its power is being increased from zero up to the reactor's rated output, or it can be extremely rapid, as in a nuclear bomb.2 Similarly, an unintended chain reaction (as sometimes occurs when a sufficient quantity of plutonium or enriched uranium is brought together in a geometry favorable for a chain reaction) is known as a "criticality accident."
Nuclear-reaction probabilities are expressed in terms of "cross-sections," with dimensions of area, such that the rates of fission or of nonfission capture associated with a flux of neutrons of N neutrons per square centimeter per sec-