Innuclear engineering,fissile material is material that can undergonuclear fission when struck by aneutron of low energy.^[1] A self-sustaining thermalchain reaction can only be achieved with fissile material. The predominantneutron energy in a system may be typified by either slow neutrons (i.e., a thermal system) or fast neutrons. Fissile material can be used to fuelthermal-neutron reactors,fast-neutron reactors andnuclear explosives.

The termfissile is distinct fromfissionable. Anuclide that can undergonuclear fission (even with a low probability) after capturing a neutron of high or low energy^[2] is referred to asfissionable. A fissionable nuclide that can undergo fission with a high probability after capturing a low-energythermal neutron is referred to asfissile.^[3] Fissionable materials include those (such asuranium-238) for which fission can be induced only by high-energy neutrons. As a result, fissile materials (such asuranium-235) are asubset of fissionable materials.

Uranium-235 fissions with low-energy thermal neutrons because thebinding energy resulting from the absorption of a neutron is greater than the threshold required for fission; therefore uranium-235 is fissile. By contrast, the binding energy released by uranium-238 absorbing a thermal neutron is less than the critical energy, so the neutron must possess additional energy for fission to be possible. Consequently, uranium-238 is fissionable but not fissile.^[4][5]

An alternative definition defines fissile nuclides as those nuclides that can be made to undergo nuclear fission (i.e., are fissionable) and also produce neutrons from such fission that can sustain a nuclear chain reaction in the correct setting. Under this definition, the only nuclides that are fissionable but not fissile are those nuclides that can be made to undergo nuclear fission but produce insufficient neutrons, in either energy or number, to sustain anuclear chain reaction. As such, while all fissile isotopes are fissionable, not all fissionable isotopes are fissile. In thearms control context, particularly in proposals for aFissile Material Cutoff Treaty, the termfissile is often used to describe materials that can be used in the fission primary of a nuclear weapon.^[6] These are materials that sustain an explosivefast neutronnuclear fissionchain reaction.

Under all definitions above, uranium-238 (²³⁸
U
) is fissionable, but not fissile. Neutrons produced by fission of²³⁸
U
have lowerenergies than the original neutron (they behave as in aninelastic scattering), usually below 1 MeV (i.e., a speed of about 14,000 km/s), the fission threshold to cause subsequent fission of²³⁸
U
, so fission of²³⁸
U
does not sustain anuclear chain reaction.

Fast fission of²³⁸
U
in the secondary stage of a thermonuclear weapon, due to the production of high-energy neutrons fromnuclear fusion, contributes greatly to theyield and tofallout of such weapons. Fast fission of²³⁸
U
tampers has also been evident in pure fission weapons.^[7] The fast fission of²³⁸
U
also makes a significant contribution to the power output of somefast-neutron reactors.

In general, mostactinide isotopes with an oddneutron number are fissile. Most nuclear fuels have an oddatomic mass number (A =Z +N = the total number ofnucleons), and an evenatomic numberZ. This implies an odd number of neutrons. Isotopes with an odd number of neutrons gain an extra 1 to 2 MeV of energy from absorbing an extra neutron, from thepairing effect which favors even numbers of both neutrons and protons. This energy is enough to supply the needed extra energy for fission by slower neutrons, which is important for making fissionable isotopes also fissile.

More generally, nuclides with an even number of protons and an even number of neutrons, and located near awell-known curve in nuclear physics of atomic number vs. atomic mass number are more stable than others; hence, they are less likely to undergo fission. They are more likely to "ignore" the neutron and let it go on its way, or else toabsorb the neutron but without gaining enough energy from the process to deform the nucleus enough for it to fission. These"even-even" isotopes are also less likely to undergospontaneous fission, and they also have relatively much longerpartial half-lives foralpha orbeta decay. Examples of these isotopes are uranium-238 andthorium-232. On the other hand, other than the lightest nuclides, nuclides with an odd number of protons and an odd number of neutrons (oddZ, oddN) are usually short-lived (a notable exception isneptunium-236 with a half-life of 154,000 years) because they readilydecay by beta-particle emission to theirisobars with an even number of protons and an even number of neutrons (evenZ, evenN) becoming much more stable. The physical basis for this phenomenon also comes from the pairing effect in nuclear binding energy, but this time from both proton–proton and neutron–neutron pairing. The relatively short half-life of such odd-odd heavy isotopes means that they are not available in quantity and are highly radioactive.

According to the fissility rule proposed by Yigal Ronen, for a heavy element withZ between 90 and 100, an isotope is fissile if and only if2 ×Z −N ∈ {41, 43, 45} (whereN =number of neutrons andZ =number of protons), with a few exceptions.^[13][14] This rule holds for all but fourteen nuclides – seven that satisfy the criterion but are nonfissile, and seven that are fissile but do not satisfy the criterion.^{[note 1]}

To be a useful fuel for nuclear fission chain reactions, the material must:

• Be in the region of thebinding energy curve where a fission chain reaction is possible (i.e., aboveradium)
• Have a high probability of fission onneutron capture
• Release more than one neutron on average per neutron capture. (Enough of them on each fission, to compensate for non-fissions and absorptions in non-fuel material)
• Have a reasonably longhalf-life
• Be available in suitable quantities.

Fissilenuclides in nuclear fuels include:

• Uranium-233, bred fromthorium-232 by neutron capture with intermediate decays steps omitted.
• Uranium-235, which occurs innatural uranium andenriched uranium
• Plutonium-239, bred from uranium-238 by neutron capture with intermediate decays steps omitted.
• Plutonium-241, bred from plutonium-240 directly by neutron capture.

Fissile nuclides do not have a 100% chance of undergoing fission on absorption of a neutron. The chance is dependent on the nuclide as well as neutron energy. For low and medium-energy neutrons, the neutron capturecross sections for fission (σ_F), the cross section for neutron capture with emission of agamma ray (σ_γ), and the percentage of non-fissions are in the table at right.

Fertile nuclides in nuclear fuels include:

• Thorium-232, which breeds uranium-233 by neutron capture with intermediate decays steps omitted.
• Uranium-238, which breeds plutonium-239 by neutron capture with intermediate decays steps omitted.
• Plutonium-240, which breeds plutonium-241 directly by neutron capture.

• Fertile material
• Fission product
• Special nuclear material