Nuclear fission

Nuclear fission was discovered by chemists Otto Hahn and Fritz Strassmann and physicists Lise Meitner and Otto Robert Frisch. Hahn and Strassmann proved that a fission reaction had taken place on 19 December 1938, and Meitner and her nephew Frisch explained it theoretically in January 1939. Frisch named the process "fission" by analogy with biological fission of living cells. In their second publication on nuclear fission in February 1939, Hahn and Strassmann predicted the existence and liberation of additional neutrons during the fission process, opening up the possibility of a nuclear chain reaction by assembling a critical mass of fissile material.

For heavy nuclides, it is an exothermic reaction which releases large amounts of energy both as electromagnetic radiation and as kinetic energy of the fragments (heating the bulk material where fission takes place). Like nuclear fusion, for fission to produce energy, the total binding energy of the resulting elements must be greater than that of the starting element. The fission barrier must also be overcome. Fissionable nuclides primarily split in interactions with fast neutrons, while fissile nuclides easily split in interactions with "slow" i.e. thermal neutrons, usually originating from moderation of fast neutrons. The ability of three isotopes (U-233, U-235, and Pu-239) to sustain a nuclear chain reaction allows nuclear power plants to operate in a delayed critical state for a controllable energy release, and also for nuclear weapons to operate at a prompt supercritical state for an uncontrolled energy release occurring in about a microsecond.

Fission is a form of nuclear transmutation because the resulting fragments (or daughter atoms) are not the same element as the original parent atom. The two (or more) nuclei produced are most often of comparable but slightly different sizes, typically with a mass ratio of products of about 3 to 2, for common fissile isotopes. Most fissions are binary fissions (producing two charged fragments), but occasionally (2 to 4 times per 1000 events), three positively charged fragments are produced, in a ternary fission. The smallest of these fragments in ternary processes ranges in size from a proton to an argon nucleus. The unpredictable composition of the products (which vary in a broad probabilistic and somewhat chaotic manner) distinguishes fission from purely quantum tunneling processes such as proton emission, alpha decay, and cluster decay, which give the same products each time.

Spontaneous fission, discovered in 1940 by Georgy Flyorov, Konstantin Petrzhak, and Igor Kurchatov, is fission not induced by an exogenous neutron, but rather a spontaneous radioactive decay occurring because the nucleus is already unstable from an overabundance of neutrons, and occurs in very high-mass-number isotopes. In contrast to nuclear fusion, which powers stars and has created all the elements of the universe, (see iron peak) one can consider nuclear fission as negligible for the evolution of the universe. Nonetheless, natural nuclear fission reactors have formed under very rare conditions.

Physical overview

Mechanism

Younes and Loveland define fission as, "...a collective motion of the protons and neutrons that make up the nucleus, and as such it is distinguishable from other phenomena that break up the nucleus. Nuclear fission is an extreme example of large-amplitude collective motion that results in the division of a parent nucleus into two or more fragment nuclei. The fission process can occur spontaneously, or it can be induced by an incident particle." The energy from a fission reaction is produced by its fission products, though a large majority of it, about 85 percent, is found in fragment kinetic energy, while about 6 percent each comes from initial neutrons and gamma rays and those emitted after beta decay, plus about 3 percent from neutrinos as the product of such decay.

Radioactive decay

Nuclear fission can occur without neutron bombardment as a type of radioactive decay. This type of fission is called spontaneous fission, and was first observed in 1940.

Nuclear reaction

During induced fission, a compound system is formed after an incident particle fuses with a target. The resultant excitation energy may be sufficient to emit neutrons, or gamma-rays, and nuclear scission. Fission into two fragments is called binary fission, and is the most common nuclear reaction. Occurring least frequently is ternary fission, in which a third particle is emitted. This third particle is commonly an α particle. Since in nuclear fission, the nucleus emits more neutrons than the one it absorbs, a chain reaction is possible.

Binary fission may produce any of the fission products, at 95±15 and 135±15 daltons. One example of a binary fission event in the most commonly used fissile nuclide, ²³⁵
U, is given as:

${\displaystyle {}^{235}\mathrm{U}+\mathrm{n}⟶{}^{236}{\mathrm{U}}^{\ast }⟶{}^{95}\mathrm{S}\mathrm{r}+{}^{139}\mathrm{X}\mathrm{e}+2\mathrm{n}+180\mathrm{M}\mathrm{e}\mathrm{V}}$

However, the binary process happens merely because it is the most probable. In anywhere from two to four fissions per 1000 in a nuclear reactor, ternary fission can produce three positively charged fragments (plus neutrons) and the smallest of these may range from so small a charge and mass as a proton (Z = 1), to as large a fragment as argon (Z = 18). The most common small fragments, however, are composed of 90% helium-4 nuclei with more energy than alpha particles from alpha decay (so-called "long range alphas" at ~16 megaelectronvolts (MeV)), plus helium-6 nuclei, and tritons (the nuclei of tritium). Though less common than binary fission, it still produces significant helium-4 and tritium gas buildup in the fuel rods of modern nuclear reactors.

Bohr and Wheeler used their liquid drop model, the packing fraction curve of Arthur Jeffrey Dempster, and Eugene Feenberg's estimates of nucleus radius and surface tension, to estimate the mass differences of parent and daughters in fission. They then equated this mass difference to energy using Einstein's mass-energy equivalence formula. The stimulation of the nucleus after neutron bombardment was analogous to the vibrations of a liquid drop, with surface tension and the Coulomb force in opposition. Plotting the sum of these two energies as a function of elongated shape, they determined the resultant energy surface had a saddle shape. The saddle provided an energy barrier called the critical energy barrier. Energy of about 6 MeV provided by the incident neutron was necessary to overcome this barrier and cause the nucleus to fission. According to John Lilley, "The energy required to overcome the barrier to fission is called the activation energy or fission barrier and is about 6 MeV for A ≈ 240. It is found that the activation energy decreases as A increases. Eventually, a point is reached where activation energy disappears altogether...it would undergo very rapid spontaneous fission."

Maria Goeppert Mayer later proposed the nuclear shell model for the nucleus. The nuclides that can sustain a fission chain reaction are suitable for use as nuclear fuels. The most common nuclear fuels are ²³⁵U (the isotope of uranium with mass number 235 and of use in nuclear reactors) and ²³⁹Pu (the isotope of plutonium with mass number 239). These fuels break apart into a bimodal range of chemical elements with atomic masses centering near 95 and 135 daltons (fission products). Most nuclear fuels undergo spontaneous fission only very slowly, decaying instead mainly via an alpha-beta decay chain over periods of millennia to eons. In a nuclear reactor or nuclear weapon, the overwhelming majority of fission events are induced by bombardment with another particle, a neutron, which is itself produced by prior fission events.

Fissionable isotopes such as uranium-238 require additional energy provided by fast neutrons (such as those produced by nuclear fusion in thermonuclear weapons). While some of the neutrons released from the fission of ²³⁸
U are fast enough to induce another fission in ²³⁸
U, most are not, meaning it can never achieve criticality. While there is a very small (albeit nonzero) chance of a thermal neutron inducing fission in ²³⁸
U, neutron absorption is orders of magnitude more likely.

Energetics

Input

Fission cross sections are a measurable property related to the probability that fission will occur in a nuclear reaction. Cross sections are a function of incident neutron energy, and those for ²³⁵
U and ²³⁹
Pu are a million times higher than ²³⁸
U at lower neutron energy levels. Absorption of any neutron makes available to the nucleus binding energy of about 5.3 MeV. ²³⁸
U needs a fast neutron to supply the additional 1 MeV needed to cross the critical energy barrier for fission. In the case of ²³⁵
U however, that extra energy is provided when ²³⁵
U adjusts from an odd to an even mass. In the words of Younes and Lovelace, "...the neutron absorption on a ²³⁵
U target forms a ²³⁶
U nucleus with excitation energy greater than the critical fission energy, whereas in the case of n + ²³⁸
U, the resulting ²³⁹
U nucleus has an excitation energy below the critical fission energy."

About 6 MeV of the fission-input energy is supplied by the simple binding of an extra neutron to the heavy nucleus via the strong force; however, in many fissionable isotopes, this amount of energy is not enough for fission. Uranium-238, for example, has a near-zero fission cross section for neutrons of less than 1 MeV energy. If no additional energy is supplied by any other mechanism, the nucleus will not fission, but will merely absorb the neutron, as happens when ²³⁸
U absorbs slow and even some fraction of fast neutrons, to become ²³⁹
U. The remaining energy to initiate fission can be supplied by two other mechanisms: one of these is more kinetic energy of the incoming neutron, which is increasingly able to fission a fissionable heavy nucleus as it exceeds a kinetic energy of 1 MeV or more (so-called fast neutrons). Such high energy neutrons are able to fission ²³⁸
U directly (see thermonuclear weapon for application, where the fast neutrons are supplied by nuclear fusion). However, this process cannot happen to a great extent in a nuclear reactor, as too small a fraction of the fission neutrons produced by any type of fission have enough energy to efficiently fission ²³⁸
U. (For example, neutrons from thermal fission of ²³⁵
U have a mean energy of 2 MeV, a median energy of 1.6 MeV, and a mode of 0.75 MeV, and the energy spectrum for fast fission is similar.)

Among the heavy actinide elements, however, those isotopes that have an odd number of neutrons (such as ²³⁵U with 143 neutrons) bind an extra neutron with an additional 1 to 2 MeV of energy over an isotope of the same element with an even number of neutrons (such as ²³⁸U with 146 neutrons). This extra binding energy is made available as a result of the mechanism of neutron pairing effects, which itself is caused by the Pauli exclusion principle, allowing an extra neutron to occupy the same nuclear orbital as the last neutron in the nucleus. In such isotopes, therefore, no neutron kinetic energy is needed, for all the necessary energy is supplied by absorption of any neutron, either of the slow or fast variety (the former are used in moderated nuclear reactors, and the latter are used in fast-neutron reactors, and in weapons).

According to Younes and Loveland, "Actinides like ²³⁵
U that fission easily following the absorption of a thermal (25 meV) neutron are called fissile, whereas those like ²³⁸
U that do not easily fission when they absorb a thermal neutron are called fissionable."

Output

After an incident particle has fused with a parent nucleus, if the excitation energy is sufficient, the nucleus breaks into fragments. This is called scission, and occurs at about 10⁻²⁰ seconds. The fragments can emit prompt neutrons at between 10⁻¹⁸ and 10⁻¹⁵ seconds. At about 10⁻¹¹ seconds, the fragments can emit gamma rays. At 10⁻³ seconds β decay, β-delayed neutrons, and gamma rays are emitted from the decay products.

Typical fission events release about two hundred million eV (200 MeV) of energy for each fission event. The exact isotope which is fissioned, and whether or not it is fissionable or fissile, has only a small impact on the amount of energy released. This can be easily seen by examining the curve of binding energy (image below), and noting that the average binding energy of the actinide nuclides beginning with uranium is around 7.6 MeV per nucleon. Looking further left on the curve of binding energy, where the fission products cluster, it is easily observed that the binding energy of the fission products tends to center around 8.5 MeV per nucleon. Thus, in any fission event of an isotope in the actinide mass range, roughly 0.9 MeV are released per nucleon of the starting element. The fission of ²³⁵U by a slow neutron yields nearly identical energy to the fission of ²³⁸U by a fast neutron. This energy release profile holds for thorium and the various minor actinides as well.

When a uranium nucleus fissions into two daughter nuclei fragments, about 0.1 percent of the mass of the uranium nucleus appears as the fission energy of ~200 MeV. For uranium-235 (total mean fission energy 202.79 MeV), typically ~169 MeV appears as the kinetic energy of the daughter nuclei, which fly apart at about 3% of the speed of light, due to Coulomb repulsion. Also, an average of 2.5 neutrons are emitted, with a mean kinetic energy per neutron of ~2 MeV (total of 4.8 MeV). The fission reaction also releases ~7 MeV in prompt gamma ray photons. The latter figure means that a nuclear fission explosion or criticality accident emits about 3.5% of its energy as gamma rays, less than 2.5% of its energy as fast neutrons (total of both types of radiation ~6%), and the rest as kinetic energy of fission fragments (this appears almost immediately when the fragments impact surrounding matter, as simple heat).

Some processes involving neutrons are notable for absorbing or finally yielding energy — for example neutron kinetic energy does not yield heat immediately if the neutron is captured by a uranium-238 atom to breed plutonium-239, but this energy is emitted if the plutonium-239 is later fissioned. On the other hand, so-called delayed neutrons emitted as radioactive decay products with half-lives up to several minutes, from fission-daughters, are very important to reactor control, because they give a characteristic "reaction" time for the total nuclear reaction to double in size, if the reaction is run in a "delayed-critical" zone which deliberately relies on these neutrons for a supercritical chain-reaction (one in which each fission cycle yields more neutrons than it absorbs). Without their existence, the nuclear chain-reaction would be prompt critical and increase in size faster than it could be controlled by human intervention. In this case, the first experimental atomic reactors would have run away to a dangerous and messy "prompt critical reaction" before their operators could have manually shut them down (for this reason, designer Enrico Fermi included radiation-counter-triggered control rods, suspended by electromagnets, which could automatically drop into the center of Chicago Pile-1). If these delayed neutrons are captured without producing fissions, they produce heat as well.

Binding energy

The binding energy of the nucleus is the difference between the rest-mass energy of the nucleus and the rest-mass energy of the neutron and proton nucleons. The binding energy formula includes volume, surface and Coulomb energy terms that include empirically derived coefficients for all three, plus energy ratios of a deformed nucleus relative to a spherical form for the surface and Coulomb terms. Additional terms can be included such as symmetry, pairing, the finite range of the nuclear force, and charge distribution within the nuclei to improve the estimate. Normally binding energy is referred to and plotted as average binding energy per nucleon.

According to Lilley, "The binding energy of a nucleus B is the energy required to separate it into its constituent neutrons and protons." $${\displaystyle m(\mathbf{A},\mathbf{Z})=\mathbf{Z}{m}_H+\mathbf{N}{m}_n-\mathbf{B}/c^2}$$ where A is mass number, Z is atomic number, m_H is the atomic mass of a hydrogen atom, m_n is the mass of a neutron, and c is the speed of light. Thus, the mass of an atom is less than the mass of its constituent protons and neutrons, assuming the average binding energy of its electrons is negligible. The binding energy B is expressed in energy units, using Einstein's mass-energy equivalence relationship. The binding energy also provides an estimate of the total energy released from fission.

The curve of binding energy is characterized by a broad maximum near mass number 60 at 8.6 MeV, then gradually decreases to 7.6 MeV at the highest mass numbers. Mass numbers higher than 238 are rare. At the lighter end of the scale, peaks are noted for helium-4, and the multiples such as beryllium-8, carbon-12, oxygen-16, neon-20 and magnesium-24. Binding energy due to the nuclear force approaches a constant value for large A, while the Coulomb acts over a larger distance so that electrical potential energy per proton grows as Z increases. Fission energy is released when a A is larger than approx. 60. Fusion energy is released when lighter nuclei combine.

Carl Friedrich von Weizsäcker's semi-empirical mass formula may be used to express the binding energy as the sum of five terms, which are the volume energy, a surface correction, Coulomb energy, a symmetry term, and a pairing term:

$${\displaystyle B=a_v\mathbf{A}-a_s{\mathbf{A}}^{2/3}-a_c\frac{{\mathbf{Z}}^2}{{\mathbf{A}}^{1/3}}-a_a\frac{(\mathbf{N}-\mathbf{Z}{)}^2}{\mathbf{A}}\pm \mathrm{\Delta }}$$ where the nuclear binding energy is proportional to the nuclear volume, while nucleons near the surface interact with fewer nucleons, reducing the effect of the volume term. According to Lilley, "For all naturally occurring nuclei, the surface-energy term dominates and the nucleus exists in a state of equilibrium." The negative contribution of Coulomb energy arises from the repulsive electric force of the protons. The symmetry term arises from the fact that effective forces in the nucleus are stronger for unlike neutron-proton pairs, rather than like neutron–neutron or proton–proton pairs. The pairing term arises from the fact that like nucleons form spin-zero pairs in the same spatial state. The pairing is positive if N and Z are both even, adding to the binding energy.

In fission there is a preference for fission fragments with even Z, which is called the odd–even effect on the fragments' charge distribution. This can be seen in the empirical fragment yield data for each fission product, as products with even Z have higher yield values. However, no odd–even effect is observed on fragment distribution based on their A. This result is attributed to nucleon pair breaking.

In nuclear fission events the nuclei may break into any combination of lighter nuclei, but the most common event is not fission to equal mass nuclei of about mass 120; the most common event (depending on isotope and process) is a slightly unequal fission in which one daughter nucleus has a mass of about 90 to 100 daltons and the other the remaining 130 to 140 daltons.

Stable nuclei, and unstable nuclei with very long half-lives, follow a trend of stability evident when Z is plotted against N. For lighter nuclei less than N = 20, the line has the slope N = Z, while the heavier nuclei require additional neutrons to remain stable. Nuclei that are neutron- or proton-rich have excessive binding energy for stability, and the excess energy may convert a neutron to a proton or a proton to a neutron via the weak nuclear force, a process known as beta decay.

Neutron-induced fission of U-235 emits a total energy of 207 MeV, of which about 200 MeV is recoverable, Prompt fission fragments amount to 168 MeV, which are easily stopped with a fraction of a millimeter. Prompt neutrons total 5 MeV, and this energy is recovered as heat via scattering in the reactor. However, many fission fragments are neutron-rich and decay via β⁻ emissions. According to Lilley, "The radioactive decay energy from the fission chains is the second release of energy due to fission. It is much less than the prompt energy, but it is a significant amount and is why reactors must continue to be cooled after they have been shut down and why the waste products must be handled with great care and stored safely."

Chain reactions

John Lilley states, "...neutron-induced fission generates extra neutrons which can induce further fissions in the next generation and so on in a chain reaction. The chain reaction is characterized by the neutron multiplication factor k, which is defined as the ratio of the number of neutrons in one generation to the number in the preceding generation. If, in a reactor, k is less than unity, the reactor is subcritical, the number of neutrons decreases and the chain reaction dies out. If k > 1, the reactor is supercritical and the chain reaction diverges. This is the situation in a fission bomb where growth is at an explosive rate. If k is exactly unity, the reactions proceed at a steady rate and the reactor is said to be critical. It is possible to achieve criticality in a reactor using natural uranium as fuel, provided that the neutrons have been efficiently moderated to thermal energies." Moderators include light water, heavy water, and graphite.

According to John C. Lee, "For all nuclear reactors in operation and those under development, the nuclear fuel cycle is based on one of three fissile materials, ²³⁵U, ²³³U, and ²³⁹Pu, and the associated isotopic chains. For the current generation of LWRs, the enriched U contains 2.5~4.5 wt% of ²³⁵U, which is fabricated into UO₂ fuel rods and loaded into fuel assemblies."

Lee states, "One important comparison for the three major fissile nuclides, ²³⁵U, ²³³U, and ²³⁹Pu, is their breeding potential. A breeder is by definition a reactor that produces more fissile material than it consumes and needs a minimum of two neutrons produced for each neutron absorbed in a fissile nucleus. Thus, in general, the conversion ratio (CR) is defined as the ratio of fissile material produced to that destroyed...when the CR is greater than 1.0, it is called the breeding ratio (BR)...²³³U offers a superior breeding potential for both thermal and fast reactors, while ²³⁹Pu offers a superior breeding potential for fast reactors."

Fission reactors

Critical fission reactors are the most common type of nuclear reactor. In a critical fission reactor, neutrons produced by fission of fuel atoms are used to induce yet more fissions, to sustain a controllable amount of energy release. Devices that produce engineered but non-self-sustaining fission reactions are subcritical fission reactors. Such devices use radioactive decay or particle accelerators to trigger fissions.

Critical fission reactors are built for three primary purposes, which typically involve different engineering trade-offs to take advantage of either the heat or the neutrons produced by the fission chain reaction:

• power reactors are intended to produce heat for nuclear power, either as part of a generating station or a local power system such as a nuclear submarine.
• research reactors are intended to produce neutrons and/or activate radioactive sources for scientific, medical, engineering, or other research purposes.
• breeder reactors are intended to produce nuclear fuels in bulk from more abundant isotopes. The better known fast breeder reactor makes ²³⁹Pu (a nuclear fuel) from the naturally very abundant ²³⁸U (not a nuclear fuel). Thermal breeder reactors previously tested using ²³²Th to breed the fissile isotope ²³³U (thorium fuel cycle) continue to be studied and developed.

While, in principle, all fission reactors can act in all three capacities, in practice the tasks lead to conflicting engineering goals and most reactors have been built with only one of the above tasks in mind. (There are several early counter-examples, such as the Hanford N reactor, now decommissioned).

As of 2019, the 448 nuclear power plants worldwide provided a capacity of 398 GWE, with about 85% being light-water cooled reactors such as pressurized water reactors or boiling water reactors. Energy from fission is transmitted through conduction or convection to the nuclear reactor coolant, then to a heat exchanger, and the resultant generated steam is used to drive a turbine or generator.

Fission bombs

The objective of an atomic bomb is to produce a device, according to Serber, "...in which energy is released by a fast neutron chain reaction in one or more of the materials known to show nuclear fission." According to Rhodes, "Untamped, a bomb core even as large as twice the critical mass would completely fission less than 1 percent of its nuclear material before it expanded enough to stop the chain reaction from proceeding. Tamper always increased efficiency: it reflected neutrons back into the core and its inertia...slowed the core's expansion and helped keep the core surface from blowing away." Rearrangement of the core material's subcritical components would need to proceed as fast as possible to ensure effective detonation. Additionally, a third basic component was necessary, "...an initiator—a Ra + Be source or, better, a Po + Be source, with the radium or polonium attached perhaps to one piece of the core and the beryllium to the other, to smash together and spray neutrons when the parts mated to start the chain reaction." However, any bomb would "necessitate locating, mining and processing hundreds of tons of uranium ore...", while U-235 separation or the production of Pu-239 would require additional industrial capacity.