Brief history

The discovery of fission, experimentally in late 1938 and theoretically explained in early 1939, represented a culmination of decades of work in the developing fields of radioactivity and nuclear physics. A key event occurred in 1934, when Italian-born U.S. physicist Enrico Fermi claimed that neutron capture by an isotope could lead eventually to a residual nucleus of atomic number, Z, one unit higher than the isotope, thus leading to new radioactive elements. German radiochemist Otto Hahn, Austrian-born Swedish physicist Lise Meitner (Fig. 2), and German chemist Fritz Strassmann subsequently applied this novel neutron irradiation technique to create transuranic elements—elements with an atomic number beyond uranium (Z = 92), the heaviest naturally occurring element. See also: Atomic number; Neutron; Uranium

Fig. 2 Otto Hahn and Lise Meitner working in their lab.

Although this undertaking eventually proved successful, it initially yielded confusing chemical results by seemingly also producing a lighter element, barium (Z = 56), in very high yields. Through meticulous radiochemical techniques, Hahn and Strassmann confirmed in 1939 that barium was indeed present among the products, along with many other intermediate-mass nuclei, following the bombardment of uranium by neutrons. Their work further revealed that the energy released in the bombardment was orders of magnitude greater than any previously known decay. Ida Noddack, another German chemist who had worked with Fermi, had earlier proposed that lighter elements could be formed by this type of bombardment. However, it was Meitner and Austrian-born British physicist Otto Frisch, now supported by the undisputed results of Hahn and Strassmann, who provided the correct understanding of the counterintuitive experimental findings in 1939. They explained that the uranium nuclei following neutron capture are highly unstable and split in a process that Frisch coined as “fission,” in analogy to the biological process of cell division. For example, one of many possible fission reactions these scientists may have explored is written as:

Nuclear binding energy

When an ensemble of free nucleons (protons and neutrons) come together, the nucleus that is formed has less mass than the sum of the masses of the individual free nucleons. This mass difference is emitted in the form of energy and is called the binding energy of that nucleus. The binding energy that is released during the formation of a nucleus is what would have to be supplied to decompose the nucleus back into its individual components. The average binding energy is approximately 8 MeV per added nucleon for stable nuclei, and decreases slowly for exotic isotopes of a given element. Careful examination of the variation of the binding energy per nucleon (BE/A) with total mass, as in the curve shown in Fig. 3, has the interesting behavior of a rapid increase followed by a slow decline. A larger binding energy per nucleon implies a more tightly bound and thus a more stable nucleus. The peak in stability, as seen in Fig. 3, can be seen to occur around mass A = 56. Consequently, it is possible that a nucleus of greater mass (A > 56) could find it energetically favorable to convert to a more stable system by breaking into lighter fragments nearer to this peak. The small binding energies of the lightest nuclei do not favor breaking into many small pieces. The transformation of a very heavy nucleus into two major fragments is the fission process, and the difference in binding energy (or, equivalently, mass) between the initial nucleus and the final system provides fission’s large energy release. See also: Mass; Nuclear binding energy; Nucleon

Fig. 3 The curve of binding energy per nucleon as a function of number of nucleons, A. The curve reaches a maximum near A = 56 and drops measurably by A = 235. A larger binding energy per nucleon results in a more stable and tightly bound nucleus.

Liquid-drop model

The earliest description of a nucleus that could successfully characterize the binding energy curve of Fig. 3 was the so-called charged liquid-drop model. By the mid-1930s, a variety of experiments had demonstrated that nuclei are generally spherical and incompressible, reminiscent of a liquid droplet, and the nucleons could be viewed analogously to molecules. This phenomenological treatment of the collective behavior of the overall nucleus was first developed by Russian-born U.S. physicist George Gamow, German physicist Werner Heisenberg, and German theoretical physicist Carl Friedrich von Weizsäcker.

The fundamental liquid-drop model provides a parametric equation for the binding energy that contains the following five terms:

1. Volume term: Each nucleon feels the same attraction from its nearest neighbors due to the strong force. This term provides the overall stability of the nucleus.
2. Surface term: A correction to the volume term resulting from the finite size of the nucleus. Some nucleons must reside on or near the nuclear surface and therefore have fewer nearest neighbors than nucleons in the interior and so are less tightly bound. This term is then proportional to the nuclear surface area and reduces overall binding energy. This effect creates the surface tension along the “skin” of a droplet.
3. Coulomb term: A repulsive term that tends to disrupt the nucleus and thus reduces the overall binding energy. The nucleus contains protons in close proximity to one another, each of which has an electrostatic repulsion for every other proton in the nucleus.
4. Symmetry term: A quantum mechanical correction term arising in part from the Pauli exclusion principle. Protons and neutrons are distinguishable particle types and as a result can exist in the same quantum states. It is always energetically favorable for a nucleus to fill the lowest quantum states first, and thus equal numbers of protons, Z, and neutrons, N, would reside in the same states and be in close proximity, which enhances the nuclear attractive force. The greater the asymmetry between proton and neutron numbers, the more this term reduces binding energy. See also: Exclusion principle
5. Pairing term: A final quantum correction due to the intrinsic angular momentum (spin) of the nucleons to account for the fact that paired nucleons (with opposite spins) are more bound than unpaired nucleons. This term depends separately on the numbers of protons and neutrons and thus can add to, have no effect on, or detract from the overall nuclear binding energy, depending on whether Z and N are both even, either Z or N is odd, or both Z and N are odd, respectively.

Ultimately, the liquid-drop model remains an approximation yet very successfully predicts the general trends of nuclear binding energy.

Meitner and Frisch applied this liquid-drop interpretation to explain their fission discovery in 1939. Specifically, they predicted that an external perturbation, such as the absorption of an incident neutron, can create surface waves that lead to a change in the shape of a liquid drop or nucleus. After the delicate energy balance of the round liquid drop is disturbed, the Coulomb force among the protons can cause an elongation of the drop. If the produced deformation is sufficiently large, the Coulomb repulsion among the elongated portions of the drop can produce a two-lobe structure and push the lobes farther apart until surface tension is totally overcome. The Coulomb force can then drive the system to the scission point, where the necking of the structure disappears, causing a complete split, or fission, of the initial nuclear drop into two droplets. A visualization of this description is shown in Fig. 4.

Fig. 4 Starting from left, a representation of the fission process through the phenomenological analogy of the deformation and splitting of a single liquid drop.

Later in the same year, Danish physicist Niels Bohr and U.S. theoretical physicist John Archibald Wheeler performed the first extensive calculations on nuclear fission using this model and demonstrated quantitatively the important competition in the splitting process between the nucleus’s repulsive electrostatic Coulomb force and its attractive surface tension. Detailed quantum mechanical and statistical models have been developed since to continue the study and description of the complex fission process. Nuclear fission remains an active area of research to this day because of the complexity of the process and the interplay of quantum mechanics and macroscopic forces, with work still to be done by experimentalists, theorists, and computational scientists. See also: Quantum mechanics

Characteristics of fission

Fragment mass distribution

Every fission event can be different, and the fission fragments from the splitting process are not determined uniquely but rather follow a random statistical path. That is, every nuclide/isomer (product) has a certain probability, termed its independent fission yield, that it will be produced by fission, usually given as a percentage. This independent yield also depends on the parent nucleus that fissions as well as on the type of perturbation (thermal neutron absorption, fast neutron absorption, etc.) that leads to fission. As an example, three independent fission yield distributions are shown as a function of mass, A, for neutron-induced fission in Fig. 5. The overall distributions are doubly peaked, emphasizing that fission generally produces two fission fragments. It can additionally be noted that fission into equal or nearly equal fragments (A1 ≃ A2) is highly improbable in these cases and instead there is generally a light fragment (A1 ∼ 100) produced with a heavy fragment (A2 ∼ 132). The exact locations of the high-mass peaks correspond to isotopes with high binding energies predicted from quantum shell effects and remain fixed, though the complex path to fission gives a variety of fragments. The production of equal-mass fragments from actinide targets becomes more likely only as the fission-inducing particles become very energetic.

Fig. 5 Independent fission yields by mass for neutron fission of ²³⁵U, ²³⁸U, and ²³⁹Pu. The distribution is noticeably doubly peaked and asymmetric in its mass yields. (Credit: Los Alamos National Laboratory)

Ternary fission (three fragments) is possible but rare (∼ 0.4% probability per fission) and quaternary fission is even more rare.

Fission cross sections

The heaviest nuclei have positive binding energies and thus there is an activation energy or “fission barrier” associated with initiating the fission process. A nucleus can undergo fission spontaneously when its excitation energy is greater than that of the fission barrier. This barrier can be thought of as a quantum mechanical potential, as indicated in Fig. 6 for one dimension, arising as a result of the competing effects of surface tension and electrostatic repulsion. Quantitative characterization of the fission barrier, however, is an extremely complex subject and is not well represented by the basic phenomenological liquid-drop model. An added complexity is that quantum mechanics allows “tunneling” through barriers even when the excitation energy is less than the barrier energy. The tunneling probability increases exponentially as the energy gets close to the top of the barrier, and some of the heaviest nuclei undergo spontaneous fission without any external perturbation. See also: Tunneling in solids

Fig. 6 Modeling of the fission process in terms of a fission barrier. A nucleus starts at the ground state and if it absorbs sufficient energy and becomes excited, it can deform into a configuration known as the transition state or saddle-point configuration, at the peak of the barrier, where the rate of change of the Coulomb energy is equal to the rate of change of the nuclear surface energy. If the nucleus deforms beyond this point, it is irretrievably committed to fission.

Nuclei can be classified by whether or not they will have excitation energy sufficient to fission after absorbing a zero-energy incident neutron:

• Fissile nuclei, such as ²³⁵U, can absorb a neutron of zero kinetic energy and reach an excitation energy already over the fission barrier.
• Fissionable nuclei, such as ²³⁸U, have a threshold to fission and require that the incident neutron bring in additional kinetic energy to overcome the fission barrier.

This fissile versus fissionable property broadly results in two different magnitudes of the fission cross section (akin to probability for reaction), as seen in Fig. 7, which shows neutron-induced fission of ²³⁵U and ²³⁸U. Notably, the shapes of the two curves are somewhat similar, and both increase at low energies that are inversely proportional to neutron velocity. ²³⁵U has a very high fission probability in the thermal region. ²³⁸U has a very low fission probability in the thermal region, and only past a certain threshold, at higher neutron energies, do the fission probabilities between the two uranium isotopes become similar. Accordingly, the pairing term in the liquid-drop model is central in accounting for fissile or fissionable behavior of nuclei. In this case, neutron capture in ²³⁵U produces an even–even nucleus and more excitation energy than neutron capture by ²³⁸U, which produces an even–odd nucleus.

Fig. 7 Cross sections for neutron-induced fission of fissile ²³⁵U and fissionable ²³⁸U.

Applications of fission

Each neutron emitted as a result of a fission event is capable of producing another fission event if it is captured in a neighboring heavy nucleus, which itself could yield more neutrons that could lead to more fissions, and so on. This process is known as a chain reaction. The condition for a chain reaction is usually expressed in terms of the neutron multiplication factor, k, defined as:

When k = 1, each fission event goes on to create one other fission event on average and the chain reaction continues and is called critical. A critical chain reaction is in a steady state. This is in contrast to when k < 1, called subcritical, when the fissioning of the material cannot continue indefinitely and eventually the reaction stops. A steady state is also not achieved when k > 1, a condition called supercritical, when more and more neutrons are produced at every stage of fission, causing an unstable, runaway chain reaction. This concept of supercriticality is illustrated in Fig. 8. See also: Chain reaction (physics)

Fig. 8 A neutron-induced supercritical fission chain reaction. The number of fission-inducing neutrons increases in each succeeding stage of the chain.

Maintaining a critical fission environment given the proper fuel, geometry, coolant, neutron absorbers, and material parameters allows a sustained and steady release of energy, which is the basis for power-generating fission reactors. In brief, power reactors are devices for extracting the kinetic energy of fission fragments as heat and converting the heat energy to electrical energy, generally by boiling water and driving a turbine with the resulting steam. It is important to note that the delayed neutron emissions, though small in intensity, are essential for the control of nuclear reactors. No mechanical system could respond rapidly enough to prevent statistical variations in the prompt neutrons from causing the reactor to run out of control, but it is indeed possible to achieve mechanical control using the delayed neutrons. See also: Nuclear power

Fermi led a team that created the world’s first artificial sustained nuclear chain reaction with the so-called Chicago Pile-1 nuclear reactor in 1942. Natural nuclear reactors have also formed on occasion, such as at the Oklo Uranium Mine in Gabon, Africa, where it was discovered that nearly 2 billion years ago, sustained fission reactions took place over the course of 300,000 years. See also: Nuclear reactor

Fission reactors are also essential for production of medical isotopes. Large quantities of therapeutic and diagnostic isotopes, such as 99Mo/99mTc, can be retrieved from the fission products from reactors and are used globally in clinics and hospitals. See also: Nuclear medicine; Radiology

Supercriticality, and the associated exponential increase in energy release, is the basis of atomic (fission) bombs and two-stage thermonuclear (hydrogen) bombs. The materials, geometry, timing, fuel properties, and controls of these weapon systems are inherently different from those in commercial fission reactors. See also: Atomic bomb; Hydrogen bomb; Nuclear explosion; Thermonuclear reaction

Fission additionally plays a role in stellar nucleosynthesis to terminate the rapid neutron capture process (r-process). See also: Nucleosynthesis

Morgan Fox