# Nuclear fission

Animation of a neutron-induced nuclear fission based on the droplet model with three newly released neutrons
Example of a neutron-induced nuclear fission of uranium-235

Nuclear fission refers to processes in nuclear physics in which an atomic nucleus is broken down into two or more smaller nuclei while releasing energy. Less often, nuclear fission is also called nuclear fission ( Latin fissio "cleavage", English nuclear fission ). Fission must not be confused with nuclear fusion , the merging of two atomic nuclei. The substances newly created by the cleavage are called fission products .

## General information on the physics of fission

Fission is only observed with sufficiently heavy nuclides , from thorium -232 upwards. Only with them is the decomposition into lighter nuclei easy and possible with the release of binding energy . The splitting according to the droplet model can be clearly understood through oscillation and tearing of the nucleus: The animated large view of the above picture shows how the nucleus (red ) is hit by a neutron (blue), elongates and constricts in the middle. The long range of the mutual electrical repulsion of the protons then outweighs the attractive nuclear force (see atomic nucleus ) with its short range and drives the two ends apart, so that the nucleus disintegrates into two or three fragments - highly excited, medium-weight nuclei. By changing the binding energy, the total mass decreases accordingly ( mass defect ). In addition to the fragment cores ( fissure fragments ), a few individual neutrons are usually released, typically two or, as in the picture, three.

The energy spectrum of these neutrons has the form of a Maxwell distribution , so it is continuous and extends up to about 15  MeV . The absolute temperature, which is decisive in the Boltzmann statistics, has hardly any physical significance here, but is treated as a free parameter in order to adapt the curve to the measured shape of the spectrum. The mean neutron energy is around 2 MeV. It depends somewhat on the split nuclide and in the case of the neutron-induced split (see below) also on the energy of the splitting neutron. Because of the asymmetry of the Maxwell distribution curve, the mean energy is different from the most probable energy, the maximum of the curve; this is around 0.7 MeV.

About 99% of the neutrons are emitted as prompt neutrons directly during the fission within about 10-14 seconds. The rest, the delayed neutrons , are released from the fission fragments milliseconds to minutes later.

## Spontaneous split

Some types of atomic nucleus ( nuclides ) split without any external influence. This spontaneous fission is a type of radioactive decay . In terms of quantum mechanics, it can be explained by the tunnel effect , similar to the alpha decay .

Spontaneous fission finds practical application as a source of free neutrons . For this purpose usually is californium - isotope used. ${\ displaystyle ^ {252} \ mathrm {Cf}}$

## Neutron Induced Fission

The neutron-induced fission, a nuclear reaction, is of great technical importance . A free neutron comes so close to an atomic nucleus that it can be absorbed by it. The nucleus gains the binding energy and any kinetic energy of this neutron, is in an excited state and splits. Instead of fission, other processes are also possible, for example neutron capture . The excited atomic nucleus is excited by emitting one or more gamma quanta and changes to its ground state.

The neutron-induced fission is basically possible - with a smaller or larger cross section - for all elements with atomic numbers Z from 90 ( thorium ) and has been observed for many of their isotopes .

Because of its importance for civil energy generation and for nuclear weapons , the following mainly deals with neutron-induced fission.

## Fissure fragments

The total number of protons and neutrons is retained with each nuclear fission. By far the most common case is the split into only two new nuclei (split fragments ); A third fragment ( ternary cleavage) with usually a very small mass number up to a maximum of about 30 is formed in only a few per thousand of all splits .

With two fission fragments, many different nuclide pairs are possible. Usually a lighter (mass number around 90) and a heavier fissure fragment (mass number around 140) arise. The frequency distribution (the yield plotted as a function of the mass number of the fission fragment) therefore has two maxima.

As an example, two possibilities of splitting plutonium-239 after absorption of a neutron (n) are mentioned:

 ${\ displaystyle {} _ {\ 94} ^ {239} \ mathrm {Pu} + {} _ {0} ^ {1} \ mathrm {n} \ to {} _ {\ 56} ^ {144} \ mathrm {Ba} + {} _ {38} ^ {94} \ mathrm {Sr} +2 \ {} _ {0} ^ {1} \ mathrm {n}}$ ${\ displaystyle {} _ {\ 94} ^ {239} \ mathrm {Pu} + {} _ {0} ^ {1} \ mathrm {n} \ to {} _ {\ 51} ^ {130} \ mathrm {Sb} + {} _ {\ 43} ^ {107} \ mathrm {Tc} +3 \ {} _ {0} ^ {1} \ mathrm {n}}$
Fission by thermal neutrons: Schematic frequency of the fission fragments (vertical) as a function of the fission product mass number A (horizontal)

The fission fragments are medium-weight nuclides with a relatively high proportion of neutrons. They took over this surplus of neutrons from the original nucleus. They are therefore unstable and in some cases initially emit more neutrons. These delayed neutrons can also trigger further nuclear fission; they are important for the controllability of nuclear reactors .

The fission products, which are still unstable afterwards, continue to reduce their surplus of neutrons through successive beta-minus decays . Since the mass number of the atomic nucleus remains unchanged during beta decay, the nuclides that arise one after the other from a given fission fragment nucleus form an isobaric chain ; they are therefore atomic nuclei of different chemical elements, but with the same number of masses. This chain of transformation ends when a stable nuclide has formed. The half-lives are short at the beginning of the chain, but can be many years for the final decays. Exact numerical values ​​for the frequency of the various isobar chains, depending on the split nuclide and the energy of the split neutron, can be found in the literature.

## Energy release and energy balance

### Energy release

Average atomic nucleus
binding energy per nucleon as a function of the number of nucleons in the atomic nucleus for all known nuclides according to AME2016

The two fission products together have a higher mass defect than the heavy starting core. Because of the equivalence of mass and energy , this difference in mass defects is released as energy. In the following explanation, it is assumed for the sake of simplicity that a 235 U nucleus takes up a neutron and then breaks up into two equal fragments with a mass number of 118 (in the case of nuclear fission actually occurring, the nuclei that are formed usually have different weights, and a few individual neutrons remain). Average values ​​of the binding energy per nucleon from the graph are used for the calculation. The energy is given in the unit mega electron volt (MeV).

• To simplify matters, 235 individual nucleons (92 protons and 143 neutrons) and the captured neutron are first computationally combined to form a nucleus. During this process, energy would be released. Conversely, to completely split a U-236 nucleus into its nucleons, this amount of energy is necessary.${\ displaystyle 236 \ times 7 {,} 7 \ ​​{\ text {MeV}} = 1817 \ {\ text {MeV}}}$
• If a fragment is put together, one would get .${\ displaystyle 118 \ times 8 {,} 6 \ {\ text {MeV}} = 1015 \ {\ text {MeV}}}$
• When a uranium-235 core is split into two equal parts, the energy difference must be released.${\ displaystyle \ left (2 \ times 1015 \ right) \ {\ text {MeV}} - 1817 \ {\ text {MeV}} = 213 \ {\ text {MeV}}}$
• This energy is given off by the fact that both fragments and the released neutrons fly apart at a very high speed. In the surrounding material, the fragments are slowed down and generate "frictional heat", more precisely: they transfer their kinetic energy in individual collisions to many atoms of the surrounding material, one after the other, until they are slowed down to the speed that corresponds to the material temperature.

### Energy balance

The energy released during nuclear fission of around 200 MeV per fission is distributed among the particles and radiation generated during nuclear fission. The table shows the energy values ​​of a typical fission process. Most of this energy can be used in a nuclear reactor; only the energy of the escaping antineutrinos and part of the gamma radiation is not converted into heat.

Type of energy / type of radiation Average energy
Kinetic energy of the fissure fragments 167 MeV
kinetic energy of neutrons 5 MeV
Electrons from fission fragment beta decay 8 MeV
Gamma radiation from fissure fragments 6 MeV
Electron antineutrinos from fission fragment beta decay 12 MeV
Total energy per split 204 MeV

## Cleavage

Some actinides and their main breakdown products. The actinides, which can be easily split by thermal neutrons, are written in
bold . The isotopes are sorted according to their affiliation to decay series and / or their half-life .
The picture shows the cross section for the cleavage reaction of U-233. U-235, U-238 and Pu-239 as a function of the neutron energy. The left area corresponds to thermal neutrons , the right to fast neutrons.

### Thermal neutrons

By thermal neutrons - d. H. those with relatively low kinetic energy  - are mostly only isotopes with an odd number of neutrons that can be easily split. Only these atomic nuclei gain pair energy by absorbing a neutron . “Easily fissile” means that the effective cross-section of the nucleus for fission by a thermal neutron is hundreds to thousands of barns . “Poorly fissile” means that this effective cross-section is only of the order of 1 barn or smaller.

Example:

Americium , as element 95, has an even number of neutrons with its odd number of protons for odd numbers of nucleons , while plutonium , as the 94th element, with its even number of protons for odd numbers of nucleons also has odd numbers of neutrons . This is why americium 241 Am is difficult to split with thermal neutrons (3.1 barn), in contrast to plutonium 241 Pu (1010 barn).

### Fast neutrons

The newly released neutrons during the fission have kinetic energies in the MeV range. With such fast neutrons, nuclides with an even number of neutrons can also be fissioned; the pair energy then has hardly any effect on the cross section. However, the cross-sections for the “fast fission” do not reach the high values ​​of some “thermal” fission.

With some fissile materials, the rapid fission leads to a particularly high yield of new neutrons per fissioned core. This is used in breeder reactors .

In the three-stage bomb, very fast neutrons with more than 14 MeV are generated by nuclear fusion of hydrogen isotopes. These split uranium-238 cores in the bomb shell consisting of depleted uranium . The explosive power of the bomb and the fallout are greatly increased.

## Critical mass

The smallest mass of a fissile material in which a chain reaction can be sustained is called the critical mass . It depends on the presence and amount of a moderator substance and on the geometric arrangement. A thin sheet of metal would lose almost all neutrons to the outside, while neutrons within a compact object are more likely to hit other atomic nuclei. The smallest critical mass is achieved with a spherical arrangement. This can be further reduced by compressing the material; there is no absolute lower limit. The geometry dependency of the critical mass is used to avoid the criticality leading to a chain reaction when manufacturing or processing nuclear fuels . For example, chemical reactions are carried out in shallow tubs in which the material is distributed over large areas.

## Technical importance

### Nuclear reactors

The neutron-induced fission as a chain reaction in nuclear reactors is of economic importance . Mainly the nuclides uranium-235 and plutonium-239 are used. Nuclear reactors based on thorium- 232 and uranium-233 were also planned or tested .

At around 200 MeV per atomic nucleus, the energy released by nuclear fission is many times higher than in chemical reactions (typically around 20 eV per molecule). The energy occurs mainly as the kinetic energy of the fission fragments, to a lesser extent also in the radiation from their radioactive decay. The delayed neutrons, which are crucial for the controllability of nuclear reactors, are also released from the fission fragments after the actual fission reaction.

In reactors, the kinetic energy of the fission products and the energy of the radiation generated are converted into heat by collisions with the surrounding material . Only the resulting electron antineutrinos , part of the gamma radiation and part of the free neutrons escape from the reaction zone, the reactor core .

### Nuclear weapons

The exponentially growing nuclear fission chain reaction of a promptly supercritical arrangement of fissile materials serves as an energy source for “normal” nuclear weapons . The “destructive energy” is released primarily as light radiation, heat and radioactivity and secondarily in the form of a pressure wave . In the case of hydrogen bombs , a nuclear fission serves as a detonator for a nuclear fusion , i.e. the fusion of light atomic nuclei.

## Other induced fission

The collision of a high-energy gamma quantum (in the MeV energy range) can lead to the splitting of a heavy nucleus ( photocleavage ). This is to be distinguished from the nuclear photo effect , in which only a neutron, a proton or an alpha particle is released from the nucleus, but the nucleus is not split.

The collision of a charged particle can also lead to nuclear fission if it transfers sufficient energy to the nucleus. For example, were proton - and muon observed induced fissions.

Even a compound core with a very large nuclear spin , such as can arise in heavy ion reactions, can reduce its excitation energy by splitting.

These splitting processes do not have technical applications.

## Research history

Experimental setup in the Deutsches Museum , with which Otto Hahn and Fritz Straßmann discovered nuclear fission in 1938

It has been known since the work of Ernest Rutherford that atomic nuclei can be changed by bombarding them with fast particles. With the discovery of the neutron by James Chadwick in 1932 , it became clear that there had to be many ways in which atomic nuclei could be transformed. Among other things, attempts were made to produce new, even heavier nuclides by introducing neutrons into heavy nuclei.

Postage stamp of the Deutsche Bundespost (1964) : 25 years of the discovery of nuclear fission by Otto Hahn and Fritz Straßmann

According to the assumptions of Enrico Fermi , who already saw fission products of uranium in Rome but misinterpreted them, u. a. Ida Noddack-Tacke the correct assumption of the splitting of the newly formed nucleus. However, in 1934 these speculative assumptions were still considered dubious, and no physicist checked them experimentally, not even Ida Noddack herself. Otto Hahn and his assistant Fritz Straßmann then succeeded on December 17, 1938 at the Kaiser Wilhelm Institute for Chemistry in Berlin with the proof of neutron-induced nuclear fission of uranium through the radiochemical detection of the fission product barium . They published their discovery on January 6, 1939 in the journal "Die Naturwissenschaften". By this time Lise Meitner had already been in Sweden for a few months, where she had emigrated with Hahn's help, as she had to flee Nazi Germany as a Jew. Together with her nephew Otto Frisch , who also emigrated , she was able to publish a first physical interpretation of the splitting process in the English "Nature" on February 10, 1939, as Hahn was the first to inform her about the radiochemical results by letter. Otto Hahn and Fritz Straßmann are therefore considered to be the discoverers of nuclear fission, and Lise Meitner and Otto Frisch are the first to publish a correct theoretical explanation of the process. Fresh and the expression comes fission nuclear , or "fission", which was then adopted internationally, while Hahn had originally the name "uranium fission" is used.

On January 16, 1939, Niels Bohr traveled to the USA to discuss physical problems with Albert Einstein for a few months . Shortly before his departure from Denmark, Frisch and Meitner told him about their interpretation of Hahn-Straßmann's test results. Bohr shared this with his former student John Archibald Wheeler and other interested parties after his arrival in the USA . It was through them that the news spread to other physicists, including Enrico Fermi of Columbia University . Fermi recognized the possibility of a controlled fission chain reaction and carried out the first successful reactor experiment in the Chicago Pile with his team in Chicago in 1942 .

Commons : Nuclear fission  - collection of images, videos and audio files
Wiktionary: Nuclear fission  - explanations of meanings, word origins, synonyms, translations

## Individual evidence

1. The technical term in physics and nuclear engineering is 'split', not 'split'
2. A. Ziegler, HJ Allelein (Ed.): Reactor technology - physical-technical basics. 2nd edition, Springer-Vieweg 2013, ISBN 978-3-642-33845-8 , page 54
3. ^ J. Magill, G. Pfennig, R. Dreher, Z. Sóti: Karlsruher Nuklidkarte. 8th edition. Nucleonica GmbH, Eggenstein-Leopoldshafen 2012, ISBN 92-79-02431-0 (wall map), ISBN 978-3-00-038392-2 (folding map), ISBN 92-79-02175-3 (accompanying brochure).
4. Marcus Wöstheinrich: Emission of ternary particles from the reactions 229 Th (n th , f), 233 U (n th , f) and 239 Pu (n th , f) . Tübingen 1999, DNB  963242830 , urn : nbn: de: bsz: 21-opus-349 (dissertation, University of Tübingen).
5. Data collection of the International Atomic Energy Agency
6. ^ EB Paul: Nuclear and Particle Physics . North-Holland, 1969, p. 250
7. ^ Bernard Leonard Cohen : Concepts of Nuclear Physics . McGraw-Hill, New York 1971, ISBN 0-07-011556-7 , p. 265
8. ^ Cyriel Wagemans (ed.): The nuclear Fission Process . CRC Press 1991, ISBN 0-8493-5434-X , page 219
9. Enrico Fermi: Possible production of element of atomic number higher than 92 . In: Nature . tape 133 , 1934, pp. 898-899 , doi : 10.1038 / 133898a0 .
10. Ida Noddack: About the element 93 . In: Angewandte Chemie . tape 47 , 1934, pp. 653-655 , doi : 10.1002 / anie.19340473707 .
11. Quote: "It is conceivable that when heavy nuclei are bombarded with neutrons, these nuclei disintegrate into several larger fragments that are isotopes of known elements, but not neighbors of the irradiated elements."
12. Otto Hahn and Fritz Straßmann: About the detection and behavior of the alkaline earth metals formed when the uranium is irradiated with neutrons . In: Natural Sciences . tape 27 , 1939, pp. 11-15 , doi : 10.1007 / BF01488241 .