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In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a
beta particle A beta particle, also called beta ray or beta radiation (symbol β), is a high-energy, high-speed electron or positron emitted by the radioactive decay of an atomic nucleus during the process of beta decay. There are two forms of beta decay, β� ...
(fast energetic electron or
positron The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. It has an electric charge of +1 '' e'', a spin of 1/2 (the same as the electron), and the same mass as an electron. When a positron collides ...
) is emitted from an atomic nucleus, transforming the original
nuclide A nuclide (or nucleide, from nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy state. The word ''nuclide'' was coined by Truman ...
to an isobar of that nuclide. For example, beta decay of a neutron transforms it into a proton by the emission of an electron accompanied by an
antineutrino A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is ...
; or, conversely a proton is converted into a neutron by the emission of a positron with a neutrino in so-called ''
positron emission Positron emission, beta plus decay, or β+ decay is a subtype of radioactive decay called beta decay, in which a proton inside a radionuclide nucleus is converted into a neutron while releasing a positron and an electron neutrino (). Positron emis ...
''. Neither the beta particle nor its associated (anti-)neutrino exist within the nucleus prior to beta decay, but are created in the decay process. By this process, unstable atoms obtain a more stable ratio of protons to neutrons. The probability of a nuclide decaying due to beta and other forms of decay is determined by its nuclear binding energy. The binding energies of all existing nuclides form what is called the nuclear band or
valley of stability In nuclear physics, the valley of stability (also called the belt of stability, nuclear valley, energy valley, or beta stability valley) is a characterization of the stability of nuclides to radioactivity based on their binding energy. Nuclide ...
. For either electron or positron emission to be energetically possible, the energy release ( see below) or ''Q'' value must be positive. Beta decay is a consequence of the
weak force Weak may refer to: Songs * "Weak" (AJR song), 2016 * "Weak" (Melanie C song), 2011 * "Weak" (SWV song), 1993 * "Weak" (Skunk Anansie song), 1995 * "Weak", a song by Seether from '' Seether: 2002-2013'' Television episodes * "Weak" (''Fear t ...
, which is characterized by relatively lengthy decay times. Nucleons are composed of
up quark The up quark or u quark (symbol: u) is the lightest of all quarks, a type of elementary particle, and a significant constituent of matter. It, along with the down quark, forms the neutrons (one up quark, two down quarks) and protons (two up quark ...
s and
down quark The down quark or d quark (symbol: d) is the second-lightest of all quarks, a type of elementary particle, and a major constituent of matter. Together with the up quark, it forms the neutrons (one up quark, two down quarks) and protons (two up ...
s, and the weak force allows a
quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All commonly o ...
to change its
flavour Flavor or flavour is either the sensory perception of taste or smell, or a flavoring in food that produces such perception. Flavor or flavour may also refer to: Science * Flavors (programming language), an early object-oriented extension to Li ...
by emission of a
W boson In particle physics, the W and Z bosons are vector bosons that are together known as the weak bosons or more generally as the intermediate vector bosons. These elementary particles mediate the weak interaction; the respective symbols are , , and ...
leading to creation of an electron/antineutrino or positron/neutrino pair. For example, a neutron, composed of two down quarks and an up quark, decays to a proton composed of a down quark and two up quarks. Electron capture is sometimes included as a type of beta decay, because the basic nuclear process, mediated by the weak force, is the same. In electron capture, an inner atomic electron is captured by a proton in the nucleus, transforming it into a neutron, and an electron neutrino is released.


Description

The two types of beta decay are known as ''beta minus'' and ''beta plus''. In beta minus (β) decay, a neutron is converted to a proton, and the process creates an electron and an electron antineutrino; while in beta plus (β+) decay, a proton is converted to a neutron and the process creates a positron and an electron neutrino. β+ decay is also known as
positron emission Positron emission, beta plus decay, or β+ decay is a subtype of radioactive decay called beta decay, in which a proton inside a radionuclide nucleus is converted into a neutron while releasing a positron and an electron neutrino (). Positron emis ...
. Beta decay conserves a quantum number known as the
lepton number In particle physics, lepton number (historically also called lepton charge) is a conserved quantum number representing the difference between the number of leptons and the number of antileptons in an elementary particle reaction. Lepton number ...
, or the number of electrons and their associated neutrinos (other leptons are the muon and tau particles). These particles have lepton number +1, while their antiparticles have lepton number −1. Since a proton or neutron has lepton number zero, β+ decay (a positron, or antielectron) must be accompanied with an electron neutrino, while β decay (an electron) must be accompanied by an electron antineutrino. An example of electron emission (β decay) is the decay of
carbon-14 Carbon-14, C-14, or radiocarbon, is a radioactive isotope of carbon with an atomic nucleus containing 6 protons and 8 neutrons. Its presence in organic materials is the basis of the radiocarbon dating method pioneered by Willard Libby and col ...
into
nitrogen-14 Natural nitrogen (7N) consists of two stable isotopes: the vast majority (99.6%) of naturally occurring nitrogen is nitrogen-14, with the remainder being nitrogen-15. Fourteen radioisotopes are also known, with atomic masses ranging from 10 to 2 ...
with a
half-life Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable ato ...
of about 5,730 years: : → + + In this form of decay, the original element becomes a new chemical element in a process known as
nuclear transmutation Nuclear transmutation is the conversion of one chemical element or an isotope into another chemical element. Nuclear transmutation occurs in any process where the number of protons or neutrons in the nucleus of an atom is changed. A transmut ...
. This new element has an unchanged mass number , but an
atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...
that is increased by one. As in all nuclear decays, the decaying element (in this case ) is known as the ''parent nuclide'' while the resulting element (in this case ) is known as the ''daughter nuclide''. Another example is the decay of hydrogen-3 ( tritium) into
helium-3 Helium-3 (3He see also helion) is a light, stable isotope of helium with two protons and one neutron (the most common isotope, helium-4, having two protons and two neutrons in contrast). Other than protium (ordinary hydrogen), helium-3 is the ...
with a half-life of about 12.3 years: : → + + An example of positron emission (β+ decay) is the decay of magnesium-23 into
sodium-23 There are 22 isotopes of sodium (11Na), ranging from to , and two isomers ( and ). is the only stable (and the only primordial) isotope. It is considered a monoisotopic element and it has a standard atomic weight of . Sodium has two radioactiv ...
with a half-life of about 11.3 s: : → + + β+ decay also results in nuclear transmutation, with the resulting element having an atomic number that is decreased by one. The beta spectrum, or distribution of energy values for the beta particles, is continuous. The total energy of the decay process is divided between the electron, the antineutrino, and the recoiling nuclide. In the figure to the right, an example of an electron with 0.40 MeV energy from the beta decay of 210Bi is shown. In this example, the total decay energy is 1.16 MeV, so the antineutrino has the remaining energy: . An electron at the far right of the curve would have the maximum possible kinetic energy, leaving the energy of the neutrino to be only its small rest mass.


History


Discovery and initial characterization

Radioactivity was discovered in 1896 by Henri Becquerel in uranium, and subsequently observed by
Marie Marie may refer to: People Name * Marie (given name) * Marie (Japanese given name) * Marie (murder victim), girl who was killed in Florida after being pushed in front of a moving vehicle in 1973 * Marie (died 1759), an enslaved Cree person in ...
and
Pierre Curie Pierre Curie ( , ; 15 May 1859 – 19 April 1906) was a French physicist, a pioneer in crystallography, magnetism, piezoelectricity, and radioactivity. In 1903, he received the Nobel Prize in Physics with his wife, Marie Curie, and Henri Becquer ...
in thorium and in the new elements
polonium Polonium is a chemical element with the symbol Po and atomic number 84. Polonium is a chalcogen. A rare and highly radioactive metal with no stable isotopes, polonium is chemically similar to selenium and tellurium, though its metallic character ...
and radium. In 1899, Ernest Rutherford separated radioactive emissions into two types: alpha and beta (now beta minus), based on penetration of objects and ability to cause ionization. Alpha rays could be stopped by thin sheets of paper or aluminium, whereas beta rays could penetrate several millimetres of aluminium. In 1900, Paul Villard identified a still more penetrating type of radiation, which Rutherford identified as a fundamentally new type in 1903 and termed gamma rays. Alpha, beta, and gamma are the first three letters of the Greek alphabet. In 1900, Becquerel measured the
mass-to-charge ratio The mass-to-charge ratio (''m''/''Q'') is a physical quantity relating the ''mass'' (quantity of matter) and the ''electric charge'' of a given particle, expressed in units of kilograms per coulomb (kg/C). It is most widely used in the electrody ...
() for beta particles by the method of J.J. Thomson used to study cathode rays and identify the electron. He found that for a beta particle is the same as for Thomson's electron, and therefore suggested that the beta particle is in fact an electron. In 1901, Rutherford and
Frederick Soddy Frederick Soddy FRS (2 September 1877 – 22 September 1956) was an English radiochemist who explained, with Ernest Rutherford, that radioactivity is due to the transmutation of elements, now known to involve nuclear reactions. He also prove ...
showed that alpha and beta radioactivity involves the transmutation of atoms into atoms of other chemical elements. In 1913, after the products of more radioactive decays were known, Soddy and
Kazimierz Fajans Kazimierz Fajans (Kasimir Fajans in many American publications; 27 May 1887 – 18 May 1975) was a Polish American physical chemist of Polish-Jewish origin, a pioneer in the science of radioactivity and the discoverer of chemical element protact ...
independently proposed their radioactive displacement law, which states that beta (i.e., ) emission from one element produces another element one place to the right in the
periodic table The periodic table, also known as the periodic table of the (chemical) elements, is a rows and columns arrangement of the chemical elements. It is widely used in chemistry, physics, and other sciences, and is generally seen as an icon of ch ...
, while alpha emission produces an element two places to the left.


Neutrinos

The study of beta decay provided the first physical evidence for the existence of the neutrino. In both alpha and gamma decay, the resulting alpha or gamma particle has a narrow energy
distribution Distribution may refer to: Mathematics * Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations *Probability distribution, the probability of a particular value or value range of a vari ...
, since the particle carries the energy from the difference between the initial and final nuclear states. However, the kinetic energy distribution, or spectrum, of beta particles measured by Lise Meitner and
Otto Hahn Otto Hahn (; 8 March 1879 – 28 July 1968) was a German chemist who was a pioneer in the fields of radioactivity and radiochemistry. He is referred to as the father of nuclear chemistry and father of nuclear fission. Hahn and Lise Meitner ...
in 1911 and by Jean Danysz in 1913 showed multiple lines on a diffuse background. These measurements offered the first hint that beta particles have a continuous spectrum. In 1914, James Chadwick used a magnetic spectrometer with one of Hans Geiger's new counters to make more accurate measurements which showed that the spectrum was continuous. The distribution of beta particle energies was in apparent contradiction to the law of conservation of energy. If beta decay were simply electron emission as assumed at the time, then the energy of the emitted electron should have a particular, well-defined value. For beta decay, however, the observed broad distribution of energies suggested that energy is lost in the beta decay process. This spectrum was puzzling for many years. A second problem is related to the
conservation of angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
. Molecular band spectra showed that the nuclear spin of
nitrogen-14 Natural nitrogen (7N) consists of two stable isotopes: the vast majority (99.6%) of naturally occurring nitrogen is nitrogen-14, with the remainder being nitrogen-15. Fourteen radioisotopes are also known, with atomic masses ranging from 10 to 2 ...
is 1 (i.e., equal to the reduced Planck constant) and more generally that the spin is integral for nuclei of even mass number and half-integral for nuclei of odd mass number. This was later explained by the proton-neutron model of the nucleus. Beta decay leaves the mass number unchanged, so the change of nuclear spin must be an integer. However, the electron spin is 1/2, hence angular momentum would not be conserved if beta decay were simply electron emission. From 1920 to 1927,
Charles Drummond Ellis Sir Charles Drummond Ellis (b. Hampstead, 11 August 1895; died Cookham 10 January 1980) was an English physicist and scientific administrator. His work on the magnetic spectrum of the beta-rays helped to develop a better understanding of nuclear ...
(along with Chadwick and colleagues) further established that the beta decay spectrum is continuous. In 1933, Ellis and
Nevill Mott Sir Nevill Francis Mott (30 September 1905 – 8 August 1996) was a British physicist who won the Nobel Prize for Physics in 1977 for his work on the electronic structure of magnetic and disordered systems, especially amorphous semiconductors ...
obtained strong evidence that the beta spectrum has an effective upper bound in energy. Niels Bohr had suggested that the beta spectrum could be explained if
conservation of energy In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means that ...
was true only in a statistical sense, thus this principle might be violated in any given decay. However, the upper bound in beta energies determined by Ellis and Mott ruled out that notion. Now, the problem of how to account for the variability of energy in known beta decay products, as well as for conservation of momentum and angular momentum in the process, became acute. In a famous letter written in 1930, Wolfgang Pauli attempted to resolve the beta-particle energy conundrum by suggesting that, in addition to electrons and protons, atomic nuclei also contained an extremely light neutral particle, which he called the neutron. He suggested that this "neutron" was also emitted during beta decay (thus accounting for the known missing energy, momentum, and angular momentum), but it had simply not yet been observed. In 1931, Enrico Fermi renamed Pauli's "neutron" the "neutrino" ('little neutral one' in Italian). In 1933, Fermi published his landmark theory for beta decay, where he applied the principles of quantum mechanics to matter particles, supposing that they can be created and annihilated, just as the light quanta in atomic transitions. Thus, according to Fermi, neutrinos are created in the beta-decay process, rather than contained in the nucleus; the same happens to electrons. The neutrino interaction with matter was so weak that detecting it proved a severe experimental challenge. Further indirect evidence of the existence of the neutrino was obtained by observing the recoil of nuclei that emitted such a particle after absorbing an electron. Neutrinos were finally detected directly in 1956 by
Clyde Cowan Clyde Lorrain Cowan Jr (December 6, 1919 – May 24, 1974) was an American physicist, the co-discoverer of the neutrino along with Frederick Reines. The discovery was made in 1956 in the neutrino experiment. Frederick Reines received the Nobel Pr ...
and
Frederick Reines Frederick Reines ( ; March 16, 1918 – August 26, 1998) was an American physicist. He was awarded the 1995 Nobel Prize in Physics for his co-detection of the neutrino with Clyde Cowan in the neutrino experiment. He may be the only scientist ...
in the Cowan–Reines neutrino experiment. The properties of neutrinos were (with a few minor modifications) as predicted by Pauli and Fermi.


 decay and electron capture

In 1934, Frédéric and Irène Joliot-Curie bombarded aluminium with alpha particles to effect the nuclear reaction  +  →  + , and observed that the product isotope emits a positron identical to those found in cosmic rays (discovered by
Carl David Anderson Carl David Anderson (September 3, 1905 – January 11, 1991) was an American physicist. He is best known for his discovery of the positron in 1932, an achievement for which he received the 1936 Nobel Prize in Physics, and of the muon in 1936. B ...
in 1932). This was the first example of  decay (
positron emission Positron emission, beta plus decay, or β+ decay is a subtype of radioactive decay called beta decay, in which a proton inside a radionuclide nucleus is converted into a neutron while releasing a positron and an electron neutrino (). Positron emis ...
), which they termed
artificial radioactivity Induced radioactivity, also called artificial radioactivity or man-made radioactivity, is the process of using radiation to make a previously stable material radioactive. The husband and wife team of Irène Joliot-Curie and Frédéric Joliot-Curie ...
since is a short-lived nuclide which does not exist in nature. In recognition of their discovery the couple were awarded the
Nobel Prize in Chemistry ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then "M ...
in 1935. The theory of electron capture was first discussed by
Gian-Carlo Wick Gian Carlo Wick (15 October 1909 – 20 April 1992) was an Italian theoretical physicist who made important contributions to quantum field theory. The Wick rotation, Wick contraction, Wick's theorem, and the Wick product are named after him.
in a 1934 paper, and then developed by
Hideki Yukawa was a Japanese theoretical physicist and the first Japanese Nobel laureate for his prediction of the pi meson, or pion. Biography He was born as Hideki Ogawa in Tokyo and grew up in Kyoto with two older brothers, two older sisters, and two y ...
and others. K-electron capture was first observed in 1937 by Luis Alvarez, in the nuclide 48V. Alvarez went on to study electron capture in 67Ga and other nuclides.


Non-conservation of parity

In 1956,
Tsung-Dao Lee Tsung-Dao Lee (; born November 24, 1926) is a Chinese-American physicist, known for his work on parity violation, the Lee–Yang theorem, particle physics, relativistic heavy ion (RHIC) physics, nontopological solitons, and soliton stars ...
and
Chen Ning Yang Yang Chen-Ning or Chen-Ning Yang (; born 1 October 1922), also known as C. N. Yang or by the English name Frank Yang, is a Chinese theoretical physicist who made significant contributions to statistical mechanics, integrable systems, gauge the ...
noticed that there was no evidence that
parity Parity may refer to: * Parity (computing) ** Parity bit in computing, sets the parity of data for the purpose of error detection ** Parity flag in computing, indicates if the number of set bits is odd or even in the binary representation of the ...
was conserved in weak interactions, and so they postulated that this symmetry may not be preserved by the weak force. They sketched the design for an experiment for testing conservation of parity in the laboratory. Later that year,
Chien-Shiung Wu ) , spouse = , residence = , nationality = ChineseAmerican , field = Physics , work_institutions = Institute of Physics, Academia SinicaUniversity of California at BerkeleySmith CollegePrinceton UniversityColumbia UniversityZhejiang Unive ...
and coworkers conducted the
Wu experiment The Wu experiment was a particle and nuclear physics experiment conducted in 1956 by the Chinese American physicist Chien-Shiung Wu in collaboration with the Low Temperature Group of the US National Bureau of Standards. The experiment's purpose ...
showing an asymmetrical beta decay of at cold temperatures that proved that parity is not conserved in beta decay. This surprising result overturned long-held assumptions about parity and the weak force. In recognition of their theoretical work, Lee and Yang were awarded the Nobel Prize for Physics in 1957. However Wu, who was female, was not awarded the Nobel prize.


β decay

In  decay, the
weak interaction In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction ...
converts an atomic nucleus into a nucleus with
atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...
increased by one, while emitting an electron () and an electron
antineutrino A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is ...
().  decay generally occurs in neutron-rich nuclei. The generic equation is: : → + + where and are the mass number and
atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...
of the decaying nucleus, and X and X′ are the initial and final elements, respectively. Another example is when the free neutron () decays by  decay into a proton (): : → + + . At the fundamental level (as depicted in the Feynman diagram on the right), this is caused by the conversion of the negatively charged () down quark to the positively charged () up quark by emission of a boson; the boson subsequently decays into an electron and an electron antineutrino: : → + + .


β+ decay

In  decay, or positron emission, the weak interaction converts an atomic nucleus into a nucleus with atomic number decreased by one, while emitting a positron () and an electron neutrino (). ' decay generally occurs in proton-rich nuclei. The generic equation is: : → + + This may be considered as the decay of a proton inside the nucleus to a neutron: :p → n + + However,  decay cannot occur in an isolated proton because it requires energy, due to the mass of the neutron being greater than the mass of the proton.  decay can only happen inside nuclei when the daughter nucleus has a greater
binding energy In physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. In the former meaning the term is predominantly use ...
(and therefore a lower total energy) than the mother nucleus. The difference between these energies goes into the reaction of converting a proton into a neutron, a positron, and a neutrino and into the kinetic energy of these particles. This process is opposite to negative beta decay, in that the weak interaction converts a proton into a neutron by converting an up quark into a down quark resulting in the emission of a or the absorption of a . When a boson is emitted, it decays into a
positron The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. It has an electric charge of +1 '' e'', a spin of 1/2 (the same as the electron), and the same mass as an electron. When a positron collides ...
and an electron neutrino: : → + + .


Electron capture (K-capture)

In all cases where  decay (positron emission) of a nucleus is allowed energetically, so too is electron capture allowed. This is a process during which a nucleus captures one of its atomic electrons, resulting in the emission of a neutrino: : + → + An example of electron capture is one of the decay modes of krypton-81 into bromine-81: : + → + All emitted neutrinos are of the same energy. In proton-rich nuclei where the energy difference between the initial and final states is less than ,  decay is not energetically possible, and electron capture is the sole decay mode. If the captured electron comes from the innermost shell of the atom, the K-shell, which has the highest probability to interact with the nucleus, the process is called K-capture. If it comes from the L-shell, the process is called L-capture, etc. Electron capture is a competing (simultaneous) decay process for all nuclei that can undergo β+ decay. The converse, however, is not true: electron capture is the ''only'' type of decay that is allowed in proton-rich nuclides that do not have sufficient energy to emit a positron and neutrino.


Nuclear transmutation

If the proton and neutron are part of an atomic nucleus, the above described decay processes transmute one chemical element into another. For example: : Beta decay does not change the number () of
nucleon In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number (nucleon number). Until the 1960s, nucleons were ...
s in the nucleus, but changes only its
charge Charge or charged may refer to: Arts, entertainment, and media Films * ''Charge, Zero Emissions/Maximum Speed'', a 2011 documentary Music * ''Charge'' (David Ford album) * ''Charge'' (Machel Montano album) * '' Charge!!'', an album by The Aqu ...
 . Thus the set of all
nuclide A nuclide (or nucleide, from nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy state. The word ''nuclide'' was coined by Truman ...
s with the same  can be introduced; these ''isobaric'' nuclides may turn into each other via beta decay. For a given there is one that is most stable. It is said to be beta stable, because it presents a local minimum of the
mass excess The mass excess of a nuclide is the difference between its actual mass and its mass number in daltons. It is one of the predominant methods for tabulating nuclear mass. The mass of an atomic nucleus is well approximated (less than 0.1% difference f ...
: if such a nucleus has numbers, the neighbour nuclei and have higher mass excess and can beta decay into , but not vice versa. For all odd mass numbers , there is only one known beta-stable isobar. For even , there are up to three different beta-stable isobars experimentally known; for example, , , and are all beta-stable. There are about 350 known beta-decay stable nuclides.


Competition of beta decay types

Usually unstable nuclides are clearly either "neutron rich" or "proton rich", with the former undergoing beta decay and the latter undergoing electron capture (or more rarely, due to the higher energy requirements, positron decay). However, in a few cases of odd-proton, odd-neutron radionuclides, it may be energetically favorable for the radionuclide to decay to an even-proton, even-neutron isobar either by undergoing beta-positive or beta-negative decay. An often-cited example is the single isotope (29 protons, 35 neutrons), which illustrates three types of beta decay in competition. Copper-64 has a half-life of about 12.7 hours. This isotope has one unpaired proton and one unpaired neutron, so either the proton or the neutron can decay. This particular nuclide (though not all nuclides in this situation) is almost equally likely to decay through proton decay by
positron emission Positron emission, beta plus decay, or β+ decay is a subtype of radioactive decay called beta decay, in which a proton inside a radionuclide nucleus is converted into a neutron while releasing a positron and an electron neutrino (). Positron emis ...
() or electron capture () to , as it is through neutron decay by electron emission () to .


Stability of naturally occurring nuclides

Most naturally occurring nuclides on earth are beta stable. Nuclides that are not beta stable have
half-lives Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable ato ...
ranging from under a second to periods of time significantly greater than the
age of the universe In physical cosmology, the age of the universe is the time elapsed since the Big Bang. Astronomers have derived two different measurements of the age of the universe: a measurement based on direct observations of an early state of the universe ...
. One common example of a long-lived isotope is the odd-proton odd-neutron nuclide , which undergoes all three types of beta decay (, and electron capture) with a half-life of .


Conservation rules for beta decay


Baryon number is conserved

B=\frac where * n_q is the number of constituent quarks, and * n_ is the number of constituent antiquarks. Beta decay just changes neutron to proton or, in the case of positive beta decay ( electron capture) proton to neutron so the number of individual
quarks A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All commonly o ...
doesn't change. It is only the baryon flavor that changes, here labelled as the isospin. Up and down
quarks A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All commonly o ...
have total isospin I=\frac and isospin projections I_\text=\begin \frac & \text \\ -\frac & \text \end All other quarks have . In general I_\text=\frac (n_\text - n_\text)


Lepton number is conserved

L \equiv n_ - n_ so all leptons have assigned a value of +1, antileptons −1, and non-leptonic particles 0. \begin & \text & \rightarrow & \text & + & \text^- & + & \bar_\text \\ L: & 0 &=& 0 & + & 1 & - & 1 \end


Angular momentum

For allowed decays, the net orbital angular momentum is zero, hence only spin quantum numbers are considered. The electron and antineutrino are
fermions In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and ...
, spin-1/2 objects, therefore they may couple to total S=1 (parallel) or S=0 (anti-parallel). For forbidden decays, orbital angular momentum must also be taken into consideration.


Energy release

The value is defined as the total energy released in a given nuclear decay. In beta decay, is therefore also the sum of the kinetic energies of the emitted beta particle, neutrino, and recoiling nucleus. (Because of the large mass of the nucleus compared to that of the beta particle and neutrino, the kinetic energy of the recoiling nucleus can generally be neglected.) Beta particles can therefore be emitted with any kinetic energy ranging from 0 to . A typical is around 1 
MeV In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. ...
, but can range from a few keV to a few tens of MeV. Since the rest mass of the electron is 511 keV, the most energetic beta particles are ultrarelativistic, with speeds very close to the speed of light. In the case of Re, the maximum speed of the beta particle is only 9.8% of the speed of light. The following table gives some examples:


β decay

Consider the generic equation for beta decay : → + + . The value for this decay is :Q=\left _N\left(\ce\right) - m_N\left(\ce\right)-m_e-m_\right^2, where m_N\left(\ce\right) is the mass of the nucleus of the atom, m_e is the mass of the electron, and m_ is the mass of the electron antineutrino. In other words, the total energy released is the mass energy of the initial nucleus, minus the mass energy of the final nucleus, electron, and antineutrino. The mass of the nucleus is related to the standard
atomic mass The atomic mass (''m''a or ''m'') is the mass of an atom. Although the SI unit of mass is the kilogram (symbol: kg), atomic mass is often expressed in the non-SI unit dalton (symbol: Da) – equivalently, unified atomic mass unit (u). 1&nbs ...
by m\left(\ce\right)c^2=m_N\left(\ce\right)c^2 + Z m_e c^2-\sum_^Z B_i. That is, the total atomic mass is the mass of the nucleus, plus the mass of the electrons, minus the sum of all ''electron'' binding energies for the atom. This equation is rearranged to find m_N\left(\ce\right), and m_N\left(\ce\right) is found similarly. Substituting these nuclear masses into the -value equation, while neglecting the nearly-zero antineutrino mass and the difference in electron binding energies, which is very small for high- atoms, we have Q=\left \left(\ce\right)-m\left(\ce\right)\right^2 This energy is carried away as kinetic energy by the electron and antineutrino. Because the reaction will proceed only when the  value is positive, β decay can occur when the mass of atom is greater than the mass of atom .


β+ decay

The equations for β+ decay are similar, with the generic equation : → + + giving Q=\left _N\left(\ce\right) - m_N\left(\ce\right)-m_e-m_\right^2. However, in this equation, the electron masses do not cancel, and we are left with Q=\left \left(\ce\right)-m\left(\ce\right)-2m_e\right^2. Because the reaction will proceed only when the  value is positive, β+ decay can occur when the mass of atom exceeds that of by at least twice the mass of the electron.


Electron capture

The analogous calculation for electron capture must take into account the binding energy of the electrons. This is because the atom will be left in an excited state after capturing the electron, and the binding energy of the captured innermost electron is significant. Using the generic equation for electron capture : + → + we have Q=\left _N\left(\ce\right) + m_e - m_N\left(\ce\right)-m_\right^2, which simplifies to Q=\left \left(\ce\right) - m\left(\ce\right)\right^2-B_n, where is the binding energy of the captured electron. Because the binding energy of the electron is much less than the mass of the electron, nuclei that can undergo β+ decay can always also undergo electron capture, but the reverse is not true.


Beta emission spectrum

Beta decay can be considered as a
perturbation Perturbation or perturb may refer to: * Perturbation theory, mathematical methods that give approximate solutions to problems that cannot be solved exactly * Perturbation (geology), changes in the nature of alluvial deposits over time * Perturbat ...
as described in quantum mechanics, and thus
Fermi's Golden Rule In quantum physics, Fermi's golden rule is a formula that describes the transition rate (the probability of a transition per unit time) from one energy eigenstate of a quantum system to a group of energy eigenstates in a continuum, as a result of ...
can be applied. This leads to an expression for the kinetic energy spectrum of emitted betas as follows: N(T) = C_L(T) F(Z,T) p E (Q-T)^2 where is the kinetic energy, is a shape function that depends on the forbiddenness of the decay (it is constant for allowed decays), is the Fermi Function (see below) with ''Z'' the charge of the final-state nucleus, is the total energy, p = \sqrt is the momentum, and is the Q value of the decay. The kinetic energy of the emitted neutrino is given approximately by minus the kinetic energy of the beta. As an example, the beta decay spectrum of 210Bi (originally called RaE) is shown to the right.


Fermi function

The Fermi function that appears in the beta spectrum formula accounts for the Coulomb attraction / repulsion between the emitted beta and the final state nucleus. Approximating the associated wavefunctions to be spherically symmetric, the Fermi function can be analytically calculated to be: F(Z,T)=\frac (2 p \rho)^ e^ , \Gamma(S+i \eta), ^2, where is the final momentum, Γ the
Gamma function In mathematics, the gamma function (represented by , the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except t ...
, and (if is the fine-structure constant and the radius of the final state nucleus) S = \sqrt, \eta = \pm Ze^2c/\hbar p(+ for electrons, − for positrons), and \rho = r_N/\hbar . For non-relativistic betas (), this expression can be approximated by: F(Z,T) \approx \frac. Other approximations can be found in the literature.


Kurie plot

A Kurie plot (also known as a Fermi–Kurie plot) is a graph used in studying beta decay developed by
Franz N. D. Kurie Franz Newell Devereux Kurie (; February 6, 1907 in Victor, Colorado – June 12, 1972) was an American physicist who, while working at Yale in 1933, showed that the neutron was neither a dumbbell-shaped combination of proton and electron, nor an ...
, in which the square root of the number of beta particles whose momenta (or energy) lie within a certain narrow range, divided by the Fermi function, is plotted against beta-particle energy. It is a straight line for allowed transitions and some forbidden transitions, in accord with the Fermi beta-decay theory. The energy-axis (x-axis) intercept of a Kurie plot corresponds to the maximum energy imparted to the electron/positron (the decay's  value). With a Kurie plot one can find the limit on the effective mass of a neutrino.


Helicity (polarization) of neutrinos, electrons and positrons emitted in beta decay

After the discovery of parity non-conservation (see History), it was found that, in beta decay, electrons are emitted mostly with negative helicity, i.e., they move, naively speaking, like left-handed screws driven into a material (they have negative longitudinal
polarization Polarization or polarisation may refer to: Mathematics *Polarization of an Abelian variety, in the mathematics of complex manifolds *Polarization of an algebraic form, a technique for expressing a homogeneous polynomial in a simpler fashion by ...
). Conversely, positrons have mostly positive helicity, i.e., they move like right-handed screws. Neutrinos (emitted in positron decay) have negative helicity, while antineutrinos (emitted in electron decay) have positive helicity. The higher the energy of the particles, the higher their polarization.


Types of beta decay transitions

Beta decays can be classified according to the angular momentum (  value) and total spin (  value) of the emitted radiation. Since total angular momentum must be conserved, including orbital and spin angular momentum, beta decay occurs by a variety of quantum state transitions to various nuclear angular momentum or spin states, known as "Fermi" or "Gamow–Teller" transitions. When beta decay particles carry no angular momentum (), the decay is referred to as "allowed", otherwise it is "forbidden". Other decay modes, which are rare, are known as bound state decay and double beta decay.


Fermi transitions

A Fermi transition is a beta decay in which the spins of the emitted electron (positron) and anti-neutrino (neutrino) couple to total spin S=0, leading to an angular momentum change \Delta J=0 between the initial and final states of the nucleus (assuming an allowed transition). In the non-relativistic limit, the nuclear part of the operator for a Fermi transition is given by \mathcal_=G_\sum_ \hat_ with G_V the weak vector coupling constant, \tau_ the isospin raising and lowering operators, and a running over all protons and neutrons in the nucleus.


Gamow–Teller transitions

A Gamow–Teller transition is a beta decay in which the spins of the emitted electron (positron) and anti-neutrino (neutrino) couple to total spin S=1, leading to an angular momentum change \Delta J=0,\pm 1 between the initial and final states of the nucleus (assuming an allowed transition). In this case, the nuclear part of the operator is given by \mathcal_=G_\sum_ \hat_\hat_ with G_ the weak axial-vector coupling constant, and \sigma the spin Pauli matrices, which can produce a spin-flip in the decaying nucleon.


Forbidden transitions

When , the decay is referred to as " forbidden". Nuclear
selection rule In physics and chemistry, a selection rule, or transition rule, formally constrains the possible transitions of a system from one quantum state to another. Selection rules have been derived for electromagnetic transitions in molecules, in atoms, ...
s require high  values to be accompanied by changes in nuclear spin () and
parity Parity may refer to: * Parity (computing) ** Parity bit in computing, sets the parity of data for the purpose of error detection ** Parity flag in computing, indicates if the number of set bits is odd or even in the binary representation of the ...
 (). The selection rules for the th forbidden transitions are: \Delta J=L-1, L, L+1; \Delta \pi=(-1)^L, where corresponds to no parity change or parity change, respectively. The special case of a transition between isobaric analogue states, where the structure of the final state is very similar to the structure of the initial state, is referred to as "superallowed" for beta decay, and proceeds very quickly. The following table lists the Δ and Δ values for the first few values of :


Rare decay modes


Bound-state β decay

A very small minority of free neutron decays (about four per million) are so-called "two-body decays", in which the proton, electron and antineutrino are produced, but the electron fails to gain the 13.6 eV energy necessary to escape the proton, and therefore simply remains bound to it, as a neutral
hydrogen atom A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen consti ...
. In this type of beta decay, in essence all of the neutron decay energy is carried off by the antineutrino. For fully ionized atoms (bare nuclei), it is possible in likewise manner for electrons to fail to escape the atom, and to be emitted from the nucleus into low-lying atomic bound states (orbitals). This cannot occur for neutral atoms with low-lying bound states which are already filled by electrons. Bound-state β decays were predicted by Daudel, Jean, and Lecoin in 1947, and the phenomenon in fully ionized atoms was first observed for 163Dy66+ in 1992 by Jung et al. of the Darmstadt Heavy-Ion Research Center. Although neutral is a stable isotope, the fully ionized 163Dy66+ undergoes β decay into the K and L shells with a half-life of 47 days. The resulting nucleus - - is stable only in the fully ionized state and will decay via electron capture into in the neutral state. The half life for the latter is 4750 years. Another possibility is that a fully ionized atom undergoes greatly accelerated β decay, as observed for 187Re by Bosch et al., also at Darmstadt. Neutral 187Re does undergo β decay with a half-life of  years, but for fully ionized 187Re75+ this is shortened to only 32.9 years. For comparison the variation of decay rates of other nuclear processes due to chemical environment is less than 1%. Due to the difference in the price of rhenium and osmium and the high share of in rhenium samples found on earth, this could some day be of commercial interest in the
synthesis of precious metals The synthesis of precious metals involves the use of either nuclear reactors or particle accelerators to produce these elements. Precious metals occurring as fission products Ruthenium, rhodium Ruthenium and rhodium are precious metals produ ...
.


Double beta decay

Some nuclei can undergo double beta decay (ββ decay) where the charge of the nucleus changes by two units. Double beta decay is difficult to study, as the process has an extremely long half-life. In nuclei for which both β decay and ββ decay are possible, the rarer ββ decay process is effectively impossible to observe. However, in nuclei where β decay is forbidden but ββ decay is allowed, the process can be seen and a half-life measured. Thus, ββ decay is usually studied only for beta stable nuclei. Like single beta decay, double beta decay does not change ; thus, at least one of the nuclides with some given has to be stable with regard to both single and double beta decay. "Ordinary" double beta decay results in the emission of two electrons and two antineutrinos. If neutrinos are
Majorana particle A Majorana fermion (, uploaded 19 April 2013, retrieved 5 October 2014; and also based on the pronunciation of physicist's name.), also referred to as a Majorana particle, is a fermion that is its own antiparticle. They were hypothesised by Et ...
s (i.e., they are their own antiparticles), then a decay known as
neutrinoless double beta decay The neutrinoless double beta decay (0νββ) is a commonly proposed and experimentally pursued theoretical radioactive decay process that would prove a Majorana nature of the neutrino particle. To this day, it has not been found. The discovery o ...
will occur. Most neutrino physicists believe that neutrinoless double beta decay has never been observed.


See also

* Common beta emitters * Neutrino *
Betavoltaics A betavoltaic device (betavoltaic cell or betavoltaic battery) is a type of nuclear battery which generates electric current from beta particles (electrons) emitted from a radioactive source, using semiconductor junctions. A common source used is ...
* Particle radiation *
Radionuclide A radionuclide (radioactive nuclide, radioisotope or radioactive isotope) is a nuclide that has excess nuclear energy, making it unstable. This excess energy can be used in one of three ways: emitted from the nucleus as gamma radiation; transferr ...
*
Tritium illumination Tritium radioluminescence is the use of gaseous tritium, a radioactive isotope of hydrogen, to create visible light. Tritium emits electrons through beta decay and, when they interact with a phosphor material, light is emitted through the proces ...
, a form of fluorescent lighting powered by beta decay *
Pandemonium effect The pandemonium effect is a problem that may appear when high resolution detectors (usually germanium detectors) are used in beta decay studies. It can affect the correct determination of the feeding to the different levels of the daughter nucl ...
*
Total absorption spectroscopy Total absorption spectroscopy is a measurement technique that allows the measurement of the gamma radiation emitted in the different nuclear gamma transitions that may take place in the daughter nucleus after its unstable parent has decayed by mean ...


References


Bibliography

* *


External links

* '
The Live Chart of Nuclides - IAEA
'' with filter on decay type *Beta decay simulation''

{{DEFAULTSORT:Beta Decay Nuclear physics Radioactivity