In nuclear physics, beta decay is a type of radioactive decay in which a proton is transformed
into a neutron, or vice versa, inside an atomic nucleus. This process allows the atom to move
closer to the optimal ratio of protons and neutrons. As a result of this transformation,
the nucleus emits a detectable beta particle, which is an electron or positron.
Beta decay is mediated by the weak force. There are two types of beta decay, known as
beta minus and beta plus. Beta minus decay produces an electron and electron antineutrino,
while beta plus decay produces a positron and electron neutrino; β+ decay is thus also
known as positron emission. An example of electron emission is the decay
of carbon-14 into nitrogen-14: 14
6C → 14 7N + e− + ν
e In this form of decay, the original element
has decayed into a new chemical element in a process known as nuclear transmutation.
This new element has an unchanged mass number A but an atomic number Z that is increased
by one. As in all nuclear decays, the decaying element (in this case 14
6C) is known as the parent nuclide while the resulting element (in this case 14
7N) is known as the daughter nuclide. The emitted electron or positron is known as a
beta particle. An example of positron emission is the decay
of magnesium-23 into sodium-23: 23
12Mg → 23 11Na + e+ + ν
e In contrast to β− decay, β+ decay is accompanied
by the emission of an electron neutrino. β+ decay also results in nuclear transmutation,
with the resulting element having an atomic number that is decreased by one.
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. An example of electron capture is the decay of krypton-81 into bromine-81:
81 36Kr + e− → 81
35Br + ν e
Electron capture is a competing 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.
β− decay
In β− decay, the weak interaction converts an atomic nucleus into a nucleus with one
higher atomic number while emitting an electron and an electron antineutrino (ν
e). The generic equation is: AZN → AZ+1N’ + e− + ν
e where A and Z are the mass number and atomic
number of the decaying nucleus. Another example is when the free neutron (1
0n) decays by β− decay into a proton: n → p + e− + ν
e. At the fundamental level, this is caused by
the conversion of the negatively charged down quark to the positively charged up quark by
emission of a W− boson; the W− boson subsequently decays into an electron and an electron antineutrino:
d → u + e− + ν e.
β− decay generally occurs in neutron-rich nuclei.
β+ decay
In β+ decay, or "positron emission", the weak interaction converts a nucleus into its
next-lower neighbor on the periodic table while emitting a positron and an electron
neutrino (ν e). The generic equation is:
AZN → AZ−1N’ + e+ + ν e
β+ 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. β+ decay can only happen
inside nuclei when the daughter nucleus has a greater binding 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. In
an opposite process to negative beta decay, the weak interaction converts a proton into
a neutron by converting an up quark into a down quark by having it emit a W+ or absorb
a W−. Electron capture
In all cases where β+ decay of a nucleus is allowed energetically, the electron capture
process is also allowed, in which the same nucleus captures an atomic electron with the
emission of a neutrino: AZN + e− → AZ−1N’ + ν
e The emitted neutrino is mono-energetic. In
proton-rich nuclei where the energy difference between initial and final states is less than
2mec2, β+ decay is not energetically possible, and electron capture is the sole decay mode.
This decay is also called K-capture because the innermost electron of an atom belongs
to the K-shell of the electronic configuration of the atom, and this has the highest probability
to interact with the nucleus. There is an analogous process possible in
theory in antimatter: antiproton-rich antimatter radioisotopes might decay via an analogous
process of positron capture, but in practice no such complex antimatter nuclides have either
been discovered or artificially constructed. Q-values
The Q value is defined as the total amount of energy released in a given nuclear decay.
In beta decay, Q is therefore also the sum of the kinetic energies of the emitted beta
particle, neutrino, and recoiling nucleus. Beta particles can therefore emitted with
any kinetic energy ranging from 0 to Q. A typical Q is around 1 MeV, 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.
Nuclear transmutation
If the proton and neutron are part of an atomic nucleus, these decay processes transmute one
chemical element into another. For example:
Beta decay does not change the number A of nucleons in the nucleus but changes only its
charge Z. Thus the set of all nuclides with the same A can be introduced; these isobaric
nuclides may turn into each other via beta decay. Among them, several nuclides are beta
stable, because they present local minima of the mass excess: 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 A the global minimum is also the unique local minimum.
For even A, there are up to three different beta-stable isobars experimentally known;
for example, 96 40Zr, 96
42Mo, and 96 44Ru are all beta-stable, though the first
one can undergo a very rare double beta decay. There are about 355 known beta-decay stable
nuclides total. Usually unstable nuclides are clearly either
"neutron rich" or "proton rich", with the former undergoing beta decay and the latter
undergoing electron capture. 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 64 29Cu, which decays by positron emission 61%
of the time to 64 28Ni, and 39% of the time by beta decay to
64 30Zn.
A beta-stable nucleus may undergo other kinds of radioactive decay. In nature, most isotopes
are beta stable, but a few exceptions exist with half-lives so long that they have not
had enough time to decay since the moment of their nucleosynthesis. One example is the
odd-proton odd-neutron nuclide 40 19K, which undergoes all three types of beta
decay with a half-life of 1.277×109 years. Double beta decay
Some nuclei can undergo double beta 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 A; thus, at least one of the nuclides with some given A 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 particles, then a decay known as neutrinoless double beta
decay will occur. Most neutrino physicists believe that neutrinoless double beta decay
has never been observed. Bound-state β− decay
A very small minority of free neutron decays 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 necessary energy to escape the proton, and therefore simply remains bound to it,
as a neutral hydrogen atom. In this type of beta decay, in essence all of the neutron
decay energy is carried off by the antineutrino. For fully ionized atoms, 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. This can not occur for neutral atoms whose low-lying
bound states are already filled by electrons. The phenomenon in fully ionized atoms was
first observed for 163Dy66+ in 1992 by Jung et al. of the Darmstadt Heavy-Ion Research
group. Although neutral 163Dy is a stable isotope, the fully ionized 163Dy66+ undergoes
β decay into the K and L shells with a half-life of 47 days.
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 42 × 109 years, but for fully ionized 187Re75+ this is shortened
by a factor of 109 to only 32.9 years. For comparison the variation of decay rates of
other nuclear processes due to chemical environment is less than 1%.
Forbidden transitions Beta decays can be classified according to
the L-value of the emitted radiation. When L > 0, the decay is referred to as "forbidden".
Nuclear selection rules require high L-values to be accompanied by changes in nuclear spin (J)
and parity (π). The selection rules for the Lth forbidden transitions are:
where Δπ = 1 or −1 corresponds to no parity change or parity change, respectively. The
special case of a 0+ → 0+ transition is referred to as "superallowed" for beta decay,
and proceeds very quickly by this decay route. The following table lists the ΔJ and Δπ
values for the first few values of L: Beta emission spectrum
Beta decay can be considered as a perturbation as described in quantum mechanics, and thus
Fermi's Golden Rule can be applied. This leads to an expression for the kinetic energy spectrum
N(T) of emitted betas as follows:
where T is the kinetic energy, CL is a shape function that depends on the forbiddenness
of the decay, F(Z, T) is the Fermi Function with Z the charge of the final-state nucleus,
E = T + mc2 is the total energy, p =√(E/c)2 −2 is the momentum, and Q is the Q value
of the decay. The kinetic energy of the emitted neutrino is given approximately by Q minus
the kinetic energy of the beta. 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:
where S =√1 − α2 Z2, η = ± αZE/pc, ρ = rN/ℏ, and Γ is the Gamma function.
For non-relativistic betas, this expression can be approximated by:
Other approximations can be found in the literature. Kurie plot
A Kurie plot is a graph used in studying beta decay developed by Franz N. D. Kurie, in which
the square root of the number of beta particles whose momenta 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 intercept of a Kurie plot corresponds to the maximum energy imparted
to the electron/positron. With Kurie plot one can find the limit on effective mass of
neutrino. History
Discovery and characterization of β− decay Radioactivity was discovered in 1896 by Henri
Becquerel in uranium, and subsequently observed by Marie and Pierre Curie in thorium and in
the new elements polonium and radium. In 1899 Ernest Rutherford separated radioactive emissions
into two types: alpha and beta, 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 Becquerel measured the mass-to-charge
ratio for beta particles by the method of J.J. Thomson used to study cathode rays and
identify the electron. He found that m/e 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 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 independently proposed
their radioactive displacement law, which states that beta emission from one element
produces another element one place to the right in the periodic table, while alpha emission
produces an element two places to the left. Neutrinos in beta decay
Historically, the study of beta decay provided the first physical evidence of the neutrino.
In 1911 Lise Meitner and Otto Hahn performed an experiment that showed that the energies
of electrons emitted by beta decay had a continuous rather than discrete spectrum. This was in
apparent contradiction to the law of conservation of energy, as it appeared that energy was
lost in the beta decay process. A second problem was that the spin of the nitrogen-14 atom
was 1, in contradiction to the Rutherford prediction of ½.
In 1920–1927, Charles Drummond Ellis established clearly that the beta decay spectrum is really
continuous, ending all controversies. It also had an effective upper bound in energy, which
was a severe blow to Bohr's suggestion that conservation of energy might be true only
in a statistical sense, and might be violated in any given decay. 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 suggested that in addition to electrons
and protons atoms also contained an extremely light neutral particle which he called the
neutron. He suggested that this "neutron" was also emitted during beta decay and had
simply not yet been observed. In 1931 Enrico Fermi renamed Pauli's "neutron" to neutrino,
and in 1934 Fermi published a very successful model of beta decay in which neutrinos were
produced. The neutrino interaction with matter was so weak that detecting it proved a severe
experimental challenge, and was not accomplished until 1956. However, the properties of neutrinos
were as predicted by Pauli and Fermi. Discovery of other types of beta decay
In 1934 Frédéric and Irène Joliot-Curie bombarded aluminium with alpha particles to
effect the nuclear reaction 4 2He + 27
13Al → 30 15P + 1
0n, and observed that the product isotope 30
15P emits a positron identical to those found in cosmic rays by Carl David Anderson in 1932.
This was the first example of β+ decay, which they termed artificial radioactivity
since 30 15P is a short-lived nuclide which does not
exist in nature. The theory of electron capture was first discussed
by Gian-Carlo Wick in a 1934 paper, and then developed by Hideki Yukawa 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.
See also Double beta decay
Electron capture Neutrino
Alpha decay Betavoltaics
Particle radiation Radionuclide
Tritium illumination, a form of fluorescent lighting powered by beta decay
Pandemonium effect Total absorption spectroscopy
References
External links The Live Chart of Nuclides - IAEA with filter
on decay type Definition of Beta Disintegration at Science
Dictionary