Double beta decay

In nuclear physics, double beta decay is a type of radioactive decay in which two neutrons are simultaneously transformed into two protons, or vice versa, inside an atomic nucleus. As in single beta decay, 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 two detectable beta particles, which are electrons or positrons.
The literature distinguishes between two types of double beta decay: ordinary double beta decay and neutrinoless double beta decay. In ordinary double beta decay, which has been observed in several isotopes, two electrons and two electron antineutrinos are emitted from the decaying nucleus. In neutrinoless double beta decay, a hypothesized process that has never been observed, only electrons would be emitted.

History

The idea of double beta decay was first proposed by Maria Goeppert Mayer in 1935.
In 1937, Ettore Majorana demonstrated that all results of beta decay theory remain unchanged if the neutrino were its own antiparticle, now known as a Majorana particle.
In 1939, Wendell H. Furry proposed that if neutrinos are Majorana particles, then double beta decay can proceed without the emission of any neutrinos, via the process now called neutrinoless double beta decay.
It is not yet known whether the neutrino is a Majorana particle, and, relatedly, whether neutrinoless double beta decay exists in nature.
As parity violation in weak interactions would not be discovered until 1956, earlier calculations showed that neutrinoless double beta decay should be much more likely to occur than ordinary double beta decay, if neutrinos were Majorana particles. The predicted half-lives were on the order of ~ years. Efforts to observe the process in laboratory date back to at least 1948 when E.L. Fireman made the first attempt to directly measure the half-life of the isotope with a Geiger counter.
Radiometric experiments through about 1960 produced negative results or false positives, not confirmed by later experiments. In 1950, for the first time the double beta decay half-life of was measured by geochemical methods to be 1.4× years,
reasonably close to the modern value. This involved detecting the concentration in minerals of the xenon produced by the decay.
In 1956, after the V − A nature of weak interactions was established, it became clear that the half-life of neutrinoless double beta decay would significantly exceed that of ordinary double beta decay. Despite significant progress in experimental techniques in 1960–1970s, double beta decay was not observed in a laboratory until the 1980s. Experiments had only been able to establish the lower bound for the half-life – about years. At the same time, geochemical experiments detected the double beta decay of and.
Double beta decay was first observed in a laboratory in 1987 by the group of Michael Moe at UC Irvine in.
Since then, many experiments have observed ordinary double beta decay in other isotopes. None of those experiments have produced positive results for the neutrinoless process, raising the half-life lower bound to approximately years. Geochemical experiments continued through the 1990s, producing positive results for several isotopes. Double beta decay is the rarest known kind of radioactive decay; as of 2019 it has been observed in only 14 isotopes, and all have a mean lifetime over yr.

Ordinary double beta decay

In a typical double beta decay, two neutrons in the nucleus are converted to protons, and two electrons and two electron antineutrinos are emitted. The process can be thought as two simultaneous beta minus decays. In order for beta decay to be possible, the final nucleus must have a larger binding energy than the original nucleus. For some nuclei, such as germanium-76, the isobar one atomic number higher has a smaller binding energy, preventing single beta decay. However, the isobar with atomic number two higher, selenium-76, has a larger binding energy, so double beta decay is allowed.
The emission spectrum of the two electrons can be computed in a similar way to beta emission spectrum using Fermi's golden rule. The differential rate is given by
where the subscripts refer to each electron, is kinetic energy, is total energy, is the Fermi function with Z the charge of the final-state nucleus, is momentum, is velocity in units of, is the angle between the electrons, and is the Q value of the decay.
For some nuclei, the process occurs as conversion of two protons to neutrons, emitting two electron neutrinos and absorbing two orbital electrons. If the mass difference between the parent and daughter atoms is more than 1.022 MeV/c², another decay is accessible, capture of one orbital electron and emission of one positron. When the mass difference is more than 2.044 MeV/c², emission of two positrons is possible. These theoretical decay branches have not been observed.

Known double beta decay isotopes

There are 35 naturally occurring isotopes capable of double beta decay. In practice, the decay can be observed when the single beta decay is forbidden by energy conservation. This happens for elements with an even atomic number and even neutron number, which are more stable due to spin-coupling. When single beta decay or alpha decay also occur, the double beta decay rate is generally too low to observe. However, the double beta decay of has been measured radiochemically. Two other nuclides in which double beta decay has been observed, and, can also theoretically single beta decay, but this decay is extremely suppressed and has never been observed. Similar suppression of energetically barely possible single beta decay occurs for ¹⁴⁸Gd and ²²²Rn, but both these nuclides are rather short-lived alpha emitters.
Fourteen isotopes have been experimentally observed undergoing two-neutrino double beta decay or double electron capture. The table below contains those nuclides with the latest experimentally measured half-lives for them. Where two uncertainties are specified, the first one is statistical uncertainty and the second is systematic.

Nuclide	Half-life, 10²¹ years	Mode	Transition	Method	Experiment
	0.064 ±	β^–β^–		direct	NEMO-3
	1.926	β^–β^–		direct	GERDA
	9.2	εε		direct	BAKSAN
	0.096 ± 0.003 ± 0.010	β^–β^–		direct	NEMO-3
	0.0235 ± 0.0014 ± 0.0016	β^–β^–		direct	NEMO-3
	0.00693 ± 0.00004	β^–β^–		direct	NEMO-3
	0.69 ± 0.07	β^–β^–	0⁺→ 0⁺₁	direct	Ge coincidence
	0.028 ± 0.001 ± 0.003 0.026	β^–β^–		direct	NEMO-3 ELEGANT IV
	7200 ± 400 1800 ± 700	β^–β^–		geochemical
	0.82 ± 0.02 ± 0.06	β^–β^–		direct	CUORE-0
	11 ± 2 ± 1	εε		direct	XENON1T
	2.165 ± 0.016 ± 0.059	β^–β^–		direct	EXO-200
		εε		geochemical
	0.00911 ± 0.00063	β^–β^–		direct	NEMO-3
	0.107	β^–β^–	0⁺→ 0⁺₁	direct	Ge coincidence
	2.0 ± 0.6	β^–β^–		radiochemical

Searches for double beta decay in isotopes that present significantly greater experimental challenges are ongoing. One such isotope is .
The following known beta-stable nuclides with A ≤ 260 are theoretically capable of double beta decay, where red are isotopes that have a double-beta rate measured experimentally and black have yet to be measured experimentally: ⁴⁶Ca,, ⁷⁰Zn,, ⁸⁰Se,, ⁸⁶Kr, ⁹⁴Zr,, ⁹⁸Mo,, ¹⁰⁴Ru, ¹¹⁰Pd, ¹¹⁴Cd,, ¹²²Sn, ¹²⁴Sn,,, ¹³⁴Xe,, ¹⁴²Ce, ¹⁴⁶Nd, ¹⁴⁸Nd,, ¹⁵⁴Sm, ¹⁶⁰Gd, ¹⁷⁰Er, ¹⁷⁶Yb, ¹⁸⁶W, ¹⁹²Os, ¹⁹⁸Pt, ²⁰⁴Hg, ²¹⁶Po, ²²⁰Rn, ²²²Rn, ²²⁶Ra, ²³²Th,, ²⁴⁴Pu, ²⁴⁸Cm, ²⁵⁴Cf, ²⁵⁶Cf, and ²⁶⁰Fm.
The following known beta-stable nuclides with A ≤ 260 are theoretically capable of double electron capture, where red are isotopes that have a double-electron capture rate measured and black have yet to be measured experimentally: ³⁶Ar, ⁴⁰Ca, ⁵⁰Cr, ⁵⁴Fe, ⁵⁸Ni, ⁶⁴Zn, ⁷⁴Se,, ⁸⁴Sr, ⁹²Mo, ⁹⁶Ru, ¹⁰²Pd, ¹⁰⁶Cd, ¹⁰⁸Cd, ¹¹²Sn, ¹²⁰Te,, ¹²⁶Xe,, ¹³²Ba, ¹³⁶Ce, ¹³⁸Ce, ¹⁴⁴Sm, ¹⁴⁸Gd, ¹⁵⁰Gd, ¹⁵²Gd, ¹⁵⁴Dy, ¹⁵⁶Dy, ¹⁵⁸Dy, ¹⁶²Er, ¹⁶⁴Er, ¹⁶⁸Yb, ¹⁷⁴Hf, ¹⁸⁰W, ¹⁸⁴Os, ¹⁹⁰Pt, ¹⁹⁶Hg, ²¹²Rn, ²¹⁴Rn, ²¹⁸Ra, ²²⁴Th, ²³⁰U, ²³⁶Pu, ²⁴²Cm, ²⁵²Fm, and ²⁵⁸No.
In particular, ³⁶Ar is the lightest observationally stable nuclide whose decay is energetically possible.