Innuclear physics,double beta decay is a type ofradioactive decay in which twoneutrons are simultaneously transformed into twoprotons, or vice versa, inside anatomic nucleus. As in singlebeta 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 detectablebeta particles, which areelectrons orpositrons.

The literature distinguishes between two types of double beta decay:ordinary double beta decay andneutrinoless double beta decay. In ordinary double beta decay, which has been observed in several isotopes, two electrons and twoelectron antineutrinos are emitted from the decaying nucleus. Inneutrinoless double beta decay, a hypothesized process that has never been observed, only electrons would be emitted.

The idea of double beta decay was first proposed byMaria Goeppert Mayer in 1935.^[1][2]In 1937,Ettore Majorana demonstrated that all results of beta decay theory remain unchanged if the neutrino were its own antiparticle, now known as aMajorana particle.^[3]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 calledneutrinoless double beta decay.^[4]It is not yet known whether the neutrino is a Majorana particle, and, relatedly, whether neutrinoless double beta decay exists in nature.^[5]

Asparity violation inweak 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 10¹⁵~10¹⁶ years.^[5] Efforts to observe the process in laboratory date back to at least 1948 whenE.L. Fireman made the first attempt to directly measure the half-life of the¹²⁴
Sn isotope with aGeiger counter.^[6]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 of¹³⁰
Te was measured by geochemical methods to be 1.4×10²¹ years,^[7]reasonably close to the modern value. This involved detecting the concentration in minerals of thexenon produced by the decay.

In 1956, after theV − 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 10²¹ years. At the same time, geochemical experiments detected the double beta decay of⁸²
Se and¹²⁸
Te.^[5]

Double beta decay was first observed in a laboratory in 1987 by the group ofMichael Moe atUC Irvine in⁸²
Se.^[8]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 10²⁵ years. Geochemical experiments continued through the 1990s, producing positive results for several isotopes.^[5] Double beta decay is the rarest known kind of radioactive decay; as of 2019 it has been observed in only 14 isotopes (includingdouble electron capture in¹³⁰
Ba observed in 2001,⁷⁸
Kr observed in 2013, and¹²⁴
Xe observed in 2019), and all have a mean lifetime over 10¹⁸ yr (table below).^[5]

In a typical double beta decay, two neutrons in the nucleus are converted to protons, and two electrons and twoelectron antineutrinos are emitted. The process can be thought as two simultaneousbeta minus decays. In order for (double) beta decay to be possible, the final nucleus must have a largerbinding energy than the original nucleus. For some nuclei, such asgermanium-76, theisobar one atomic number higher (arsenic-76) 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 tobeta emission spectrum usingFermi's golden rule. The differential rate is given by

$${\displaystyle \frac{dN(T_1,T_2,\cos \theta )}{d{T}_{1}d{T}_{2}d\cos \theta }=F(Z,T_1)F(Z,T_2)w_1{p}_1{w}_2{p}_2(Q-T_1-T_2{)}^5(1-v_1{v}_2\cos \theta )}$$

where the subscripts refer to each electron,T is kinetic energy,w is total energy,F(Z,T) is theFermi function withZ the charge of the final-state nucleus,p is momentum,v is velocity in units ofc,${\displaystyle \cos \theta }$ is the angle between the electrons, andQ is theQ 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 (double electron capture). If the mass difference between the parent and daughter atoms is more than 1.022 MeV/c² (two electron masses), another decay is accessible, capture of one orbital electron and emission of onepositron. When the mass difference is more than 2.044 MeV/c² (four electron masses), emission of two positrons is possible. These theoretical decay branches have not been observed.

There are 35 naturally occurring isotopes capable of double beta decay.^[9] In practice, the decay can be observed when the single beta decay is forbidden by energy conservation. This happens for elements with aneven atomic number and even neutron number, which are more stable due tospin-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 of²³⁸
U (also an alpha emitter) has been measured radiochemically. Two other nuclides in which double beta decay has been observed,⁴⁸
Ca and⁹⁶
Zr, 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 for¹⁴⁸Gd and²²²Rn,^[10] but both these nuclides are rather short-lived alpha emitters.

Fourteen isotopes have been experimentally observed undergoing two-neutrino double beta decay (β^–β^–) or double electron capture (εε).^[11] 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.

Searches for double beta decay in isotopes that present significantly greater experimental challenges are ongoing. One such isotope is¹³⁴
Xe.^[17]

The following known beta-stable (or almost beta-stable in the cases⁴⁸Ca,⁹⁶Zr, and²²²Rn^[10])^[18] nuclides withA ≤ 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,⁴⁸Ca,⁷⁰Zn,⁷⁶Ge,⁸⁰Se,⁸²Se,⁸⁶Kr,⁹⁴Zr,⁹⁶Zr,⁹⁸Mo,¹⁰⁰Mo,¹⁰⁴Ru,¹¹⁰Pd,¹¹⁴Cd,¹¹⁶Cd,¹²²Sn,¹²⁴Sn,¹²⁸Te,¹³⁰Te,¹³⁴Xe,¹³⁶Xe,¹⁴²Ce,¹⁴⁶Nd,¹⁴⁸Nd,¹⁵⁰Nd,¹⁵⁴Sm,¹⁶⁰Gd,¹⁷⁰Er,¹⁷⁶Yb,¹⁸⁶W,¹⁹²Os,¹⁹⁸Pt,²⁰⁴Hg,²¹⁶Po,²²⁰Rn,²²²Rn,²²⁶Ra,²³²Th,²³⁸U,²⁴⁴Pu,²⁴⁸Cm,²⁵⁴Cf,²⁵⁶Cf, and²⁶⁰Fm.^[9]

The following known beta-stable (or almost beta-stable in the case¹⁴⁸Gd) nuclides withA ≤ 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,⁷⁸Kr,⁸⁴Sr,⁹²Mo,⁹⁶Ru,¹⁰²Pd,¹⁰⁶Cd,¹⁰⁸Cd,¹¹²Sn,¹²⁰Te,¹²⁴Xe,¹²⁶Xe,¹³⁰Ba,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, and²⁵⁸No.^[9]

In particular,³⁶Ar is the lightest observationally stable nuclide whose decay is energetically possible.

If the neutrino is aMajorana particle (i.e., the antineutrino and the neutrino are actually the same particle), and at least one type of neutrino has non-zero mass (which has been established by theneutrino oscillation experiments), then it is possible for neutrinoless double beta decay to occur. Neutrinoless double beta decay is alepton number violating process. In the simplest theoretical treatment, known as light neutrino exchange, anucleon absorbs the neutrino emitted by another nucleon. The exchanged neutrinos arevirtual particles.

With only two electrons in the final state, the electrons' totalkinetic energy would be approximately thebinding energy difference of the initial and final nuclei, with the nuclear recoil accounting for the rest. Because ofmomentum conservation, electrons are generally emitted back-to-back. Thedecay rate for this process is given by$${\displaystyle \mathrm{\Gamma }=G|M{|}^2|m_{\beta \beta }{|}^2,}$$whereG is the two-body phase-space factor,M is the nuclear matrix element, andm_ββ is the effective Majorana mass of the electron neutrino. In the context of light Majorana neutrino exchange,m_ββ is given by

$${\displaystyle m_{\beta \beta }=\sum _{i=1}^3{m}_i{U}_{ei}^2,}$$

wherem_i are theneutrino masses and theU_ei are elements of thePontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix. Therefore, observing neutrinoless double beta decay, in addition to confirming the Majorana neutrino nature, can give information on the absolute neutrino mass scale and Majorana phases in the PMNS matrix, subject to interpretation through theoretical models of the nucleus, which determine the nuclear matrix elements, and models of the decay.^[19][20]

The observation of neutrinoless double beta decay would require that at least one neutrino is aMajorana particle, irrespective of whether the process is engendered by neutrino exchange.^[21]

Numerous experiments have searched for neutrinoless double beta decay. The best-performing experiments have a high mass of the decaying isotope and low backgrounds, with some experiments able to perform particle discrimination and electron tracking. In order to remove backgrounds from cosmic rays, most experiments are located in underground laboratories around the world.

Recent and proposed experiments include:

• Completed experiments:
  • Gotthard TPC
  • Heidelberg-Moscow,⁷⁶Ge detectors (1997–2001)
  • IGEX,⁷⁶Ge detectors (1999–2002)^[22]
  • NEMO, various isotopes using tracking calorimeters (2003–2011)
  • Cuoricino,¹³⁰Te in ultracold TeO₂ crystals (2003–2008)^[23]
• Experiments taking data as of November 2017:
  • AMoRE,¹⁰⁰Mo enriched CaMoO₄ crystals at YangYang underground laboratory^[24][25]
  • COBRA,¹¹⁶Cd in room temperature CdZnTe crystals
  • CUORE,¹³⁰Te in ultracold TeO₂ crystals
  • EXO, a¹³⁶Xe and¹³⁴Xe search
  • GERDA, a⁷⁶Ge detector
  • KamLAND-Zen, a¹³⁶Xe search. Data collection from 2011.^[23]
  • Majorana, using high purity⁷⁶Ge p-type point-contact detectors.^[26]
  • XMASS using liquid Xe
• Proposed/future experiments:
  • CUPID, neutrinoless double-beta decay of¹⁰⁰Mo
  • CANDLES,⁴⁸Ca in CaF_2, atKamioka Observatory
  • MOON, developing¹⁰⁰Mo detectors
  • nEXO, using liquid¹³⁶Xe in a time projection chamber^[27]
  • LEGEND, Neutrinoless Double-beta Decay of⁷⁶Ge.
  • LUMINEU, exploring¹⁰⁰Mo enriched ZnMoO₄ crystals at LSM, France.
  • NEXT, a Xenon TPC. NEXT-DEMO ran and NEXT-100 will run in 2016.
  • SNO+, a liquid scintillator, will study¹³⁰Te
  • SuperNEMO, a NEMO upgrade, will study⁸²Se
  • TIN.TIN, a¹²⁴Sn detector atINO
  • PandaX-III, an experiment with 200 kg to 1000 kg of 90% enriched¹³⁶Xe
  • DUNE, a TPC filled with liquid Argon doped with¹³⁶Xe.
  • NuDoubt^++[28] will study double beta plus decays of⁷⁸Kr in a pressurized hybrid-opaque liquid scintillation detector^[29]

While some experiments have claimed a discovery of neutrinoless double beta decay, modern searches have found no evidence for the decay.

Some members of the Heidelberg-Moscow collaboration claimed a detection of neutrinoless beta decay in⁷⁶Ge in 2001.^[30] This claim was criticized by outside physicists^{[1][31][32][33]} as well as other members of the collaboration.^[34] In 2006, a refined estimate by the same authors stated the half-life was 2.3×10²⁵ years.^[35] This half-life has been excluded at high confidence by other experiments, including in⁷⁶Ge byGERDA.^[36]

As of 2017, the strongest limits on neutrinoless double beta decay have come from GERDA in⁷⁶Ge, CUORE in¹³⁰Te, and EXO-200 and KamLAND-Zen in¹³⁶Xe.

For mass numbers with more than two beta-stable isobars, quadruple beta decay and its inverse, quadruple electron capture, have been proposed as alternatives to double beta decay in the isobars with the greatest energy excess. These decays are energetically possible in eight nuclei, thoughpartial half-lives compared to single or double beta decay are predicted to be very long; hence, quadruple beta decay is unlikely to be observed. The seven candidate nuclei for quadruple beta decay include⁹⁶Zr,¹³⁶Xe, and¹⁵⁰Nd capable of quadruple beta-minus decay, and¹²⁴Xe,¹³⁰Ba,¹⁴⁸Gd, and¹⁵⁴Dy capable of quadruple beta-plus decay or electron capture (though¹⁴⁸Gd and¹⁵⁴Dy are non-primordial alpha-emitters with geologically short half-lives). In theory, quadruple beta decay may be experimentally observable in three of these nuclei –⁹⁶Zr,¹³⁶Xe, and¹⁵⁰Nd – with the most promising candidate being¹⁵⁰Nd. Triple beta-minus decay is also possible for⁴⁸Ca,⁹⁶Zr, and¹⁵⁰Nd;^[37] triple beta-plus decay or electron capture is also possible for¹⁴⁸Gd and¹⁵⁴Dy.

Moreover, such a decay mode could also be neutrinoless in physics beyond the standard model.^[38] Neutrinoless quadruple beta decay would violate lepton number in 4 units, as opposed to a lepton number breaking of two units in the case of neutrinoless double beta decay. Therefore, there is no 'black-box theorem'^{[definition needed]} and neutrinos could be Dirac particles while allowing these type of processes. In particular, if neutrinoless quadruple beta decay is found before neutrinoless double beta decay then the expectation is that neutrinos will be Dirac particles.^[39]

As of 2019^[update], searches for triple and quadruple beta decay in¹⁵⁰Nd have not been successful.^[37]

• Double electron capture
• Beta decay
• Neutrino
• Particle radiation
• Radioactive isotope

• Double beta decay on arxiv.org

• Nuclear physics
• Radioactivity
• Neutrinos

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