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{{Short description|Type of radioactive decay}}
{{Nuclear physics|cTopic=Radioactive decay}}
In [[nuclear physics]], '''double beta decay''' is a type of [[radioactive decay]] in which two [[neutron]]s are simultaneously transformed into two [[proton]]s, 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 particle]]s, which are [[electron]]s or [[positron]]s.

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 [[Neutrino|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.<ref name="Giuliani2012">
{{cite journal
 |first1=A.  |last1=Giuliani
 |first2=A.  |last2=Poves
 |year=2012
 |title=Neutrinoless double-beta decay
 |journal=[[Advances in High Energy Physics]]
 |volume=2012 |pages=1–38
 |doi=10.1155/2012/857016 |doi-access=free
 |url=http://downloads.hindawi.com/journals/ahep/2012/857016.pdf
}}
</ref><ref>
{{cite journal
 |last=Goeppert-Mayer |first=M. |author-link=Maria Goeppert-Mayer
 |year=1935
 |title=Double beta-disintegration
 |journal=[[Physical Review]]
 |volume=48 |issue=6 |pages=512–516
 |doi=10.1103/PhysRev.48.512
 |bibcode=1935PhRv...48..512G
}}
</ref>
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]]''.<ref>
{{cite journal
 |last=Majorana |first=E.  |author-link=Ettore Majorana
 |s2cid=18973190
 |year=1937
 |title=Teoria simmetrica dell'elettrone e del positrone
 |journal=[[Il Nuovo Cimento]]
 |volume=14 |issue=4 |pages=171–184
 |doi=10.1007/BF02961314  |language=it
 |bibcode=1937NCim...14..171M
}}
</ref>
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]]''.<ref>
{{cite journal
 |last=Furry |first=W.H. |author-link=Wendell H. Furry
 |year=1939
 |title=On Transition Probabilities in Double Beta-Disintegration
 |journal=[[Physical Review]]
 |volume=56 |issue=12 |pages=1184–1193
 |bibcode=1939PhRv...56.1184F
 |doi=10.1103/PhysRev.56.1184
}}
</ref>
It is not yet known whether the neutrino is a Majorana particle, and, relatedly, whether neutrinoless double beta decay exists in nature.<ref name=Barabash2011>
{{cite journal
 |last1=Barabash |first1=A.S.
 |s2cid=118716672
 |year=2011
 |title=Experiment double beta decay: Historical review of 75&nbsp;years of research
 |journal=Physics of Atomic Nuclei
 |volume=74 |issue=4 |pages=603–613
 |arxiv=1104.2714 |bibcode=2011PAN....74..603B
 |doi=10.1134/S1063778811030070
}}
</ref>

As [[parity violation]] in [[weak interaction]]s 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 {{10^|15}}~{{10^|16}}&nbsp;years.<ref name=Barabash2011/> Efforts to observe the process in laboratory date back to at least 1948 when [[Edward L. Fireman|E.L. Fireman]] made the first attempt to directly measure the half-life of the {{SimpleNuclide|link=yes|tin|124}} isotope with a [[Geiger counter]].<ref>
{{Cite journal
 |last=Fireman |first=E. |author-link=Edward L. Fireman
 |year=1948
 |title=Double beta decay
 |journal=[[Physical Review]]
 |volume=74 |issue=9 |pages=1201–1253
 |bibcode=1948PhRv...74.1201.
 |doi=10.1103/PhysRev.74.1201
}}
</ref>
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 {{SimpleNuclide|link=yes|Tellurium|130}} was measured by geochemical methods to be 1.4×{{10^|21}}&nbsp;years,<ref>
{{Cite journal
 |last1=Inghram  |first1=M.G.
 |last2=Reynolds |first2=J.H.
 |year=1950
 |title=Double Beta-Decay of {{sup|130}}Te
 |journal=[[Physical Review]]
 |volume=78 |issue=6 |pages=822–823
 |bibcode=1950PhRv...78..822I
 |doi=10.1103/PhysRev.78.822.2
}}
</ref>
reasonably close to the modern value. This involved detecting the concentration in minerals of the [[xenon]] produced by the decay.

In 1956, after the [[Weak interaction#Violation of symmetry|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 {{10^|21}}&nbsp;years. At the same time, geochemical experiments detected the double beta decay of {{SimpleNuclide|link=yes|Selenium|82}} and {{SimpleNuclide|link=yes|Tellurium|128}}.<ref name=Barabash2011/>

Double beta decay was first observed in a laboratory in 1987 by the group of [[Michael Moe]] at [[University of California, Irvine|UC Irvine]] in {{SimpleNuclide|link=yes|Selenium|82}}.<ref>
{{cite journal
 |last1=Elliott |first1=S. R.
 |last2=Hahn |first2=A. A.
 |last3=Moe |last4=M. K.
 |year=1987
 |title=Direct evidence for two-neutrino double-beta decay in {{sup|82}}Se
 |journal=[[Physical Review Letters]]
 |volume=59 |issue=18 |pages=2020–2023
 |bibcode=1987PhRvL..59.2020E
 |doi=10.1103/PhysRevLett.59.2020
 |pmid=10035397
}}
</ref>
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 {{10^|25}}&nbsp;years. Geochemical experiments continued through the 1990s, producing positive results for several  isotopes.<ref name=Barabash2011/> Double beta decay is the rarest known kind of radioactive decay; as of 2019 it has been observed in only 14&nbsp;isotopes (including [[double electron capture]] in {{SimpleNuclide|link=yes|Barium|130}} observed in 2001, {{SimpleNuclide|link=yes|Krypton|78}} observed in 2013, and {{SimpleNuclide|link=yes|Xenon|124}} observed in 2019), and all have a mean lifetime over {{10^|18}}&nbsp;yr (table below).<ref name=Barabash2011/>

==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 antineutrino]]s are emitted. The process can be thought as two simultaneous [[beta minus decay]]s. In order for (double) beta decay to be possible, the final nucleus must have a larger [[Binding energy#Nucleus binding energy|binding energy]] than the original nucleus. For some nuclei, such as [[germanium-76]], the [[isobar (nuclide)|isobar]] 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 to [[Beta decay#Beta emission spectrum|beta emission spectrum]] using [[Fermi's golden rule]]. The differential rate is given by

<math display="block">\frac{dN(T_1, T_2, \cos\theta)}{dT_1 dT_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)</math>

where the subscripts refer to each electron, {{mvar|T}} is kinetic energy, {{math|''w''}} is total energy, {{math|''F''(''Z'', ''T'')}} is the [[Beta decay#Fermi function|Fermi function]] with ''Z'' the charge of the final-state nucleus, {{math|''p''}} is momentum, {{math|1=''v''}} is velocity in units of {{mvar|c}}, <math>\cos\theta</math> is the angle between the electrons, and {{mvar|Q}} is the [[Q value (nuclear science)|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 (double electron capture). If the mass difference between the parent and daughter atoms is more than 1.022&nbsp;MeV/''c''<sup>2</sup> (two electron masses), another decay is accessible, capture of one orbital electron and emission of one [[positron]]. When the mass difference is more than 2.044&nbsp;MeV/''c''<sup>2</sup> (four electron masses), 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.<ref name="Tretyak2002"/> In practice, the decay can be observed when the single beta decay is forbidden by energy conservation. This happens for elements with an [[Even and odd atomic nuclei|even atomic number and even neutron number]], which are more stable due to [[Spin (physics)|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 {{SimpleNuclide|link=yes|Uranium|238}} (also an alpha emitter) has been measured radiochemically. Two other nuclides in which double beta decay has been observed, {{SimpleNuclide|link=yes|Calcium|48}} and {{SimpleNuclide|link=yes|Zirconium|96}}, 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 <sup>148</sup>Gd and <sup>222</sup>Rn,<ref name=BelliBaF2>{{cite journal |last1=Belli |first1=P. |last2=Bernabei |first2=R. |last3=Cappella |first3=C. |last4=Caracciolo |first4=V. |last5=Cerulli |first5=R. |last6=Danevich |first6=F.A. |last7=Di Marco |first7=A. |last8=Incicchitti |first8=A. |last9=Poda |first9=D.V. |last10=Polischuk |first10=O.G. |last11=Tretyak |first11=V.I. |title=Investigation of rare nuclear decays with BaF<sub>2</sub> crystal scintillator contaminated by radium |date=2014 |journal=European Physical Journal A |volume=50 |issue=9 |pages=134–143 |doi=10.1140/epja/i2014-14134-6 |arxiv=1407.5844|bibcode=2014EPJA...50..134B |s2cid=118513731 }}</ref> but both these nuclides are rather short-lived alpha emitters.

Fourteen isotopes have been experimentally observed undergoing two-neutrino double beta decay (β<sup>–</sup>β<sup>–</sup>) or double electron capture (εε).<ref name="Patrignani2016">{{Cite journal
 |last1=Patrignani |first1=C.
 |display-authors=etal
 |collaboration=[[Particle Data Group]]
 |year=2016
 |title=Review of Particle Physics
 |journal=[[Chinese Physics C]]
 |volume=40 |issue=10 |pages=100001
 |bibcode=2016ChPhC..40j0001P
 |doi=10.1088/1674-1137/40/10/100001
|s2cid=125766528
 |url=http://inspirehep.net/record/1489868/files/openaccess_cpc_40_10_100001.pdf
 }} See p. 768</ref> The table below contains nuclides with the latest experimentally measured half-lives, as of December 2016, except for <sup>124</sup>Xe (for which double electron capture was first observed in 2019). Where two uncertainties are specified, the first one is statistical uncertainty and the second is systematic.

{| class="wikitable" style="text-align:center;"
!Nuclide!!Half-life, 10<sup>21</sup> years
!Mode!!Transition!!Method!!Experiment
|-
|{{SimpleNuclide|link=yes|Calcium|48}}||0.064{{±|0.007|0.006}} ± {{±|0.012|0.009}}
|''β<sup>–</sup>β<sup>–</sup>''|| || direct || [[Neutrino Ettore Majorana Observatory|NEMO-3]]<ref>{{Cite journal
 |last1=Arnold |first1=R.
 |s2cid=55485404
 |display-authors=etal
 |year=2016
 |collaboration=[[NEMO-3 Collaboration]]
 |title= Measurement of the double-beta decay half-life and search for the neutrinoless double-beta decay of <sup>48</sup>Ca with the NEMO-3 detector
 |journal=[[Physical Review D]]
 |volume=93 |issue=11
 |pages=112008
 |doi= 10.1103/PhysRevD.93.112008
|arxiv=1604.01710|bibcode=2016PhRvD..93k2008A}}</ref>
|-
|-
|{{SimpleNuclide|link=yes|Germanium|76}}|| 1.926{{±|0.094}}
|''β<sup>–</sup>β<sup>–</sup>''
| || direct || [[GERDA]]<ref name=Patrignani2016/>
|-
|{{SimpleNuclide|link=yes|Krypton|78}}|| 9.2{{±|5.5|2.6}}{{±|1.3}}
|[[Double electron capture|εε]]
| || direct || [[Baksan Neutrino Observatory|BAKSAN]]<ref name=Patrignani2016/>
|-
|{{SimpleNuclide|link=yes|Selenium|82}}|| 0.096 ± 0.003 ± 0.010 
|''β<sup>–</sup>β<sup>–</sup>''
| || direct || NEMO-3<ref name=Patrignani2016/>
|-
|{{SimpleNuclide|link=yes|Zirconium|96}}|| 0.0235 ± 0.0014 ± 0.0016 
|''β<sup>–</sup>β<sup>–</sup>''
| || direct || NEMO-3<ref name=Patrignani2016/>
|-
| rowspan=2|{{SimpleNuclide|link=yes|Molybdenum|100}}|| 0.00693 ± 0.00004
|''β<sup>–</sup>β<sup>–</sup>''
| || rowspan=2 | direct || NEMO-3<ref name=Patrignani2016/>
|-
|0.69{{±|0.10|0.08}} ± 0.07
|''β<sup>–</sup>β<sup>–</sup>''
| 0<sup>+</sup>→ 0<sup>+</sup><sub>1</sub> || Ge coincidence<ref name=Patrignani2016/>
|-
|{{SimpleNuclide|link=yes|Cadmium|116}}|| 0.028 ± 0.001 ± 0.003 <br/> 0.026{{±|0.009|0.005}}
|''β<sup>–</sup>β<sup>–</sup>''
| || direct || NEMO-3<ref name=Patrignani2016/><br/> ELEGANT IV<ref name=Patrignani2016/>
|-
|{{SimpleNuclide|link=yes|Tellurium|128}}|| 7200 ± 400 <br/>1800 ± 700 
|''β<sup>–</sup>β<sup>–</sup>''
| || geochemical || <ref name=Patrignani2016/>
|-
|{{SimpleNuclide|link=yes|Tellurium|130}}|| 0.82 ± 0.02 ± 0.06 
|''β<sup>–</sup>β<sup>–</sup>''
| || direct || [[CUORE|CUORE-0]]<ref>{{Cite journal
 |last1= Alduino |first1=C.
 |s2cid=73575079
 |display-authors=etal
 |year=2016
 |collaboration=[[CUORE-0 Collaboration]]
 |title=  Measurement of the Two-Neutrino Double Beta Decay Half-life of <sup>130</sup>Te with the CUORE-0 Experiment
 |journal=The European Physical Journal C
 |volume= 77|issue=1
 |pages=13
 |doi=10.1140/epjc/s10052-016-4498-6 
 |arxiv=1609.01666
|bibcode=2017EPJC...77...13A}}</ref>
|-
|{{SimpleNuclide|link=yes|Xenon|124}}|| 18 ± 5 ± 1
|[[Double electron capture|εε]]
| || direct || [[XENON|XENON1T]]<ref name=xenon1T>{{cite journal  |date=2019 |title=Observation of two-neutrino double electron capture in <sup>124</sup>Xe with XENON1T |journal=Nature |volume=568 |issue=7753 |pages=532–535 |doi=10.1038/s41586-019-1124-4|arxiv=1904.11002 |last1=Aprile |first1=E. |last2=Aalbers |first2=J. |last3=Agostini |first3=F. |last4=Alfonsi |first4=M. |last5=Althueser |first5=L. |last6=Amaro |first6=F. D. |last7=Anthony |first7=M. |last8=Antochi |first8=V. C. |last9=Arneodo |first9=F. |last10=Baudis |first10=L. |last11=Bauermeister |first11=B. |last12=Benabderrahmane |first12=M. L. |last13=Berger |first13=T. |last14=Breur |first14=P. A. |last15=Brown |first15=A. |last16=Brown |first16=A. |last17=Brown |first17=E. |last18=Bruenner |first18=S. |last19=Bruno |first19=G. |last20=Budnik |first20=R. |last21=Capelli |first21=C. |last22=Cardoso |first22=J. M. R. |last23=Cichon |first23=D. |last24=Coderre |first24=D. |last25=Colijn |first25=A. P. |last26=Conrad |first26=J. |last27=Cussonneau |first27=J. P. |last28=Decowski |first28=M. P. |last29=de Perio |first29=P. |last30=Di Gangi |first30=P. |pmid=31019319 |bibcode=2019Natur.568..532X |s2cid=129948831 |display-authors=1 }}</ref>
|-
|{{SimpleNuclide|link=yes|Xenon|136}}||2.165 ± 0.016 ± 0.059 
|''β<sup>–</sup>β<sup>–</sup>''
| || direct || [[Enriched Xenon Observatory|EXO-200]]<ref name=Patrignani2016/>
|-
|{{SimpleNuclide|link=yes|Barium|130}}||(0.5 – 2.7) 
|[[Double electron capture|εε]]
| || geochemical || <ref>{{cite journal |author=A. P. Meshik |author2=C. M. Hohenberg |author3=O. V. Pravdivtseva |author4=Ya. S. Kapusta |year=2001 |title=Weak decay of <sup>130</sup>Ba and <sup>132</sup>Ba: Geochemical measurements |journal=[[Physical Review C]] |volume=64 |issue=3 |pages=035205 [6 pages]  |doi=10.1103/PhysRevC.64.035205|bibcode = 2001PhRvC..64c5205M |url=https://zenodo.org/record/1063702 }}</ref><ref>{{cite journal |author=M. Pujol |author2=B. Marty |author3=P. Burnard |author4=P. Philippot |year=2009|title=Xenon in Archean barite: Weak decay of <sup>130</sup>Ba, mass-dependent isotopic fractionation and implication for barite formation |journal=[[Geochimica et Cosmochimica Acta]] |volume=73|issue=22 |pages=6834–6846 |doi=10.1016/j.gca.2009.08.002|bibcode = 2009GeCoA..73.6834P }}</ref>
|-
| rowspan=2|{{SimpleNuclide|link=yes|Neodymium|150}}|| 0.00911{{±|0.00025|0.00022}} ± 0.00063 
|''β<sup>–</sup>β<sup>–</sup>''
| ||rowspan=2| direct || NEMO-3<ref name=Patrignani2016/>
|-
| 0.107{{±|0.046|0.026}} 
|''β<sup>–</sup>β<sup>–</sup>''
| 0<sup>+</sup>→ 0<sup>+</sup><sub>1</sub> || Ge coincidence<ref name=Patrignani2016/>

|-
|{{SimpleNuclide|link=yes|Uranium|238}}|| 2.0 ± 0.6 
|''β<sup>–</sup>β<sup>–</sup>''
| || radiochemical || <ref name=Patrignani2016/>
|}
Searches for double beta decay in isotopes that present significantly greater experimental challenges are ongoing. One such isotope is  {{SimpleNuclide|link=yes|Xenon|134}}.<ref>{{cite journal|arxiv=1704.05042|title=Searches for Double Beta Decay of <sup>134</sup>Xe with EXO-200|collaboration=EXO-200 Collaboration|first1=J. B.|last1=Albert|s2cid=28537166|display-authors=etal|date=3 November 2017|journal=Physical Review D|volume=96|issue=9|pages=092001|doi=10.1103/PhysRevD.96.092001|bibcode=2017PhRvD..96i2001A}}</ref>

The following known beta-stable (or almost beta-stable in the cases <sup>48</sup>Ca, <sup>96</sup>Zr, and <sup>222</sup>Rn<ref name=BelliBaF2 />)<ref name="bellidecay">{{cite journal |last1=Belli |first1=P. |last2=Bernabei |first2=R. |last3=Danevich |first3=F. A. |last4=Incicchitti |first4=A. |last5=Tretyak |first5=V. I. |title=Experimental searches for rare alpha and beta decays |journal=European Physical Journal A |date=2019 |volume=55 |issue=8 |pages=140–1–140–7 |doi=10.1140/epja/i2019-12823-2 |issn=1434-601X |arxiv=1908.11458 |bibcode=2019EPJA...55..140B |s2cid=201664098 }}</ref> 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: <sup>46</sup>Ca, {{color|red|<sup>48</sup>Ca}}, <sup>70</sup>Zn, {{color|red|<sup>76</sup>Ge}}, <sup>80</sup>Se, {{color|red|<sup>82</sup>Se}}, <sup>86</sup>Kr, <sup>94</sup>Zr, {{color|red|<sup>96</sup>Zr}}, <sup>98</sup>Mo, {{color|red|<sup>100</sup>Mo}}, <sup>104</sup>Ru, <sup>110</sup>Pd, <sup>114</sup>Cd, {{color|red|<sup>116</sup>Cd}}, <sup>122</sup>Sn, <sup>124</sup>Sn, {{color|red|<sup>128</sup>Te}}, {{color|red|<sup>130</sup>Te}}, <sup>134</sup>Xe, {{color|red|<sup>136</sup>Xe}}, <sup>142</sup>Ce, <sup>146</sup>Nd, <sup>148</sup>Nd, {{color|red|<sup>150</sup>Nd}}, <sup>154</sup>Sm, <sup>160</sup>Gd, <sup>170</sup>Er, <sup>176</sup>Yb, <sup>186</sup>W, <sup>192</sup>Os, <sup>198</sup>Pt, <sup>204</sup>Hg, <sup>216</sup>Po, <sup>220</sup>Rn, <sup>222</sup>Rn, <sup>226</sup>Ra, <sup>232</sup>Th, {{color|red|<sup>238</sup>U}}, <sup>244</sup>Pu, <sup>248</sup>Cm, <sup>254</sup>Cf, <sup>256</sup>Cf, and <sup>260</sup>Fm.<ref name="Tretyak2002">{{Cite journal
 |last1=Tretyak |first1=V.I. 
 |last2=Zdesenko |first2=Yu.G. 
 |year=2002
 |title=Tables of Double Beta Decay Data — An Update
 |journal=[[At. Data Nucl. Data Tables]] |volume=80 |issue=1 |pages=83–116
 |doi=10.1006/adnd.2001.0873
|bibcode=2002ADNDT..80...83T }}</ref>

The following known beta-stable (or almost beta-stable in the case <sup>148</sup>Gd) 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: <sup>36</sup>Ar, <sup>40</sup>Ca, <sup>50</sup>Cr, <sup>54</sup>Fe, <sup>58</sup>Ni, <sup>64</sup>Zn, <sup>74</sup>Se, {{color|red|<sup>78</sup>Kr}}, <sup>84</sup>Sr, <sup>92</sup>Mo, <sup>96</sup>Ru, <sup>102</sup>Pd, <sup>106</sup>Cd, <sup>108</sup>Cd, <sup>112</sup>Sn, <sup>120</sup>Te, {{color|red|<sup>124</sup>Xe}}, <sup>126</sup>Xe, {{color|red|<sup>130</sup>Ba}}, <sup>132</sup>Ba, <sup>136</sup>Ce, <sup>138</sup>Ce, <sup>144</sup>Sm, <sup>148</sup>Gd, <sup>150</sup>Gd, <sup>152</sup>Gd, <sup>154</sup>Dy, <sup>156</sup>Dy, <sup>158</sup>Dy, <sup>162</sup>Er, <sup>164</sup>Er, <sup>168</sup>Yb, <sup>174</sup>Hf, <sup>180</sup>W, <sup>184</sup>Os, <sup>190</sup>Pt, <sup>196</sup>Hg, <sup>212</sup>Rn, <sup>214</sup>Rn, <sup>218</sup>Ra, <sup>224</sup>Th, <sup>230</sup>U, <sup>236</sup>Pu, <sup>242</sup>Cm, <sup>252</sup>Fm, and <sup>258</sup>No.<ref name=Tretyak2002 />

In particular, [[argon-36|<sup>36</sup>Ar]] is the lightest observationally stable nuclide whose decay is energetically possible.

==Neutrinoless double beta decay==
{{Main|Neutrinoless double beta decay}}
[[Image:Double beta decay feynman.svg|thumb|250px|right|[[Feynman diagram]] of neutrinoless double beta decay, with two neutrons decaying to two protons. The only emitted products in this process are two electrons, which can occur if the neutrino and antineutrino are the same particle (i.e. Majorana neutrinos) so the same neutrino can be emitted and absorbed within the nucleus. In conventional double beta decay, two antineutrinos — one arising from each W vertex — are emitted from the nucleus, in addition to the two electrons. The detection of neutrinoless double beta decay is thus a sensitive test of whether neutrinos are Majorana particles.]]

If the neutrino is a [[Majorana fermion|Majorana 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 the [[neutrino oscillation]] experiments), then it is possible for neutrinoless double beta decay to occur. Neutrinoless double beta decay is a [[Lepton number|lepton number violating]] process. In the simplest theoretical treatment, known as light neutrino exchange, a [[nucleon]] absorbs the neutrino emitted by another nucleon. The exchanged neutrinos are [[virtual particles]].

With only two electrons in the final state, the electrons' total [[kinetic energy]] would be approximately the [[Binding energy#Nucleus binding energy|binding energy]] difference of the initial and final nuclei, with the nuclear recoil accounting for the rest. Because of [[Momentum|momentum conservation]], electrons are generally emitted back-to-back. The [[Decay rate#Rates|decay rate]] for this process is given by
<math display="block">\Gamma = G |M|^2 |m_{\beta \beta}|^2,</math>
where ''G'' is the two-body phase-space factor, ''M'' is the nuclear matrix element, and ''m''<sub>ββ</sub> is the effective Majorana mass of the electron neutrino. In the context of light Majorana neutrino exchange, ''m''<sub>ββ</sub> is given by

<math display="block">m_{\beta \beta} = \sum_{i=1}^3 m_i U^2_{ei},</math>

where ''m<sub>i</sub>'' are the [[neutrino mass]]es and the ''U<sub>ei</sub>'' are elements of the [[Pontecorvo–Maki–Nakagawa–Sakata matrix|Pontecorvo–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.<ref>
{{cite book
 |last1=Grotz
 |first1=K.
 |last2=Klapdor
 |first2=H. V.
 |year=1990
 |title=The Weak Interaction in Nuclear, Particle and Astrophysics
 |publisher=[[CRC Press]]
 |isbn=978-0-85274-313-3
 |url-access=registration
 |url=https://archive.org/details/weakinteractioni0000grot
 }}</ref><ref>{{cite book
 |last1=Klapdor-Kleingrothaus
 |first1=H. V.
 |last2=Staudt
 |first2=A.
 |year=1998
 |title=Non-accelerator Particle Physics
 |url=http://web-docs.gsi.de/~gkalicy/books/NonAccelerator%20particle%20physics.pdf
 |edition=Reprint
 |publisher=[[IOP Publishing]]
 |isbn=978-0-7503-0305-7
 |access-date=2016-10-16
 |archive-date=2017-02-02
 |archive-url=https://web.archive.org/web/20170202023120/http://web-docs.gsi.de/~gkalicy/books/NonAccelerator%20particle%20physics.pdf
 |url-status=dead
 }}</ref>

The observation of neutrinoless double beta decay would require that at least one neutrino is a [[Majorana fermion|Majorana particle]], irrespective of whether the process is engendered by neutrino exchange.<ref>
{{cite journal
 |last1=Schechter |first1=J.
 |last2=Valle |first2=J. W. F.
 |year=1982
 |title=Neutrinoless double-β decay in SU(2)×U(1) theories
 |journal=[[Physical Review D]]
 |volume=25 |issue=11 |pages=2951–2954
 |bibcode=1982PhRvD..25.2951S
|doi=10.1103/PhysRevD.25.2951
|hdl=10550/47205
 |hdl-access=free
 }}</ref>

===Experiments===
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, <sup>76</sup>Ge detectors (1997–2001)
** IGEX, <sup>76</sup>Ge detectors (1999–2002)<ref>{{cite journal
 |last1=Aalseth |first1=C. E.
 |s2cid=123335600
 |display-authors=etal
 |date=2000
 |title=Recent Results of the IGEX <sup>76</sup>Ge Double-Beta Decay Experiment
 |journal=[[Physics of Atomic Nuclei]]
 |volume=63 |issue=7 |pages=1225–1228
 |bibcode=2000PAN....63.1225A
 |doi=10.1134/1.855774
}}</ref>
** [[Neutrino Ettore Majorana Observatory|NEMO]], various isotopes using tracking calorimeters (2003–2011)
** [[Cuoricino]], <sup>130</sup>Te in ultracold TeO<sub>2</sub> crystals (2003–2008)<ref name="Schwingenheuer2013">{{Cite journal|last1=Schwingenheuer|first1=B.|s2cid=117129820|year=2013|title=Status and prospects of searches for neutrinoless double beta decay|journal=[[Annalen der Physik]]|volume=525|issue=4|pages=269–280|arxiv=1210.7432|bibcode=2013AnP...525..269S|doi=10.1002/andp.201200222|citeseerx=10.1.1.760.5635}}</ref>
* Experiments taking data as of November 2017:
** AMoRE, <sup>100</sup>Mo enriched CaMoO<sub>4</sub> crystals at YangYang underground laboratory<ref>{{Cite journal |last=Khanbekov |first=N. D. |s2cid=123287005 |year=2013 |title=AMoRE: Collaboration for searches for the neutrinoless double-beta decay of the isotope of <sup>100</sup>Mo with the aid of <sup>40</sup>Ca<sup>100</sup>MoO<sub>4</sub> as a cryogenic scintillation detector |journal=[[Physics of Atomic Nuclei]] |volume=76 |issue=9 |pages=1086–1089 |bibcode=2013PAN....76.1086K |doi=10.1134/S1063778813090093 }}</ref><ref>{{cite journal |author1= V. Alenkov |author2= H. W. Bae |author3= J. Beyer |author4= R. S. Boiko |author5= K. Boonin |author6= O. Buzanov |author7= N. Chanthima |author8= M. K. Cheoun |author9= D. M. Chernyak |author10= J. S. Choe |author11= S. Choi |author12= F. A. Danevich |author13= M. Djamal |author14= D. Drung |author15= C. Enss |author16= A. Fleischmann |author17= A. M. Gangapshev |author18= L. Gastaldo |author19=Yu. M. Gavriljuk |author20=A. M. Gezhaev |author21= V. D. Grigoryeva |author22=V. I. Gurentsov |author23= O. Gylova |author24= C. Ha |author25= D. H. Ha |author26= E. J. Ha |author27= I. S. Hahn |author28= C. H. Jang |author29= E. J. Jeon |author30= J. A. Jeon |author31= H. S. Jo |author32= J. Kaewkhao |author33= C. S. Kang |author34= S. J. Kang |author35= W. G. Kang |author36= V. V. Kazalov |author37= S. Kempf |author38= A. Khan |author39= S. Khan |author40= D. Y. Kim |author41= G. W. Kim |author42=H. B. Kim |author43= H. J. Kim |author44= H. L. Kim |author45=H. S. Kim |author46= I. Kim |author47= S. C. Kim |author48= S. G. Kim |author49= S. K. Kim |author50= S. R. Kim |author51= W. T. Kim |author52= Y. D. Kim |author53= Y. H. Kim |author54= K. Kirdsiri |author55= Y. J. Ko |author56= V. V. Kobychev |author57= V. Kornoukhov |author58= V. V. Kuzminov |author59= D. H. Kwon |author60= C. Lee |author61= E. K. Lee |author62= H. J. Lee |author63= H. S. Lee |author64= J. S. Lee |author65= J. Y. Lee |author66= K. B. Lee |author67= M. H. Lee |author68= M. K. Lee |author69= S. W. Lee |author70= S. W. Lee |author71= S. H. Lee |author72= D. Leonard |author73= J. Li <!--more--> |display-authors=1 |date= 24 September 2019 |title= First results from the AMoRE-Pilot neutrinoless double beta decay experiment |journal= [[European Physical Journal C]] |volume= 79 |issue= 9 |at= 791 |doi= 10.1140/epjc/s10052-019-7279-1 |doi-access= free |arxiv= 1903.09483 |bibcode= 2019EPJC...79..791A }}</ref>
** [[COBRA Experiment|COBRA]], <sup>116</sup>Cd in room temperature CdZnTe crystals
** [[CUORE]], <sup>130</sup>Te in ultracold TeO<sub>2</sub> crystals
** [[Enriched Xenon Observatory|EXO]], a <sup>136</sup>Xe and <sup>134</sup>Xe search
** [[Germanium Detector Array|GERDA]], a <sup>76</sup>Ge detector
** [[Kamioka Liquid Scintillator Antineutrino Detector|KamLAND-Zen]], a <sup>136</sup>Xe search. Data collection from 2011.<ref name="Schwingenheuer2013" />
** {{smallcaps|[[MAJORANA|Majorana]]}}, using high purity <sup>76</sup>Ge p-type point-contact detectors.<ref>{{Cite journal
 |last1=Xu |first1=W.
 |s2cid=119301804
 |display-authors=etal
 |year=2015
 |title=The Majorana Demonstrator: A Search for Neutrinoless Double-beta Decay of 76Ge
 |journal=[[Journal of Physics: Conference Series]]
 |volume=606 |issue=1 |pages=012004
 |arxiv=1501.03089
 |bibcode=2015JPhCS.606a2004X
 |doi=10.1088/1742-6596/606/1/012004
}}</ref>
** XMASS using liquid Xe
* Proposed/future experiments:
** CUPID, neutrinoless double-beta decay of <sup>100</sup>Mo
** CANDLES, <sup>48</sup>Ca in CaF<sub>2,</sub> at [[Kamioka Observatory]]
** MOON, developing <sup>100</sup>Mo detectors
** nEXO, using liquid <sup>136</sup>Xe in a time projection chamber <ref>{{Cite journal|last1=Albert |first1=J. B.
|s2cid=67854591
|collaboration=nEXO Collaboration
|title=Sensitivity and Discovery Potential of nEXO to Neutrinoless Double Beta Decay
|journal=Physical Review C
|volume=97
|issue=6
|pages=065503
|arxiv=1710.05075
|doi=10.1103/PhysRevC.97.065503
|year=2018
|bibcode=2018PhRvC..97f5503A
}}</ref> 
** LEGEND, Neutrinoless Double-beta Decay of <sup>76</sup>Ge.
** LUMINEU, exploring <sup>100</sup>Mo enriched ZnMoO<sub>4</sub> crystals at LSM, France.
** NEXT, a Xenon TPC. NEXT-DEMO ran and NEXT-100 will run in 2016.
** [[SNO+]], a liquid scintillator, will study <sup>130</sup>Te
** [[Neutrino Ettore Majorana Observatory#SuperNEMO|SuperNEMO]], a NEMO upgrade, will study <sup>82</sup>Se
** TIN.TIN, a <sup>124</sup>Sn detector at [[India-based Neutrino Observatory|INO]]
** [[PandaX]]-III, an experiment with 200&nbsp;kg to 1000&nbsp;kg of 90% enriched <sup>136</sup>Xe
** [[Deep Underground Neutrino Experiment|DUNE]], a TPC filled with liquid Argon doped with <sup>136</sup>Xe.
** NuDoubt<sup>++</sup><ref name="NuDoubt2">{{cite web |date=1 August 2024 |title=NuDoubt<sup>++</sup> Experiment|url=https://nudoubt.uni-mainz.de |access-date=1 October 2024 |website=NuDoubt<sup>++</sup> |language=en}}</ref> will study double beta plus decays of <sup>78</sup>Kr in a pressurized hybrid-opaque liquid scintillation detector <ref>{{Cite journal |last1=Böhles |first1=M.
|collaboration=NuDoubt<sup>++</sup> Collaboration
|title=Combining Hybrid and Opaque Scintillator Techniques in the Search for Double Beta Plus Decays
|journal=Eur. Phys. J. C
|volume=85
|pages=121
|arxiv=2407.05999
|doi=10.1140/epjc/s10052-025-13847-1
|year=2025
}}</ref>

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

====Heidelberg-Moscow controversy====
Some members of the Heidelberg-Moscow collaboration claimed a detection of neutrinoless beta decay in <sup>76</sup>Ge in 2001.<ref>
{{Cite journal
 |last1=Klapdor-Kleingrothaus |first1=H. V.
 |last2=Dietz |first2=A.
 |last3=Harney |first3=H. L.
 |last4=Krivosheina |first4=I. V.
 |s2cid=18771906
 |year=2001
 |title=Evidence for Neutrinoless Double Beta Decay
 |journal=[[Modern Physics Letters A]]
 |volume=16 |issue=37 |pages=2409–2420
 |arxiv=hep-ph/0201231
 |bibcode=2001MPLA...16.2409K
 |doi=10.1142/S0217732301005825
}}</ref> This claim was criticized by outside physicists<ref name="Giuliani2012" /><ref>
{{Cite journal
 |last3=Vissani |first3=F.
 |last2=Strumia |first2=A.
 |last1=Feruglio |first1=F.
 |s2cid=15814788
 |year=2002
 |title=Neutrino oscillations and signals in beta and 0nu2beta experiments 
 |journal=[[Nuclear Physics]]
 |volume=637 |issue=1
 |pages=345–377
 |arxiv=hep-ph/0201291
 |doi=10.1016/S0550-3213(02)00345-0 
|bibcode=2002NuPhB.637..345F}}</ref><ref>
{{Cite journal
 |last1=Aalseth |first1=C. E.
 |s2cid=27406915
 |display-authors=etal
 |year=2002
 |title=Comment on "evidence for Neutrinoless Double Beta Decay"
 |journal=[[Modern Physics Letters A]]
 |volume=17 |issue=22 |pages=1475–1478
 |arxiv=hep-ex/0202018
 |bibcode=2002MPLA...17.1475A
 |doi=10.1142/S0217732302007715
}}</ref><ref>
{{Cite journal
 |last1=Zdesenko |first1=Y. G.
 |last2=Danevich |first2=F. A.
 |last3=Tretyak |first3=V. I.
 |title=Has neutrinoless double β decay of <sup>76</sup>Ge been really observed?
 |journal=[[Physics Letters B]]
 |volume=546 |issue=3–4 |pages=206
 |year=2002
 |bibcode=2002PhLB..546..206Z
 |doi=10.1016/S0370-2693(02)02705-3
|doi-access=free
 }}</ref> as well as other members of the collaboration.<ref>
{{cite journal
 |last1=Bakalyarov |first1=A. M.
 |last2=Balysh |first2=A. Y.
 |last3=Belyaev |first3=S. T.
 |last4=Lebedev |first4=V. I.
 |last5=Zhukov |first5=S. V.
 |year=2005
 |title=Results of the experiment on investigation of Germanium-76 double beta decay
 |journal=[[Physics of Particles and Nuclei Letters]]
 |volume=2 |issue=2005
 |pages=77–81
 |arxiv=hep-ex/0309016
 |bibcode=2003hep.ex....9016B
}}</ref> In 2006, a refined estimate by the same authors stated the half-life was 2.3{{e
 |25}}&nbsp;years.<ref>
{{Cite journal
 |last1=Klapdor-Kleingrothaus |first1=H. V.
 |last2=Krivosheina |first2=I. V.
 |year=2006
 |title=The Evidence for the Observation of 0νββ Decay: The Identification of 0νββ Events from the Full Spectra
 |journal=[[Modern Physics Letters A]]
 |volume=21 |issue=20 |pages=1547
 |bibcode=2006MPLA...21.1547K
 |doi=10.1142/S0217732306020937
}}</ref> This half-life has been excluded at high confidence by other experiments, including in <sup>76</sup>Ge by [[Germanium Detector Array|GERDA]].<ref name="gerdanature">{{Cite journal |last1=Agostini|first1=M.|s2cid=4456764|display-authors=etal |collaboration=[[GERDA Collaboration]]|year=2017|title=Background-free search for neutrinoless double-β decay of <sup>76</sup>Ge with GERDA|journal=[[Nature (journal)|Nature]]|volume=544 |issue=7648|pages=47–52|bibcode=2017Natur.544...47A |doi=10.1038/nature21717|pmid=28382980|arxiv=1703.00570}}</ref>

====Current results====
As of 2017, the strongest limits on neutrinoless double beta decay have come from GERDA in <sup>76</sup>Ge, CUORE in <sup>130</sup>Te, and EXO-200 and KamLAND-Zen in <sup>136</sup>Xe.

==Higher order simultaneous beta decay==
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, though [[partial half-life|partial 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 include <sup>96</sup>Zr, <sup>136</sup>Xe, and <sup>150</sup>Nd capable of quadruple beta-minus decay, and <sup>124</sup>Xe, <sup>130</sup>Ba, <sup>148</sup>Gd, and <sup>154</sup>Dy capable of quadruple beta-plus decay or electron capture (though <sup>148</sup>Gd and <sup>154</sup>Dy are non-primordial alpha-emitters with geologically short half-lives). In theory, quadruple beta decay may be experimentally observable in three of these nuclei – <sup>96</sup>Zr, <sup>136</sup>Xe, and <sup>150</sup>Nd – with the most promising candidate being <sup>150</sup>Nd. Triple beta-minus decay is also possible for <sup>48</sup>Ca, <sup>96</sup>Zr, and <sup>150</sup>Nd;<ref name=triplebeta/> triple beta-plus decay or electron capture is also possible for <sup>148</sup>Gd and <sup>154</sup>Dy.

Moreover, such a decay mode could also be neutrinoless in physics beyond the standard model.<ref name=betaquad>{{cite journal|last1=Heeck|first1=J.|last2=Rodejohann|first2=W.|s2cid=118632700|title=Neutrinoless Quadruple Beta Decay|journal=Europhysics Letters|volume=103|issue=3|pages=32001|date=2013|doi=10.1209/0295-5075/103/32001|arxiv=1306.0580|bibcode=2013EL....10332001H}}</ref> 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|date=December 2024}} 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.<ref name=diracneutrinos>{{cite journal|last1=Hirsch|first1=M.|last2=Srivastava|first2=R.|last3=Valle|first3=JWF.|title=Can one ever prove that neutrinos are Dirac particles?|journal=Physics Letters B|volume=781|pages=302–305|date=2018|doi =10.1016/j.physletb.2018.03.073|arxiv=1711.06181|bibcode=2018PhLB..781..302H|doi-access=free}}</ref>

{{As of|2019}}, searches for triple and quadruple beta decay in <sup>150</sup>Nd have not been successful.<ref name=triplebeta>{{Cite journal|arxiv=1906.07180|doi=10.1103/PhysRevC.100.045502|title=Search for triple and quadruple β decay of Nd150|year=2019|last1=Barabash|first1=A. S.|last2=Hubert|first2=Ph.|last3=Nachab|first3=A.|last4=Umatov|first4=V. I.|s2cid=189999159|journal=Physical Review C|volume=100|issue=4|page=045502}}</ref>

==See also==
* [[Double electron capture]]
* [[Beta decay]]
* [[Neutrino]]
* [[Particle radiation]]
* [[Radioactive isotope]]

==References==
{{reflist|30em}}

==External links==
* [http://xstructure.inr.ac.ru/x-bin/theme3.py?level=2&index1=-202525 Double beta decay on arxiv.org]

{{Nuclear_processes}}
{{neutrino detectors}}

[[Category:Nuclear physics]]
[[Category:Radioactivity]]
[[Category:Neutrinos]]