# Double beta decay

In nuclear physics, double beta decay is a type of radioactive decay in which two protons are simultaneously transformed into two neutrons, 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.

There are 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.[1] 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.[2] 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.[3] It is not yet known whether the neutrino is a Majorana particle and, relatedly, whether neutrinoless double beta exists in nature.[4]

In 1930–40s, parity violation in weak interactions was not known, and consequently 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 1015–16 years.[4] Efforts to observe the process in laboratory date back to at least 1948 when Edward L. Fireman made the first attempt to directly measure the half-life of the 124Sn isotope with a geiger counter.[5] 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 130Te was measured by geochemical methods to be 1.4×1021 years,[6] reasonably close to the modern value.

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 1960–70s, 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 of 82Se and 128Te.[4]

Double beta decay was first observed in a laboratory in 1987 by the group of Michael Moe at UC Irvine in 82Se.[7] 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.[4] Double beta decay is the rarest known kind of radioactive decay; as of 2012 it has been observed in only 12 isotopes (including double electron capture in 130Ba observed in 2001), and all have a mean lifetime over 1018 yr (table below).[4]

## Ordinary double beta decay

In 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 a sum of two beta minus decays. In order for (double) 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 nucleus one atomic number higher has a smaller binding energy, preventing single beta decay. However, the nucleus with atomic number two higher, selenium-76, has a larger binding energy, so double beta decay is allowed.

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 one positron. 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.

### Known double beta decay isotopes

There are 35 naturally occurring isotopes capable of double beta decay. The decay can be observed in practice if the single beta decay is forbidden by energy conservation. This happens for even-Z, even-N isotopes, which are more stable due to spin-coupling, seen by the pairing term in the semi-empirical mass formula.

Many isotopes are theoretically expected to double beta decay. In most cases, the double beta decay is so rare that it is nearly impossible to observe against the background. However, the double beta decay of 238U (also an alpha emitter) has been measured radiochemically. Two of the nuclides (48Ca and 96Zr) from the table below can also theoretically single beta decay but this is extremely suppressed and has never been observed.

Eleven isotopes have been experimentally observed undergoing two-neutrino double beta decay.[8] The table below contains nuclides with the latest experimentally measured half-lives, as of December 2012.[8]

Nuclide Half-life, 1021 years Transition Method Experiment
48Ca 0.044+0.005
−0.004
± 0.004
direct NEMO-3
76Ge 1.84 +0.09
−0.08
+0.11
−0.06
direct GERDA (2013)[9]
82Se 0.096 ± 0.003 ± 0.010 direct NEMO-3
96Zr 0.0235 ± 0.0014 ± 0.0016 direct NEMO-3
100Mo 0.00711 ± 0.00002 ± 0.00054 direct NEMO-3
0.69+0.10
−0.08
± 0.07
0+→ 0+1 direct Ge coincidence
116Cd 0.028 ± 0.001 ± 0.003 direct NEMO-3
128Te 7200 ± 400 geochemical
130Te 0.7 ± 0.09 ± 0.11 direct NEMO-3
136Xe 2.165 ± 0.016 ± 0.059 direct EXO-200
150Nd 0.00911+0.00025
−0.00022
± 0.00063
direct NEMO-3

Note:In the table above where two errors are specified the first one is statistical error and the second is systematic.[8]

## Neutrinoless double beta decay

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.

The processes during which two neutrinos (or antineutrinos) are emitted is known as two-neutrino double beta decay. If the neutrino is a Majorana particle (meaning that 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. In the simplest theoretical treatment, known as light neutrino exchange, the two neutrinos annihilate each other, or equivalently, a nucleon absorbs the neutrino emitted by another nucleon.

The neutrinos in the above diagram are virtual particles. With only two electrons in the final state, the electrons total kinetic energy would be approximately the binding energy difference of the initial and final nuclei (with the nucleus recoil accounting for the rest). To a very good approximation, the electrons are emitted back-to-back. The decay rate for this process is approximately given by

${\displaystyle \Gamma =~~~~{G|M|^{2}|m_{\beta \beta }|^{2}},}$

where ${\displaystyle G}$ is the two-body phase-space factor, ${\displaystyle M}$ is the nuclear matrix element, and mββ is the effective Majorana mass of the electron neutrino, given by

${\displaystyle m_{\beta \beta }=\sum _{i=1}^{3}m_{i}U_{ei}^{2}.}$

In this expression, mi is the neutrino masses (of the ith mass eigenstate), and the Uei are elements of the lepton mixing Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix. Therefore, observing neutrinoless double beta decay, in addition to confirming the Majorana neutrino nature, would give information on the absolute neutrino mass scale, potentially the neutrino mass hierarchy, and Majorana phases in the PMNS matrix.[10][11]

The deep significance of the process stems from the "black-box theorem" which that observing neutrinoless double beta decay implies at least one neutrino is a Majorana particle, irrespective of whether the process is engendered by neutrino exchange.[12]

### Experiments

Numerous experiments have searched for neutrinoless double beta decay. Recent and proposed experiments include:

• Completed experiments:
• Gotthard TPC
• Heidelberg-Moscow (see below)
• IGEX[13]
• NEMO 2 & 3 Ran Jan 2003 to Jan 2011.
• Cuoricino operated 62 TeO2 crystals with a total mass of 40.7 kg (11.3 kg of 130Te) between 2003 and 2008.[14]
• Experiments currently[when?] taking data:
• COBRA, 116Cd in room temperature CdZnTe crystals
• CUORE-0 (at CUORE), 130Te in TeO2 crystals. Data taken March to September 2013, with 7.1 kg·y exposure.
• DCBA, testing a magnetic tracking detector at KEK
• EXO, a 136Xe search
• GERDA, a 76Ge detector
• KamLAND-Zen, a 136Xe search. Data collection from 2011.[14]
• Majorana, using high purity 76Ge p-type point-contact detectors. full operation expected in late 2015.[15]
• XMASS using liquid Xe
• Proposed/future experiments:
• CANDLES, 48Ca in CaF2, at Kamioka Observatory
• MOON, developing 100Mo detectors
• AMoRE, 100Mo enriched CaMoO4 crystals at YangYang underground laboratory[16]
• LUMINEU, exploring 100Mo 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 study 130Te
• SuperNEMO, a NEMO upgrade, will study 82Se - due to start late 2015.
• TIN.TIN, a 124Sn detector at INO

### Status

Early experiments did claim discovery of neutrinoless double beta decay, but modern searches have set limits disfavoring those results. Recent published lower bounds for germanium and xenon indicate no sign of neutrinoless decay.

#### Heidelberg-Moscow Controversy

Heidelberg-Moscow collaboration initially released limits on neutrinoless beta decay in germanium-76.[1] Then some members claimed detection in 2001.[17] This claim was criticized by outside physicists[1][18][19] as well as other members of the collaboration.[20] In 2006 a refined estimate by the same authors stated the half-life was 2.3×1025 years.[21] More sensitive experiments are expected to resolve the controversy,[1] in 2014.[14]

#### Current Results

As of 2014, GERDA has reached much lower background, obtaining a half-life limit of 2.1×1025 years with 21.6 kg*yr exposure.[22] IGEX and HDM data increase the limit to 3×1025 yr and rule out detection at high confidence. Searches with 136Xe, Kamland-Zen and EXO-200, yielded a limit of 2.6×1025 yr. Using the latest nuclear matrix elements, the 136Xe results also disfavor the Heidelberg-Moscow claim.

## References

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2. ^ Majorana, Ettore (2008-09-21). "Teoria simmetrica dell'elettrone e del positrone". Il Nuovo Cimento (in Italian). 14 (4): 171–184. doi:10.1007/BF02961314. ISSN 1827-6121.
3. ^ Furry, W. H. (1939). "On Transition Probabilities in Double Beta-Disintegration". Physical Review. 56 (12): 1184–1193. Bibcode:1939PhRv...56.1184F. doi:10.1103/PhysRev.56.1184.
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7. ^ Elliott, S. R.; Hahn, A. A.; Moe; M. K. (1987). "Direct evidence for two-neutrino double-beta decay in 82Se". Physical Review Letters. 59 (18): 2020–2023. Bibcode:1987PhRvL..59.2020E. doi:10.1103/PhysRevLett.59.2020.
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14. ^ a b c Schwingenheuer, B. (2013). "Status and prospects of searches for neutrinoless double beta decay". Annalen der Physik. 525 (4): 269. arXiv:1210.7432. Bibcode:2013AnP...525..269S. doi:10.1002/andp.201200222.
15. ^ Collaboration, Majorana; Xu, W.; Abgrall, N.; Avignone III, F. T.; Barabash, A. S.; Bertrand, F. E.; Brudanin, V.; Busch, M.; Buuck, M.; Byram, D.; Caldwell, A. S.; Chan, Y-D.; Christofferson, C. D.; Cuesta, C.; Detwiler, J. A.; Efremenko, Yu.; Ejiri, H.; Elliott, S. R.; Galindo-Uribarri, A.; Giovanetti, G. K.; Goett, J.; Green, M. P.; Gruszko, J.; Guinn, I.; Guiseppe, V. E.; Henning, R.; Hoppe, E. W.; Howard, S.; Howe, M. A.; et al. (13 Jan 2015). "The Majorana Demonstrator: A Search for Neutrinoless Double-beta Decay of 76Ge". Journal of Physics: Conference Series. 606 (606): 012004. arXiv:1501.03089. doi:10.1088/1742-6596/606/1/012004.
16. ^ N. D. Khanbekov (September 2013). "AMoRE: Collaboration for searches for the neutrinoless double-beta decay of the isotope of 100Mo with the aid of 40Ca100MoO4 as a cryogenic scintillation detector". Physics of Atomic Nuclei, Volume 76, Issue 9. 76 (9): 1086. Bibcode:2013PAN....76.1086K. doi:10.1134/S1063778813090093.
17. ^ Klapdor-Kleingrothaus, H. V.; Dietz, A.; Harney, H. L.; Krivosheina, I. V. (2001). "Evidence for Neutrinoless Double Beta Decay". Modern Physics Letters A. 16 (37): 2409. arXiv:hep-ph/0201231. Bibcode:2001MPLA...16.2409K. doi:10.1142/S0217732301005825.
18. ^ Aalseth, C. E.; Avignone, F. T.; Barabash, A.; Boehm, F.; Brodzinski, R. L.; Collar, J. I.; Doe, P. J.; Ejiri, H.; Elliott, S. R.; Fiorini, E.; Gaitskell, R. J.; Gratta, G.; Hazama, R.; Kazkaz, K.; King, G. S.; Kouzes, R. T.; Miley, H. S.; Moe, M. K.; Morales, A.; Morales, J.; Piepke, A.; Robertson, R. G. H.; Tornow, W.; Vogel, P.; Warner, R. A.; Wilkerson, J. F. (2002). "Comment on "evidence for Neutrinoless Double Beta Decay"". Modern Physics Letters A. 17 (22): 1475. arXiv:hep-ex/0202018. Bibcode:2002MPLA...17.1475A. doi:10.1142/S0217732302007715.
19. ^ Zdesenko, Y. G.; Danevich, F. A.; Tretyak, V. I. (2002). "Has neutrinoless double β decay of 76Ge been really observed?". Physics Letters B. 546 (3–4): 206. Bibcode:2002PhLB..546..206Z. doi:10.1016/S0370-2693(02)02705-3.
20. ^ Bakalyarov, A. M.; Balysh, A. Y.; Belyaev, S. T.; Lebedev, V. I.; Zhukov, S. V. (2003). "Results of the experiment on investigation of Germanium-76 double beta decay". Proceedings of the NANP, Dubna, Russia.
21. ^ Klapdor-Kleingrothaus, H. V.; Krivosheina, I. V. (2006). "The Evidence for the Observation of 0νββ Decay: The Identification of 0νββ Events from the Full Spectra". Modern Physics Letters A. 21 (20): 1547. Bibcode:2006MPLA...21.1547K. doi:10.1142/S0217732306020937.
22. ^ Agostini, M.; et al. (GERDA Collaboration) (2013). "Results on Neutrinoless Double-β Decay of ^{76}Ge from Phase I of the GERDA Experiment". Physical Review Letters. 111 (12): 122503. arXiv:1307.4720. Bibcode:2013PhRvL.111l2503A. doi:10.1103/PhysRevLett.111.122503. PMID 24093254.