Double beta decay

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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.


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 124
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 130
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 82
and 128

Double beta decay was first observed in a laboratory in 1987 by the group of Michael Moe at UC Irvine in 82
.[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 13 isotopes (including double electron capture in 130
observed in 2001 and 78
observed in 2013), and all have a mean lifetime over 1018 yr (table below).[4]

Ordinary double beta decay[edit]

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 (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 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 emission spectrum using Fermi's Golden Rule. The differential rate is given by

where the subscripts refer to each electron, T is kinetic energy, F(Z, T) is the Fermi Function with Z the charge of the final-state nucleus, p is momentum, v is velocity in units of c, cosθ is the angle between the electrons, and Q 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 (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[edit]

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. See beta-stable for a list of nuclides which can theoretically undergo double beta decay.

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 238
(also an alpha emitter) has been measured radiochemically. Two of the nuclides (48
and 96
) from the table below can also theoretically single beta decay but this is extremely suppressed and has never been observed.

Thirteen isotopes have been experimentally observed undergoing two-neutrino double beta decay or double electron capture.[8] The table below contains nuclides with the latest experimentally measured half-lives, as of December 2016.

Nuclide Half-life, 1021 years Transition Method Experiment
± +0.012
direct NEMO-3[9]
1.926 ±0.094 direct GERDA[8]
9.2 +5.5
direct BAKSAN[8]
0.096 ± 0.003 ± 0.010 direct NEMO-3[8]
0.0235 ± 0.0014 ± 0.0016 direct NEMO-3[8]
0.00693 ± 0.00004 direct NEMO-3[8]
± 0.07
0+→ 0+1 Ge coincidence[8]
0.028 ± 0.001 ± 0.003
direct NEMO-3[8]
7200 ± 400
1800 ± 700
geochemical [8]
0.82 ± 0.02 ± 0.06 direct CUORE-0[10]
2.165 ± 0.016 ± 0.059 direct EXO-200[8]
(0.5 – 2.7) geochemical [11][12]
± 0.00063
direct NEMO-3[8]
0+→ 0+1 Ge coincidence[8]
2.0 ± 0.6 radiochemical [8]

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

Searches for double beta decay in isotopes which present significantly greater experimental challenges are ongoing. For example, double beta decay is expected to be observed in the isotope 134
.[13] In this case, double beta decay from 136
is a background for this search.

Neutrinoless double beta decay[edit]

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

where is the two-body phase-space factor, is the nuclear matrix element, and mββ is the effective Majorana mass of the electron neutrino, given by

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.[14][15]

The deep significance of the process stems from the "black-box theorem" which states 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.[16]


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

  • Completed experiments:
    • Gotthard TPC
    • Heidelberg-Moscow (see below)
    • IGEX[17]
    • 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.[18]
  • 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 and 134Xe search
    • GERDA, a 76Ge detector
    • KamLAND-Zen, a 136Xe search. Data collection from 2011.[18]
    • Majorana, using high purity 76Ge p-type point-contact detectors. full operation expected in late 2015.[19]
    • 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[20]
    • 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


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

Heidelberg-Moscow Controversy[edit]

The Heidelberg-Moscow collaboration initially released limits on neutrinoless beta decay in germanium-76.[1] Then some members claimed detection in 2001.[21] This claim was criticized by outside physicists[1][22][23] as well as other members of the collaboration.[24] In 2006 a refined estimate by the same authors stated the half-life was 2.3×1025 years.[25] More sensitive experiments were expected to resolve the controversy in 2014.[1][18]

Current results[edit]

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.[26] 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.

Phase II of GERDA was able to reduce the background index BI by an order of magnitude with respect to Phase I by introducing 20 new BEGe detectors and instrumenting the liquid argon. For BEGe detectors the BI=0,7·10−3 counts/(keV·kg·yr) which translates to less than one count for the full exposure of 100 kg·yr. The half-life limit for neutrinoless double beta decay in 76Ge amounts to 5.3×1025 years (90% C.L.) at a sensitivity of 4.0×1025 years.[27]

See also[edit]


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  2. ^ Majorana, E. (1937). "Teoria simmetrica dell’elettrone e del positrone". Il Nuovo Cimento (in Italian). 14 (4): 171–184. Bibcode:1937NCim...14..171M. doi:10.1007/BF02961314. 
  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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  15. ^ Klapdor-Kleingrothaus, H. V.; Staudt, A. (1998). Non-accelerator Particle Physics (PDF) (Reprint ed.). IOP Publishing. ISBN 0-7503-0305-0. 
  16. ^ Schechter, J.; Valle, J. W. F. (1982). "Neutrinoless double-β decay in SU(2)×U(1) theories". Physical Review D. 25 (11): 2951–2954. Bibcode:1982PhRvD..25.2951S. doi:10.1103/PhysRevD.25.2951. 
  17. ^ Aalseth, C. E.; et al. (2000). "Recent Results of the IGEX 76Ge Double-Beta Decay Experiment". Physics of Atomic Nuclei. 63 (7): 1225–1228. Bibcode:2000PAN....63.1225A. doi:10.1134/1.855774. 
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  19. ^ Xu, W.; et al. (2015). "The Majorana Demonstrator: A Search for Neutrinoless Double-beta Decay of 76Ge". Journal of Physics: Conference Series. 606 (1): 012004. Bibcode:2015JPhCS.606a2004X. arXiv:1501.03089Freely accessible. doi:10.1088/1742-6596/606/1/012004. 
  20. ^ Khanbekov, N. D. (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. 76 (9): 1086. Bibcode:2013PAN....76.1086K. doi:10.1134/S1063778813090093. 
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  24. ^ Bakalyarov, A. M.; Balysh, A. Y.; Belyaev, S. T.; Lebedev, V. I.; Zhukov, S. V. (2005). "Results of the experiment on investigation of Germanium-76 double beta decay". Physics of Particles and Nuclei Letters. 2: 77–81. Bibcode:2003hep.ex....9016B. arXiv:hep-ex/0309016Freely accessible. 
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  27. ^ GERDA Collaboration Agostini, M.; et al. (GERDA Collaboration) (2017). "Background-free search for neutrinoless double-β decay of 76Ge with GERDA". Nature. 544 (7648): 47. Bibcode:2017Natur.544...47A. arXiv:1703.00570Freely accessible. doi:10.1038/nature21717. 

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