Schwarz–Christoffel mapping

Double beta decay is a radioactive decay process where a nucleus releases two beta rays as a single process.

History

The idea of double beta decay was first proposed by Maria Goeppert-Mayer in 1935. In 1937 Ettore Majorana theoretically demonstrated that all results of beta decay theory remain unchanged if the neutrino is its own anti-particle, i.e. if it is a Majorana particle. In 1939 Wendell H. Furry for the first time proposed that, if neutrino is a Majorana particle, double beta decay can proceed without emission of any neutrino at all; the process which is now called the neutrinoless beta decay.

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 are Majorana particles). The predicted half-lives were on the order of 10^15–16 years. Efforts to observe the process in laboratory date back to at least 1948 when Edward L. Fireman made the first attempt to measure the half-life of the Template:SimpleNuclide isotope. Radiometric experiments through about 1960 produced either negative results or false positives, which were not confirmed by later experiments. In 1950 for the first time the half-life of the Template:SimpleNuclide isotope was measured by geochemical methods. The result, 1.4Template:E years, was 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 the experimental techniques in 1960–70s, double beta decay was not observed until the 1980s in a laboratory setting. The experiments had only been able to establish the lower bound for the half-life—about 10²¹ years. On the other hand in the geochemical experiments double beta decay of Template:SimpleNuclide and Template:SimpleNuclide isotopes was detected.

Double beta decay was first observed in a laboratory counter experiment in 1987 by a group led by Michael Moe at the UC Irvine on isotope Template:SimpleNuclide. Since then many experiments have been conducted, which observed ordinary double beta decay in a number of other isotopes. However none of those experiments has produced positive results for the neutrinoless process, pushing the lower bound for its half-life up to 10²⁵ years. The geochemical experiments continued until the end of 1990s and produced positive results for a few more isotopes. Double beta decay is the rarest known kind of radioactive decay; as of 2012 it has been observed for only 12 isotopes (including double electron capture in Template:SimpleNuclide observed in 2001), and all of them have a mean lifetime of more than 10¹⁸ yr (see table below).

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 with atomic number one higher has a smaller binding energy, preventing a singular beta decay from occurring. However, the nucleus with atomic number two higher, selenium-76, has a larger binding energy, so the double beta decay process is allowed.

For some nuclei, the process occurs as conversion of two protons to neutrons, with emission of two electron neutrinos and absorption of 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 branch is accessible, with capture of one orbital electron and emission of one positron. When the mass difference is more than 2.044 MeV/c² (four electron masses), the emission of two positrons is possible. These theoretically possible double beta decay branches have not yet been observed.

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List of known double beta decay isotopes

There are 35 naturally occurring isotopes that are capable of undergoing double beta decay. However, only eleven isotopes have been experimentally observed undergoing two-neutrino double beta decay.

Many isotopes are, in theory, capable both of double beta decay and other decays. In most cases, the double beta decay is so rare as to be nearly impossible to observe against the background of other radiation. However, the double beta decay rate of Template:SimpleNuclide (also an alpha emitter) has been measured radiochemically; Template:SimpleNuclide is produced by this type of radioactivity. Two of the nuclides (Template:SimpleNuclide and Template:SimpleNuclide) from the list above can decay also via single beta decay but this decay is extremely suppressed and has never been observed.

The table below contains information about nuclides with experimentally measured half-lives. The results are as of December 2012. Only the latest direct measurements are reported if available. In other cases a geochemical estimate is given. The first error is statistical and the second is systematic.

Nuclide	Half-life, 1021 years	Transition	Method	Experiment
Template:SimpleNuclide	0.044Template:±Template:Elucidate ± 0.004		direct	NEMO-3
Template:SimpleNuclide	1.74 ± 0.01 Template:±Template:Elucidate		direct	DOERR
Template:SimpleNuclide	0.096 ± 0.003 ± 0.010Template:Elucidate		direct	NEMO-3
Template:SimpleNuclide	0.0235 ± 0.0014 ± 0.0016Template:Elucidate		direct	NEMO-3
Template:SimpleNuclide	0.00711 ± 0.00002 ± 0.00054Template:Elucidate		direct	NEMO-3
	0.69Template:± ± 0.07	0+→ 0+1	direct	Ge coincidence
Template:SimpleNuclide	0.028 ± 0.001 ± 0.003Template:Elucidate		direct	NEMO-3
Template:SimpleNuclide	7200 ± 400Template:Elucidate		geochemical
Template:SimpleNuclide	0.7 ± 0.09 ± 0.11Template:Elucidate		direct	NEMO-3
Template:SimpleNuclide	2.165 ± 0.016 ± 0.059Template:Elucidate		direct	EXO-200
Template:SimpleNuclide	0.00911Template:±Template:Elucidate ± 0.00063		direct	NEMO-3
Template:SimpleNuclide	2.0 ± 0.6		geochemical

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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 described in the previous section are also known as two-neutrino double beta decay, as two neutrinos (or antineutrinos) are emitted. 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 of neutrinoless double beta decay (light neutrino exchange), in essence the two neutrinos annihilate each other, or equivalently, one nucleon absorbs the neutrino emitted by another nucleon of the nucleus.

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

The decay rate for this process is given (approximately) by

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

where $G$ is the two-body phase-space factor, $M$ is the nuclear matrix element, and m_ββ is the so-called effective Majorana neutrino mass given by

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

In this latter expression, the m_i are the neutrino masses (of the i^th mass eigenstate), and the U_ei are elements of the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix. Hence the observation of neutrinoless double beta decay, in addition to confirming the Majorana nature of the neutrino, would give information on the absolute neutrino mass scale, and potentially also on the neutrino mass hierarchy and the Majorana phases appearing in the PMNS matrix.

Neutrinoless double beta decay experiments

Numerous experiments have been carried out to search for neutrinoless double beta decay. Some recent and proposed future experiments include:

• Completed experiments:
  • Gotthard TPC
  • Heidelberg-Moscow
  • IGEX
  • NEMO1, 2 and 3
• Experiments currently taking data:
  • COBRA
  • CUORICINO and CUORE (CUORE)
  • DCBA
  • EXO
  • GERDA
  • MOON
  • KamLAND-Zen
• Proposed/future experiments:
  • CANDLES and XMASS at Kamioka Observatory
  • MAJORANA
  • NEXT
  • SNO+
  • SuperNEMO

Controversy with Heidelberg-Moscow collaboration

In 2001 Heidelberg-Moscow collaboration released their data, which set limits on the neutrinoless beta decay in Germanium-76. The low limit for the half-life was 1.9Template:E years, while the upper limit on the neutrino mass was estimated at 0.3–0.6 eV. However in the same year a part of the collaboration claimed that they actually observed the neutrinoless beta decay with the half-life of about 1.5Template:E years corresponding to the neutrino mass of about 0.4 eV. This claim was criticized by outside physicists as well as by other members of the collaboration. In 2006 a refined estimate was published by the same others stating that the half-life was 2.3Template:E years. The latter result was based on improved data treatment procedures as well as included data over a longer period of time.

As of 2012 the situation is unclear but future more sensitive experiments are expected to eventually resolve this controversy.

See also

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

References

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External links

• Double beta decay on arxiv.org

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