Double beta decay

In the process of beta decay, unstable nuclei decay by converting a neutron in the nucleus to a proton and emitting an electron and an electron antineutrino. In order for 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 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.

In double-beta decay, two neutrons in the nucleus are converted to protons, and two electrons and two electron anti-neutrinos are emitted. This process was first observed in laboratory in 1986 (the first effort of experimental observation was dated by 1948). Geochemical observation of the decay products (by extraction of Kr and Xe from very old Se and Te minerals) are known since 1950. Double-beta decay is the rarest known kind of radioactive decay; it was observed for only 10 isotopes, and all of them have a mean life time of more than 1019 yr.

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.

List of known double-beta decay isotopes
More than 60 naturally occurring isotopes are capable of undergoing double-beta decay. Only ten of them were observed to decay via the two-neutrino mode: CalciumLink, GermaniumLink, SeleniumLink,ZirconiumLink, MolybdenumLink, CadmiumLink, TelluriumLink, TelluriumLink, NeodymiumLink, and UraniumLink.

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 UraniumLink (also an alpha emitter) has been measured radiochemically; PlutoniumLink is produced by this type of radioactivity. Two of the nuclides (CalciumLink and ZirconiumLink) from the list above can decay also via single beta decay but this decay is extremely suppressed and has never been observed.

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Neutrinoless double-beta decay
The processes described above are also known as two neutrino double-beta decay, as two neutrinos (or anti-neutrinos) are emitted. If the neutrino is a Majorana particle, meaning that the anti-neutrino and the neutrino are actually the same particle, 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. A Feynman diagram for this process is shown in the following figure:



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&beta;&beta; is given by


 * $$m_{\beta \beta} = \sum_{i=1}^3 m_i U^2_{ei}.$$

In this latter expression, the mi are the neutrino masses (of the ith mass eigenstate), and the Uei 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 (see also )
 * IGEX
 * NEMO1 and 2


 * Current and proposed experiments
 * COBRA
 * CUORICINO and CUORE
 * EXO
 * GERDA
 * MAJORANA
 * MOON
 * NEMO3 and SuperNEMO

Klapdor-Kleingrothaus et al.'s claimed observation of neutrinoless double-beta decay
A subgroup of the Heidelberg-Moscow collaboration led by H. V. Klapdor-Kleingrothaus published a series of controversial papers claiming to have observed neutrinoless double-beta decay in GermaniumLink with statistical significance of &gt; 99.9999998%. This claim has been criticized by many in the nuclear and particle physics communities, but Klapdor-Kleingrothaus et al. have vigorously defended their work. Their measured value of m&beta;&beta; between ~0.2-0.5 eV (depending on the choice of nuclear matrix element) has yet to be confirmed by other experiments.

The following lists, in chronological order, the key publications and preprints related to the claim and the criticism thereof.


 * H. V. Klapdor-Kleingrothaus et al., "Evidence for Neutrinoless Double Beta Decay", Mod. Phys. Lett. A 16 (2001) p. 2409, arXiv:hep-ph/0201231. This is the original paper, claiming a 2-3&sigma; observation (depending on the statistical method used to measure the significance).
 * C. E. Aalseth et al., "Comment on 'Evidence for Neutrinoless Double Beta Decay'", Mod. Phys. Lett. A 17 (2002) p. 1475, arXiv:hep-ex/0202018.
 * H. V. Klapdor-Kleingrothaus, "Reply to a Comment of article 'Evidence for Neutrinoless Double Beta Decay'", arXiv:hep-ph/0205228 (2002) (not peer-reviewed).
 * H. L. Harney, "Reply to the Comment on 'Evidence for Neutrinoless Double Beta Decay'", arXiv:hep-ph/0205293 (2002) (not peer-reviewed).
 * H. V. Klapdor-Kleingrothaus et al., "Neutrinoless Double Beta Decay: Status of Evidence", Found. Phys. 32 (2002) 1181, arXiv:hep-ph/0302248.
 * H. V. Klapdor-Kleingrothaus et al., "Search for neutrinoless double beta decay with enriched 76Ge in Gran Sasso 1990–2003", Phys. Lett. B 586 (2004) p. 198. Statistical significance increases to &gt;4&sigma;.
 * H. V. Klapdor-Kleingrothaus and I. V. Krivosheina, "The Evidence for the Observation of 0&nu;&beta;&beta; Decay: the Identification of 0&nu;&beta;&beta; Events from the Full Spectra", Mod. Phys. Lett. A 21 (2006) p. 1547. Statistical significance increases to &gt;6&sigma;.