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The Neutrinoless Double Beta Decay

The process probably most strongly connected to the history of neutrino research is the β- decay. This nuclear reaction provided first hints for the particle's existence back in 1930 and is still an important object of investigation today, especially in regard to setting limits on the electron neutrino mass.
The β- decay is a transformation of the atomic nucleus mediated by the weak interaction. In order to reach a more stable state, one of the nucleus's neutrons converts to a proton while emitting an electron and an electron antineutrino. This leaves the atomic mass number A unchanged, but leads to an increase of the ordering number Z by one, which goes hand in hand with a change of the chemical element:

The analogous β+ decay features a proton converting to a neutron and the emission of both a positron and an electron neutrino:

β decays are, as all processes in nature, driven by the purpose of reaching a state with a lower energy, a more stable state of the nucleus. Concretely, the decay goes form heavy to light nuclei. The exact nuclear masses can be calculated under the use of the semi-empirical mass formula. An example for the resulting mass distributions for some example nuclei is shown in the following figures.
The distribution for odd values of A is pretty straightforward. It is continuous and follows the form of one parabola. The nucleus at the lowest point of this parabola is the nucleus with the smallest mass and also the most stable nucleus. The other nuclei can therefore decay in order to get closer to this stable state.

The situation is different, however, for the nuclei with an even value of A. In order to build a nucleus with an even amount of nucleons, one has the two possibilities of either using both an even number of protons and neutrons or an odd number of both types of particles. Even-even nuclei are in average less massive than their odd-odd neighbors; the two different types of nuclei each follow their own parabola. This makes the pattern of whether a nucleus can decay via β- or β+ decay, and respectively whether it can decay at all, more complicated.
As a result, the Cadmium nucleus (Z=48) for example, while in fact not being the most stable state, cannot decay at all by β decay. This does not mean, that this nucleus generally cannot decay, however. A more stable state, which could be reached, exists. To get there, physics can go the direct way: a decay from Cadmium to Palladium (Z=46) without the detour of Silver (Z=47). This - basically the simultaneous occurrence of two ordinary β decays - is called double beta decay (2νββ decay).

This exotic process was first discussed in 1935 and after that it took 50 years until its first observation in 1987, where the 2νβ-β- decay of the isotope 82Se was measured.
Because a double beta decay involves twice the amount of particle interactions as a standard beta decay, its occurrence is accordingly less likely. While there are β decays with half-lives of under one second, the half-lives of 2νββ decays lie in the order of 1020 years and higher. That easily excels the universe's age of approximately 14x109 years.

Yet, in 1939 the existence of an even more peculiar and seldom process was hypothesized: A neutrinoless version of the double beta decay.
This decay is just what its name says: a double beta decay, but without the emission of any neutrinos. Hence the particles involved in a neutrinoless double β- decay (0νβ-β- decay) are the following:

Such a process without any doubt counts as physics beyond the Standard Model. It violates the conservation of the lepton number. Instead of both leptons - the electrons - and antileptons - the corresponding antineutrinos - being produced in equal numbers, as it is the case for the 2νβ-β- decay, only the leptons are emitted. Thus the lepton number increases by two during the decay. There is no real motivation in the Standard Model, why the lepton number should be conserved, however, something contrary has never been observed.
The existence of 0νβ-β- decays has not been proven by now, but there are multiple theories for physics beyond the Standard Model, which predict and explain the process. Usually, though, the exotic decay is explained with the existence of Majorana neutrinos - basically neutrinos which are indistinguishable from their antiparticles.

The spectrum of the 0νββ decay, compared to the spectrum of the neutrino accompanied process, looks as shown in the figure to the left. In contrast to the broad energy distribution of the electrons emitted in the neutrino accompanied decay, the electrons from the neutrinoless decay always carry the exact same energy. This is necessary because the neutrinos, which could carry the rest of the available energy, are missing. The peak of the summed energies from the electrons emitted in the 0νβ-β- decay sits exactly at the endpoint of the 2νβ-β- spectrum. Because of that for the investigation of the neutrinoless process a high energy resolution is essential. Otherwise the spectrum of the neutrino accompanied decay will overlay the 0νβ-β- spectrum too strongly and make it indistinguishable from the more frequent process.

An observation of such a neutrinoless double beta decay would prove the existence of lepton number violation, confirm that neutrinos are Majorana particles and help to determine the neutrino's mass.
The detector concept of COBRA is designed with the main objective of observing such a 0νββ decay.


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