Neutrinoless Double Beta Decay

The mass M of an atom depends on its number of protons Z, the number of neutrons N and the binding energy EB.
For atoms with the same atomic mass number A = Z + N, so called isobars, it can be described with the semi empiric Bethe-Weizsaecker formula as a parabola depending on Z. As nature always seeks to reach the state of lowest energy, a transition within this mass parabola
from a mother nuclei to a daughter nuclei with a lower mass and therefore lower energy state is possible.
It takes place via conversion of protons p and neutrons n to each other, so called β-decays. They can occur as β-, β+ and electron capture (EC) decay. All β-decays change the nuclear charge Z, but leave A unchanged. Regarding the nuclei (A;Z) and the masses of the atoms, these decays can be described as follows:

Mass parabola for isobaric nuclei with even atomic mass number A. It is split into two parabolas due to the nuclear pair energy. β-decays that change the nuclear charge Z by a value of ±1 can only occur if the energy of the daughter nuclei is smaller than the energy of the parent nuclei. If this condition is not fullfilled, two consecutive β-decays are possible (dashed lines).

For a β+ decay, the energy delivered by the transition from one nucleus to the other, usually quoted as the mass difference between the mother and the daughter atom has to be larger than 2m_e = 1022 keV.
For isobars with an even mass number (and therefore with an odd-odd (o,o) or eveneven (e,e) number of N and Z), the mass parabola splits in two shifted parabolas due to the nuclear pairing energy. Because β-decays change Z by a value of 1, a (N;Z) = (e; e) nucleus becomes a (N;Z) = (o; o) one and vice versa. Caused by the shift between the parabolas an even-even nucleus might not be capable to decay into its odd-odd neighbouring nucleus because of the other one's higher energy.
But a transition into a second nearest state with a lower energy via two consecutive β-decays always is possible, see figure below. Such a double beta decay (2-νββ) in the form of (Z,A) → (Z+2,A) + 2e^- + 2 ν_e was proposed first by M. Goeppert-Mayer in 1935.
There are 35 isotopes in nature which fulfil the requirements of double beta decay. Because the anti neutrinos carry away energy, the distribution S(T) of the sum of the electron energies is a continuous one.

Tobias Koettig, TU Dortmund