# Double Beta Decay

Double beta decay (2νββ) is a nuclear transition in which an initial nucleus (Z,A), with proton number Z and total nucleon number A decays to (Z + 2,A) emitting two electrons and two antineutrinos in the process. Double beta decay was first discussed by M. Goeppert-Mayer [1] in the form of

$(Z,A) \quad \rightarrow \quad (Z+2, A) \quad + \quad 2e^{-} \quad + \quad 2\bar{\nu}_{e} \qquad \qquad (1)$

It is a transition among isobaric isotopes. This transition occurs regardless of whether neutrinos are their own antiparticles or not, i.e. Majorana or Dirac. 2νββ has been observed in a number of experiments.

A typical ββ candidate is an even-even nucleus (Z,A) which pairing forces make more bound than its (Z + 1,A) neighbour, but less so than the (Z + 2,A) nuclide, see Figure 1. For a specific atomic number the masses around the stable isotope can be approximated by a parabola as shown in Figure 2. Isotopes from the left side decay via β − -decay and isotopes on the right via β + -decay and electron capture. In the case of odd-odd and even-even nuclei, those with an odd (even) number of neutrons and odd (even) number of protons an additional term shows up, the nuclear pairing energy, with the same magnitude but opposite sign. This leads to a splitting of the mass parabola into two [2].

Figure 2: Ground state mass parabola for isobaric nuclei, showing the necessary configuration for double beta decay. Only the one (a) on the even-even (E-E) shell, whose β-decay is blocked (b) but which could decay via two subsequent steps (c) is allowed to do double beta decay. The shift of the parabola of the odd-odd (O-O) nuclei is due to the nuclear pairing energy [2].

A special situation among the ground states of nuclei can occur. Certain nuclei are able to decay into the second nearest neighbour, if two subsequent decays via an intermediate state could happen i.e. double beta decay. It is a higher order process and can be seen as two simultaneous beta decays, see Figures 3 and 4. This can only happen for isotopes on the lower parabola, which is the one containing even-even nuclei. A necessary requirement for beta decay to occur is m(Z, A) > m(Z + 2, A) and for practical purposes, β-decay has to be forbidden m(Z, A) < m(Z + 1, A), or at least strongly suppressed. In nature, 35 isotopes are known which show the specific ground state configuration, necessary for double beta decay [2].

Figure 3: Principle of double beta decay. Left, the simultaneous decay of two neutrons as an allowed higher order process (2νββ-decay). Right, the lepton-number violating mode (0νββ-decay) where the neutrino only occurs as a virtual particle. This process is not allowed in the Standard Model [3], [2].

Figure 4: Feynman Diagrams for 2νββ (left) and 0νββ (right) [4].

### References

[1] M. Goeppert-Mayer, Double Beta-Disintegration, Phys. Rev., 48 (1935) 512

[2] K. Zuber, Double Beta Decay, Contemp. Phys. 45 (2004) 491-502

[3] Kai Zuber, Neutrino Physics, Institute of Physics (2004)

[4] F.T. Avignone III et al., Double Beta Decay, Majorana Neutrinos, and Neutrino Mass, arxiv:0708.1033v2 [nucl-ex] (2007)

Figure 1: Double beta decay candidate isotope level scheme