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4 2 Neutrino physics
mass scales nor the neutrino mass hierarchy.
The electron neutrino mass mνe could be determined, by investigating
the end point energy of the tritium beta decay spectrum, like the Katrin
experiment is doing currently.
However, this cannot determine whether the neutrino is a Majorana
particle and therewith its own antiparticle or not. In the short term, the
measurement of the neutrinoless double beta decay might answer this
question and determine the effective neutrino mass 〈mνe〉.
2.1 Double beta decay
A second order process to the beta decay is the double beta decay. It
can be regarded as two subsequent β-decays via a virtual intermediate
state.
The double beta decay was first discussed by Goeppert-Mayer in 1935,
predicting half lives of more than 10 17 years [7]. The double beta decay
is a nuclear process, changing the proton number Z by two units,
while leaving the atomic mass A unchanged. It is allowed in the Standard
Model of Particle Physics and can appear with β − , β + and electron
capture (EC) processes in four different decay modes:
(Z, A) → (Z + 2, A) + 2¯ν + 2β −
(Z, A) → (Z − 2, A) + 2ν + 2β +
e − + (Z, A) → (Z − 2, A) + 2ν + β +
[2νβ − β − ] (2.1)
[2νβ + β + ] (2.2)
[2νβ + EC] (2.3)
2e − + (Z, A) → (Z − 2, A) + 2ν [2νECEC] (2.4)
According to the Bethe-Weizsäcker formula, the nucleus mass
m(Z, A) ∝ const. + aZ + bZ 2 + δp only depends on Z for a given atomic
number A and forms a parabola. The pairing energy δp for isotopes
with odd A is zero, leading to a single parabola with a single stable isotope.
The mass parabola splits into two parabolae for even A, separated
by an energy of 2δp with δp = ±11.46 MeV/A 1/2 for odd-odd or eveneven
numbers of neutrons and protons. Here, the double beta decay
nuclei are positioned at the lower parabola, as is shown in figure 2.1.
The ββ-decay is allowed for nuclei, where the mass of the ground state
is larger than the mass of the daughter nucleus: m(Z, A) > M(Z ±2, A).
As the decay times of single beta decay are much shorter than these
of double beta decays, the single beta decay must be forbidden or at
least strongly suppressed (case of 48 Ca) to make ββ-decays visible.
For 35 known isotopes the single beta decay is forbidden, because of