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# Double electron capture

Double electron capture is a decay mode of atomic nucleus. For a nuclide (A, Z) with number of nucleons A and atomic number Z, double electron capture is only possible if the mass of the nuclide of (A, Z-2) is lower.

In this mode of decay, two of the orbital electrons are captured by two protons in the nucleus, forming two neutrons. Two neutrinos are emitted in the process. Since the protons are changed to neutrons, the number of neutrons increases by 2, the number of protons Z decreases by 2, and the atomic mass A remains unchanged. By changing the number of protons, double electron capture transforms the nuclide into a new element.

Example: $\mathrm{{}^{78}_{36}Kr}+\mathrm{2 e^-} \rightarrow\mathrm{{}^{78}_{34}Se}+{2\nu}$

In most of cases this decay mode is masked by more probable modes (single electron capture etc.), but when all these modes are forbidden or strongly suppressed, double electron capture becomes the main mode of decay. There exist 35 naturally occurring isotopes that can undergo double electron capture. However, there are no confirmed observations of this process. The one reason is that the probability of double electron capture is enormously small (the theoretical predictions of half-lives for this mode lies well above 1020 years). The second reason is that the only detectable particles created in this process are X-rays and Auger electrons that are emitted by the excited atomic shell. In the range of their energies (~1-10 keV), the background is usually high. Thus, the experimental detection of double electron capture is more difficult than that for double beta decay.

If the mass difference between the mother and daughter atoms is more than two masses of electron (1.022 MeV), the energy released in the process is enough to allow another mode of decay: electron capture with positron emission. It occurs simultaneously with double electron capture, their branching ratio depending on nuclear properties. When the mass difference is more than four electron masses (2.044 MeV), the third mode - double positron decay - is allowed. Only 6 naturally occurring nuclides can decay via these three modes simultaneously.

## Neutrinoless double electron capture

The above described process with capture of two electrons and emission of two neutrinos (two-neutrino double electron capture) is allowed by the Standard Model of particle physics: no conservation laws (including lepton number conservation) are violated. However, if the lepton number is not conserved, another kind of the process can occur: the so-called neutrinoless double electron capture. In this case, two electrons are captured by nucleus, but neutrinos are not emitted. The energy released in this process is carried away by an internal bremsstrahlung gamma quantum. This mode of decay has never been observed experimentally, and would contradict the Standard Model if it were observed.

Example: $\mathrm{{}^{78}_{36}Kr}+\mathrm{2 e^-} \rightarrow\mathrm{{}^{78}_{34}Se}$