Abstract
The \(\beta \) and double-\(\beta \) decay channels, which are not accompanied by excitation of the electron shells, are suppressed due to the nonorthogonality of the electron wave functions of the parent and daughter atoms. The effect is sensitive to the contribution of the outer electron shells. Since valence electrons participate in chemical bonding and collectivize in metals, the decay rates of the unstable nuclides are modified when they are embedded in a host material. Core electrons are less affected by the environment, and their overlap amplitudes are more stable. The suppression effect is estimated for \( \beta ^- \) decay of \(^{87}\)Kr, electron capture in \(^{163}\)Ho, and \(2\beta ^-\) decays of \(^{76}\)Ge, \(^{100}\)Mo, \(^{130}\)Te, and \(^{136}\)Xe. The overlap amplitude of the electron shells enters the relationship between the half-life of neutrinoless \(2\beta \) decay and the effective electron neutrino Majorana mass.
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Data Availability Statement
This manuscript has associated data in a data repository. [Authors’ comment: All codes used in this :manuscript for calculations are available upon request by contacting with the corresponding author.]
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Acknowledgements
The authors are indebted to F. Danevich for the discussion of experimental limitations in the \(\beta \) spectrum measurements. This work is partially supported by RFBR Grant No. 18-02-00733.
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Communicated by F. Gulminelli
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Krivoruchenko, M.I., Tyrin, K.S. Overlap of electron shells in \(\beta \) and double-\(\beta \) decays. Eur. Phys. J. A 56, 16 (2020). https://doi.org/10.1140/epja/s10050-019-00003-z
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DOI: https://doi.org/10.1140/epja/s10050-019-00003-z