Energy Spectrum of β Electrons in Neutrinoless Double-β Decay Including the Excitation of the Electron Shell of Atoms

Abstract

Double-β decay is accompanied with a high probability by the excitation of the electron shell of the daughter atom; as a result, the energy carried away by β electrons decreases. The mean value and standard deviation of the excitation energy of the electron shell of the daughter atom in the double-β decay of germanium $$_{{32}}^{{76}}{\text{Ge}} \to \;_{{34}}^{{76}}{\text{Se}}\text{*} + \;2{{\beta }^{ - }}( + 2{{\bar {\nu }}_{e}})$$ have been determined within the Thomas–Fermi and relativistic Dirac–Hartree–Fock methods. Using the estimates thus obtained, a two-parameter model of the energy spectrum of β electrons in the neutrinoless mode has been developed including the redistribution of the reaction energy between the decay products. The shift of the total energy of β electrons does not exceed 50 eV with a probability of 90%. However, the mean excitation energy is ~400 eV, i.e., an order of magnitude higher, whereas the standard deviation is ~2900 eV, which is apparently due to a significant contribution from inner electron levels to the energy characteristics of the process. The distortion of the shape of the peak of the 0ν2β decay should be taken into account when analyzing the data of detectors with a resolution of ~100 eV or higher.