This article is cited in
2 papers
FIELDS, PARTICLES, AND NUCLEI
Energy spectrum of $\beta$ electrons in neutrinoless double-$\beta$ decay including the excitation of the electron shell of atoms
M. I. Krivoruchenkoa,
K. S. Tyrina,
F. F. Karpeshinb a National Research Center Kurchatov Institude, Moscow, 123182 Russia
b Mendeleev All-Russia Institute for Metrology, St. Petersburg, 190005 Russia
Abstract:
Double-
$\beta$ 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
$\beta$ electrons decreases. The mean value and standard deviation of the excitation energy of the electron shell of the daughter atom in the double-
$\beta$ decay of germanium $_{32}^{76}\mathrm{Ge} \rightarrow \ _{34}^{76}\mathrm{Se}^* + 2\beta^-(+~2\bar{\nu_e})$ 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
$\beta$ 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
$\beta$ electrons does not exceed
$50$ eV with a probability of
$90\%$. However, the mean excitation energy is
$\sim400$ eV, i.e., an order of magnitude higher, whereas the standard deviation is
$\sim2900$ 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
$0\nu2\beta$ decay should be taken into account when analyzing the data of detectors with a resolution of
$\sim100$ eV or higher.
Received: 29.04.2023
Revised: 05.05.2023
Accepted: 05.05.2023
DOI:
10.31857/S1234567823120029