^{1,2,3}

^{4}

^{3,5}

^{2,3,4}

^{3}.

We consider alternative modes of two-neutrino and neutrinoless double-

Among the most challenging problems of modern neutrino physics are the mechanism of neutrino mixing and the nature of neutrino masses (Dirac or Majorana). If diagonal neutrinos

The neutrinoless (two-neutrino) double-

In 1961, Bahcall

The neutrinoless double-

In this paper, we develop a formalism for description of the bound-state two-neutrino and neutrinoless double-

A schematic view of the

The outline of the paper is as follows. In Sec.

The electronic structure of atoms is described by the shell-model relativistic wave functions obtained as solutions to the Dirac equation in a self-consistent centrally symmetric potential which is a superposition of the nuclear Coulomb potential and the screening potential of the electron shell. The corresponding bispinors with separated radial (

The radial functions

The Fermi function

The Fermi function in Eq.

In the discrete spectrum, the radial wave functions

The radial wave functions enter the bound-state

The double-

The inverse

The energy conservation in the

The phase-space factors of the

The multiconfiguration Dirac-Hartree-Fock package

The radial functions

The radial functions

If the convergence cannot be achieved within a specified number of iterations, the radial functions

If both methods fail for the charge

Finally, the squares of the radial functions with the principal quantum numbers above

In the atomic spectroscopy, power functions are often used to fit the dependence of observables on the atomic number

Figure

The squared radial wave functions

The squared radial wave functions

The Fermi sum

A simple qualitative explanation of the dependence of the bound-electron radial wave functions on

The same result follows from the requirement of orthogonality of the wave function of the bound

In Table

The double-

The Fermi sum

The decay-rate ratio

The decay-rate ratio

In Table

The half-lives

The half-lives

The double-

The

The

The

The one-electron spectra are studied with unprecedented accuracy in the tracking-and-calorimetry double-

While the calorimetric measurements are unable to distinguish between the

The

For data analysis, it is often desirable to specify the ratios

The ratios

At temperatures

In plasma conditions, there is a shift and broadening of the atomic levels which affect the bound-state decay rates

In this paper, we study the bound-state two-neutrino and neutrinoless double-

The bound-state double-

Since under the standard conditions for pressure and temperature most of the double-

The authors are grateful to R. Dvornický for useful discussions of techniques adopted in the atomic-structure calculations. Special thanks go to the participants of the MEDEX'17 meeting in Prague (May 29–June 2, 2017) for their helpful comments and suggestions. This work was supported by the VEGA Grant Agency of the Slovak Republic under Contract No. 1/0922/16, the Slovak Research and Development Agency under Contract No. APVV-14-0524, the Ministry of Education, Youth, and Sports of the Czech Republic under the ERDF Grant No. CZ.02.1.01/0.0/0.0/16_013/0001733, the Grant of the Plenipotentiary Representative of the Czech Republic in JINR under Contract No. 192 from 05/04/2018, the RFBR Grant No. 18-02-00733, and the Grant of the Heisenberg-Landau Program under Contract No. HLP-2015-18.