[en] In this thesis the absolute mass scale and statistical properties of neutrinos are investigated in the context of the single and double β-decay processes. To our knowledge the first relativistic calculation of the β-decay of tritium is presented. By taking the advantage of the elementary particle treatment of ³H and ³He the form for the β-decay endpoint spectrum of tritium is obtained, considering the effects of higher order terms of hadron current and nuclear recoil. This approach is used also to study the role of interactions beyond the Standard Model (effective scalar and tensor interactions) in the β-decay of tritium. Till now the unknown energy distribution of emitted electrons for the first unique forbidden β-decay of ¹⁸⁷Re is calculated. It is found that the p-wave emission of electron dominates over the s-wave in this process. It is shown that the Kurie plot near the endpoint of the first unique forbidden β-decay of ¹⁸⁷Re and of the second unique forbidden β-decay of ¹¹⁵In is within a good accuracy linear in the limit of massless neutrinos like the Kurie plot of the super-allowed β-decay of ³H. Next, it is assumed that the Pauli exclusion principle is violated for neutrinos, and thus, neutrinos obey at least partly the Bose-Einstein statistics. It is shown that this violation strongly changes the two-neutrino double β-decay rates and modifies the energy distributions of the emitted electrons. The case of pure bosonic neutrinos is excluded by the present data. Further, a discussion is given on possible realization of the Single State Dominance hypothesis in the case of the two-neutrino double β-decay of ¹50Nd. The obtained theoretical results within this thesis are important for the tritium experiment KATRIN, which is under construction, and for the planed rhenium experiment MARE as well as for the next generation of double β-decay experiments like SuperNEMO, EXO, SNO+, etc. (author)

[en] The aims and results of thesis have been achieved and presented at conferences and published in several international journals. The results and findings presented in thesis are important for the KATRIN tritium β-decay experiment, which is under construction and for planned MARE rhenium β-decay experiment as well as for the next-generation double β-decay experiments like SuperNEMO, EXO, SNO+, etc. (Author)

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[en] The measurement of the electron spectrum in β decays close to the end point provides a robust direct determination of the values of neutrino masses. The most sensitive experiments use tritium and rhenium β decays because these transitions have low Q value. Recent measurement with Penning traps established that the β decay of ¹¹⁵In(9/2⁺) to the first excited state of ¹¹⁵Sn(3/2⁺) is a transition with the smallest Q value among β decays. The decay is associated with a change of spin and parity ΔJ^π = 3⁺ (ΔL = 2, ΔS = 1) of nucleus, i.e., classified as unique second forbidden β decay. Our investigation shows that in this transition electrons are predominantly emitted in d_5/2 partial waves. In addition, it is found that the Kurie function associated with this transition near the end point within a good accuracy reflects a behavior the Kurie function of superallowed β transitions.

[en] We have extended the light Majorana neutrino mass formalism for the neutrinoless double beta decay by including effects of the p_1_/_2-waves of emitted electrons and nucleon recoil. Within a standard approximation the decay rate is factorized as a sum of products of kinematical phase space factors and nuclear matrix elements. By using exact Dirac wave function with finite nuclear size and electron screening numerical computation of phase space integrals was performed. The obtained results allow to conclude that the effect of the p-wave and nucleon recoil is small, but not negligible. A more precise conclusion requires a calculation of corresponding nuclear matrix elements within an appropriate nuclear structure method. (author)

[en] Already long time ago the shape of the electron spectrum in β-decays of ³H and ¹⁸⁷Re has been recognized as an important tool for understanding of neutrino masses. The sensitivity of KATRIN (in preparation, tritium β-decay) and the MARE (under consideration, ¹⁸⁷Reβ-decay) experiments to neutrino mass will reach the sub eV domain. In view of this experimental progress there is a request for a highly accurate theoretical description of the electron endpoint spectra. By taking the advantage of the elementary particle treatment of ³H and ³He the relativistic form for β-decay endpoint spectrum of tritium is obtained by taking into account also the effect of nuclear recoil. Further, the currently unknown shape of the electron spectrum for the β-decay of ¹⁸⁷Re is presented. It is found that the first forbidden ¹⁸⁷Re(5/2⁺)→¹⁸⁷Os(1/2^-)β-decay transition is accompanied with emission of mostly p_3/2-state electrons.

[en] A discussion is given on possible realization of the Single State Dominance (SSD) hypothesis in the case of the two-neutrino double beta decay (2νββ-decay) of ^l50Nd with 1^- ground state of the intermediate nucleus. We conclude that the SSD hypothesis is expected to be ruled out by precision measurement of differential characteristics of this process in running NEMO 3 or planed SuperNEMO experiments unlike some unknown low-lying 1⁺ state of ¹⁵⁰Pm does exist. This problem can be solved via (d,²He) charge-exchange experiment on ^l50Sm. Further, we address the question about possible violation of the Pauli exclusion principle for neutrinos and its consequences for the energy distributions of the 2νββ-decay of ^l50Nd. This phenomenon might be a subject of interest of NEMO 3 and SuperNEMO experiments as well

[en] The Baikal-GVD neutrino telescope currently consists of 8 clusters of 288 optical modules (photodetectors). One cluster comprises 8 strings, each of which is subdivided into 3 sections of 12 optical modules. This paper presents the methods of time synchronization between the different GVD components (optical modules, sections, clusters) and estimations of time synchronization accuracy. (paper)

[en] We assume that the Pauli exclusion principle is violated for neutrinos, and thus, neutrinos obey at least partly the Bose-Einstein statistics. The parameter sin²χ is introduced that characterizes the bosonic (symmetric) fraction of the neutrino wave function. Consequences of the violation of the exclusion principle for the two-neutrino double beta decays (2νββ-decays) are considered. This violation strongly changes the rates of the decays and modifies the energy and angular distributions of the emitted electrons. Pure bosonic neutrinos are excluded by the present data. In the case of partly bosonic (or mixed-statistics) neutrinos the analysis of the existing data allows to put the conservative upper bound sin²χ<0.6. The sensitivity of future measurements of the 2νββ-decay to sin²χ is evaluated