|(CNS + RIBF NP Seminar#266)
The fundamental properties of the neutrinos have been the most important issue in particle physics, astro-physics and cosmology. Nevertheless, more than 60 years after experimental discovery of neutrinos we do not know number, absolute masses, nature (Dirac or Majorana), CP properties, magnetic moments and statistical properties of neutrinos. The atomic nucleus is a laboratory, which allows us to measure and determine these properties or to establish useful limits on unknown parameters of particle physics side. In this presentation the attention is paid to weak nuclear processes in the context of massive neutrinos. The problem of direct measurement of neutrino masses with help of nuclear beta-decay and electron capture is discussed. The recent progress in theoretical description of the 0νββ-decay is shortly reviewed. The question is raised whether light and heavy neutrino contributions to 0νββ-decay are experimentally distinguishable. A possible impact of the nuclear environment on the light neutrino mass mechanism of the 0nbb-decay is addressed. The subject of interest is also resonant neutrinoless double-electron capture by atoms. The present-day results of the calculation of double-beta decay nuclear matrix elements are discussed. A connection between the 2νββ-decay and 0νββ- decay matrix elements is analyzed. An impact of the quenching of axial-vector coupling constant on double-beta decay processes is investigated. A possibility to conclude about statistical properties of neutrinos, nuclear structure etc by measuring energy distributions of emitted electrons in the 2νββ-decay is studied.