Double beta decay: A problem of particle, nuclear and atomic physics

A brief review of recent progress in the field of double beta decay is presented. Different aspects from particle, nuclear and atomic physics of both two-neutrino (2νββ) and neutrinoless (0νββ) modes of the double β decay are discussed. It is argued that the R-parity violating supersymmetry (SUSY) contributes to the 0νββ-decay predominantly via charged pion-exchange between decaying nucleons. Further, a problem of reliable determination of the 0νββ-decay nuclear matrix elements (NMEs) is addressed. It is manifested that the uncertainty associated with the calculation of the 0νββ-decay NMEs can be diminished by suitably chosen nuclear probes. A new possibility for the study of lepton number non-conservation is proposed, namely oscillations plus deexcitations of neutral atoms. A phenomenological analysis of this process leads to a resonant enhancement of the neutrinoless double electron capture, that has a Breit-Wigner form.