Neutrino emitting modes of double beta decay

Four types of nuclear double beta decays accompanied with emission of two neutrinos are compared: (1) capture of double atomic electrons, (2) capture of one atomic electron and emission of one positron, (3) emission of two positrons and (4) emission of two electrons. Under the assumption that a charge distribution is uniform inside nucleus, bound state solutions of the Dirac equation are given analytically by using transcendental functions. Practically, both captures of the K and LI electrons are taken into account. Half-lives for the 0+ → 0+ transitions are calculated by using relativistic wave functions and are shorter than those by solutions of the Schroedinger equation. It is also shown that the approximated non-relativistic Coulomb correction factor used previously is not appropriate to discuss positron energy spectra and total transition rates. Concerning the capture process of the atomic electron, the 124Xe double beta decay is the shortest half-life, if there is no anomalous cancellation of the nuclear matrix elements. (author)