Neutrino Emitting Modes of Double Beta Decay

Abstract
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.