Recent developments in theoretical description of two-neutrino double beta decay

Some recent developments in the theoretical description of the two-neutrino double beta decay (2ν2β-decay) matrix elements are presented. We discuss the intermediate nucleus approach (INA), the S-matrix approach and the Operator Expansion Method (OEM), which offer different insight into the problem of 2ν2β-decay. From a detailed study within the OEM it follows that one of the basic features of 2ν2β-decay is the energy difference of the initial and final nuclei. The decisive role of the Coulomb interaction within the OEM is exhibited. The introduction of the time integral representation for the 2ν2β-decay matrix element, which is derived within the field theory approach, allows a more consistent analysis. It is shown that the results obtained within the INA in the quasiboson approximation scheme are questionable from the physics point of view and that higher order approximations are important. From a field theory analysis of the 2ν2β-decay amplitude it follows that the summation over the intermediate nuclear states corresponds to a summation over a class of meson exchange diagrams. A new electron-gamma exchange mechanism for 2ν2β-decay is proposed. (author)