Nuclear Physics of Double Beta Decay

Study of the neutrinoless $\beta\beta$ decay allows us to put a stringent limit on the effective neutrino Majorana mass, a quantity of fundamental importance. To test our ability to evaluate the nuclear matrix elements that govern the decay rate, it is desirable to be able to describe the allowed two-neutrino decay. It is argued that only low-lying virtual intermediate states are important for that process, and thus it appears that the large-scale shell model evaluation, free from the various difficulties of QRPA, is the preferred method. In the $0\nu$ decay, it is shown that there is a substantial cancellation between the paired and broken pair pieces of the nuclear wave function. Thus, despite the popular claim to the contrary, one expects that the $0\nu$ rate is also sensitive to the details of nuclear structure. This is reflected in the spread of the theoretical values, leading to the uncertainty of about factor 2-3 in the deduced $<m_{\nu}>$ limit. Finally, brief comment about the $0\nu$ decay with the exchange of a very heavy neutrino are made.