Nuclear structure and double beta decay

Study of the neutrinoless double beta decay, $0\nu\beta\beta$, includes a variety of problems of nuclear structure theory. They are reviewed here. The problems range from the mechanism of the decay, i.e. exchange of the light Majorana neutrino neutrino versus the exchange of some heavy, so far unobserved particle. Next, the proper expressions for the corresponding operator are described that should include the effects of the nucleon size and of the recoil order terms in the hadronic current. The issue of proper treatment of the short range correlations, in particular for the case of the heavy particle exchange, is discussed also. The variety of methods employed these days in the theoretical evaluation of the nuclear matrix elements $M^{0\nu}$ is briefly described and the difficulties causing the spread and hence uncertainty in the values of $M^{0\nu}$ are discussed. Finally, the issue of the axial current quenching, and of the resonance enhancement in the case of double electron capture are described.