Matrix Elements for Neutrinoless Double Beta Decay

The status of calculation of the neutrinoless double beta decay (0νββ-decay) nuclear matrix elements (NMEs) is reviewed. The 0νββ-decay NMEs obtained in the framework of the Quasiparticle Random Phase Approximation (QRPA), Large Scale Shell Model (LSSM), Interacting Boson Model (IBM), Projected Hartree-Fock Bogoliubov approach (P-HFB) and Energy Density Functional Method (EDF) are presented and discussed. The problem of reliable determination of the 0νββ-decay NMEs is addressed. It is manifested that the uncertainty associated with the calculation of the 0νββ-decay NMEs can be diminished by suitable chosen nuclear probes. Further, the recent development in the field of double beta decay showed that the search for the neutrinoless double electron capture process (0νECEC) may establish the Majorana nature of neutrinos. This possibility should be considered as alternative and complementary to searches for the 0νββ-decay.