The nuclear matrix elements for double beta decay

The status of the calculation of the neutrinoless double beta decay (0νββ-decay) nuclear matrix elements (NMEʼs) is reviewed. The spread of published values of NMEʼs is discussed. The main attention is paid to the recent progress achieved in the evaluation of the 0νββ-decay NMEʼs in the framework of the quasiparticle random phase approximation (QRPA). The obtained results are compared with those of the nuclear shell model. The problem of reliable determination of the 0νββ-decay NMEʼs is addressed. The uncertainty in NMEʼs are analyzed and further progress in calculation of the 0νββ-decay NMEʼs is outlined.