Neutrinoless double beta decay matrix elements

Recently a positive indication of the neutrinoless double beta decay (0nubetabeta-decay) of Ge-76 has been announced, which implies neutrino is a Majorana particle with non-zero mass. By using the nuclear matrix elements calculated within the renormalized QRPA we discuss perspectives of confirming the detection of this process for nuclei of experimental interest. The interpretation of the positive signal for the 0nubetabeta-decay depends on the issue, what is the dominant mechanism of this process. We point out that if the ratio of the 0nubetabeta-decay half-lifes for transitions to the 0(+) first excited and ground states is determined both theoretically and experimentally, it might be possible to conclude, which of the 0nubetabeta-decay mechanisms is dominant. A relevant information can be obtained also by comparing the 0nubetabeta-decay ground state transitions for Xe-134 and Xe-136 isotopes. The corresponding studies require that the associated nuclear matrix elements are evaluated with high reliability. This problem remains to be a challenging subject of the nuclear structure theory.