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In this paper we will review the “state of the art” of the calculations of the nuclear matrix element (NME) of the neutrinoless double-beta decays (0νββ) for the nuclei 48Ca, 76Ge, 82Se, 124Sn, 128Te, 130Te and 136Xe in the framework of the Interacting Shell Model (ISM), and compare them with the NME's obtained using the Quasi-particle RPA approach (QRPA). We will also discuss the effect of the competition between the pairing and quadrupole correlations in the value of these NME's. In particular we will show that, as the difference in deformation between parent and grand-daughter grows, the NME's of both the neutrinoless and the two neutrino modes decrease rapidly.
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