Disassembling the Nuclear Matrix Elements of the Neutrinoless double beta Decay

In this article we analyze the nuclear matrix elements (NME) of the neutrinoless double beta decays of the nuclei 48-Ca, 76-Ge, 82-Se, 124-Sn, 130-Te and 136-Xe in the framework of the Interacting Shell Model (ISM). We study the relative value of the different contributions to them, such as higher order terms in the nuclear current, finite nuclear size effects and short range correlations, as well as their evolution with the maximum seniority permitted in the wave functions. We discuss also the build-up of the NME's as a function of the distance between the decaying neutrons. We calculate the decays to final 0+ first excited states and find that these decays are at least 25 times more supressed with respect to the ground state to ground state transition.