Shell Model Analysis of the Neutrinoless Double Beta Decay of $^{48}$Ca

The neutrinoless double beta ($0νββ$) decay process could provide crucial information to determine the absolute scale of the neutrino masses, and it is the only one that can establish whether neutrino is a Dirac or a Majorana particle. A key ingredient for extracting the absolute neutrino masses from $0νββ$ decay experiments is a precise knowledge of the nuclear matrix elements (NME) describing the half-life of this process. We developed a new shell model approach for computing the $0νββ$ decay NME, and we used it to analyze the $0νββ$ mode of $^{48}$Ca. The dependence of the NME on the short range correlations parameters, on the average energy of the intermediate states, on the finite-size cutoff parameters, and on the effective interaction used for the many-body calculations is discussed.

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