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

• Received 19 November 2009

DOI:https://doi.org/10.1103/PhysRevC.81.024321