We present an extensive study of nuclear matrix elements (NME) for the neutrinoless double beta decay of the nuclei $^{ 48}$Ca, $^{ 76}$Ge, $^{ 82}$Se, $^{ 96}$Zr, $^{ 100}$Mo, $^{ 116}$Cd, $^{ 124}$Sn, $^{ 128}$Te, $^{ 130}$Te, $^{ 136}$Xe, and $^{ 150}$Nd based on state-of-the-art energy density functional methods using the Gogny D1S functional. Beyond mean-field effects are included within the generating coordinate method with particle number and angular momentum projection for both initial and final ground states. We obtain a rather constant value for the NME's around 4.7 with the exception of $^{ 48}$Ca and $^{ 150}$Nd, where smaller values are found. We analyze the role of deformation and pairing in the evaluation of the NME and present detailed results for the decay of $^{ 150}$Nd.
Categories: nucl-th