Neutrinoless double beta decay of deformed nuclei within QRPA with realistic interaction

In this paper a microscopic state-of-the-art approach to calculation of the nuclear matrix element $M^{0\nu }$ for neutrinoless double beta decay with an account for nuclear deformation is presented in length and applied for ${}^{76}$Ge, ${}^{150}$Nd and ${}^{160}$Gd. The proton-neutron quasiparticle random phase approximation (QRPA) with a realistic residual interaction [the Brueckner $G$ matrix derived from the charge-depending Bonn (Bonn-CD) nucleon-nucleon potential] is used as the underlying nuclear structure model. The effects of the short range correlations and the quenching of the axial vector coupling constant $g_A$ are analyzed. The results show that neutrinoless double beta decay of ${}^{150}$Nd, to be measured soon by the SNO+ collaboration, provides one of the best probes of the Majorana neutrino mass. This confirms our preliminary conclusion in Ref. {Fang10}.