In this paper a microscopic 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 ${}^{76}\mathrm{Ge}$, ${}^{150}\mathrm{Nd}$, and ${}^{160}\mathrm{Gd}$. The proton-neutron quasiparticle random-phase approximation with a realistic residual interaction (the Brueckner $G$ matrix derived from the charge-depending Bonn 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 suggest that neutrinoless double-$\beta$ decay of ${}^{150}\mathrm{Nd}$, to be measured soon by the SNO$+$ Collaboration, may provide one of the best probes of the Majorana neutrino mass. This confirms our preliminary conclusion in Fang et al. [Phys. Rev. C 82, 051301(R) (2010)].

• Received 12 January 2011

DOI:https://doi.org/10.1103/PhysRevC.83.034320