Abstract
In this paper a microscopic approach to calculation of the nuclear matrix element ${M}^{0\ensuremath{\nu}}$ for neutrinoless double-$\ensuremath{\beta}$ 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-$\ensuremath{\beta}$ 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)].
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