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In this article we present a more detailed version of our recent RapidCommunication [Phys. Rev. C 90, 051301(R) (2014)] where we calculate thenuclear matrix elements for neutrinoless double-$\beta$ decay of $^{76}$Ge. Forthe calculations we use a novel method that has perfect convergence propertiesand allows one to obtain the nonclosure nuclear matrix elements for $^{76}$Gewith a 1% accuracy. We present a new way of calculation of the optimal closureenergy, using this energy with the closure approximation provides the mostaccurate closure nuclear matrix elements. In addition, we present a newanalysis of the heavy-neutrino-exchange nuclear matrix elements, and we compareoccupation probabilities and Gamow-Teller strength with experimental data.

Shell-model calculation of neutrinoless double-$\beta$ decay of $^{76}$Ge