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

Abstract

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