In this paper, with restored isospin symmetry, we evaluated the neutrinoless double-$\beta$-decay nuclear matrix elements for ${}^{76}\mathrm{Ge}, {}^{82}\mathrm{Se}, {}^{130}\mathrm{Te}, {}^{136}\mathrm{Xe}$, and ${}^{150}\mathrm{Nd}$ for both the light and heavy neutrino mass mechanisms using the deformed quasiparticle random-phase approximation approach with realistic forces. We give detailed decompositions of the nuclear matrix elements over different intermediate states and nucleon pairs, and discuss how these decompositions are affected by the model space truncations. Compared to the spherical calculations, our results show reductions from $30\%$ to about $60\%$ of the nuclear matrix elements for the calculated isotopes mainly due to the presence of the BCS overlap factor between the initial and final ground states. The comparison between different nucleon-nucleon (NN) forces with corresponding short-range correlations shows that the choice of the NN force gives roughly $20\%$ deviations for the light exchange neutrino mechanism and much larger deviations for the heavy neutrino exchange mechanism.

• Received 5 December 2017

DOI:https://doi.org/10.1103/PhysRevC.97.045503