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We present a generator-coordinate method for realistic shell-model Hamiltonians that closely approximates the full shell model calculations of the matrix elements for the neutrinoless double-$\beta$ decay of Sn124, Te130, and Xe136. We treat not only quadrupole deformations but also the proton-neutron pairing amplitudes as generator coordinates. We validate this method by calculating and comparing spectroscopic quantities with the exact shell model results and experimental data. Our Hamiltonian-based generator-coordinate method produces 0$\nu$$\beta$$\beta$ matrix elements much closer to the shell model ones, compared to the existing energy-density-functional-based generator-coordinate approaches. The remaining overestimation of 0$\nu$$\beta$$\beta$ nuclear matrix element suggests that additional correlations may be needed to be taken into account for Sn124, Te130, and Xe136 when calculating with the Hamiltonian-based generator-coordinate method. The validation of this method may open the possibility of calculating 0$\nu$$\beta$$\beta$ matrix element of Nd150 in a large shell-model space.

@article{jiao_neutrinoless_2018, abstract = {We present a generator-coordinate method for realistic shell-model Hamiltonians that closely approximates the full shell model calculations of the matrix elements for the neutrinoless double-$\beta$ decay of Sn124, Te130, and Xe136. We treat not only quadrupole deformations but also the proton-neutron pairing amplitudes as generator coordinates. We validate this method by calculating and comparing spectroscopic quantities with the exact shell model results and experimental data. Our Hamiltonian-based generator-coordinate method produces 0$\nu$$\beta$$\beta$ matrix elements much closer to the shell model ones, compared to the existing energy-density-functional-based generator-coordinate approaches. The remaining overestimation of 0$\nu$$\beta$$\beta$ nuclear matrix element suggests that additional correlations may be needed to be taken into account for Sn124, Te130, and Xe136 when calculating with the Hamiltonian-based generator-coordinate method. The validation of this method may open the possibility of calculating 0$\nu$$\beta$$\beta$ matrix element of Nd150 in a large shell-model space.}, annote = {Publisher: American Physical Society}, author = {Jiao, C. F. and Horoi, M. and Neacsu, A.}, doi = {10.1103/PhysRevC.98.064324}, issn = {24699993}, journal = {Physical Review C}, month = {dec}, number = {6}, pages = {64324}, title = {{Neutrinoless double- $\beta$ decay of Sn 124, Te 130, and Xe 136 in the Hamiltonian-based generator-coordinate method}}, url = {https://link.aps.org/doi/10.1103/PhysRevC.98.064324}, volume = {98}, year = {2018} }

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