Neutrinoless double-β decay of 124Sn, 130Te, and 136Xe in the Hamiltonian-based generator-coordinate method

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 Sn-124, Te-130, and Xe-136. 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 Sn-124, Te-130, and Xe-136 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 Nd-150 in a large shell-model space.