Neutrinoless double-β decay matrix elements in large shell-model spaces with the generator-coordinate method

We use the generator-coordinate method (GCM) with realistic shell-model interactions to closely approximate full shell-model calculations of the matrix elements for the neutrinoless double-β decay of ⁴⁸Ca, ⁷⁶Ge, and ⁸²Se. We work in one major shell for the first isotope, in the f_{5 /2}p g_{9 /2} space for the second and third, and finally in two major shells for all three. Our coordinates include not only the usual axial deformation parameter β , but also the triaxiality angle γ and neutron-proton pairing amplitudes. In the smaller model spaces our matrix elements agree well with those of full shell-model diagonalization, suggesting that our Hamiltonian-based GCM captures most of the important valence-space correlations. In two major shells, where exact diagonalization is not currently possible, our matrix elements are only slightly different from those in a single shell.