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-beta decay of Ca-48, Ge-76, and Se-82. We work in one major shell for the first isotope, in the f(5/2)pg(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 beta, but also the triaxiality angle gamma 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.