Nuclear Structure Aspects of Neutrinoless Double- β Decay

We decompose the neutrinoless double-β decay matrix elements into sums of products over the intermediate nucleus with two less nucleons. We find that the sum is dominated by the Jπ=0+ ground state of this intermediate nucleus for both the light and heavy neutrino decay processes. This provides a new theoretical tool for comparing and improving nuclear structure models. It also provides the connection to two-nucleon transfer experiments.