  The discovery that neutrinos have finite rest mass has led to renewed
interest in neutrinoless double beta decay. The development of large-scale
experiments to search for neutrinoless double beta decay has increased the
probability of a credible observation of the process in the near future. The
reliability of calculations of the associated nuclear matrix elements is likely
soon to become a critical issue. In this paper experimental techniques that
access properties of the ground-state wave functions of double beta decay
candidates, the occupancies of valence single- particle orbitals and pairing
correlations, are summarized and the experimental data for candidate nuclei are
reviewed. The results are discussed in relation to questions concerning which
aspects of nuclear structure may play an important role in determining the
nuclear matrix elements for neutrinoless double beta decay.
