Can one measure nuclear matrix elements of neutrinoless double β decay?

By making use of the isospin conservation by strong interaction, the Fermi 0νββ nuclear matrix element MF0ν is transformed to acquire the form of an energy-weighted double Fermi transition matrix element. This useful representation allows reconstruction of the total MF0ν provided a small isospin-breaking Fermi matrix element between the isobaric analog state in the intermediate nucleus and the ground state of the daughter nucleus could be measured, e.g., by charge-exchange reactions. Such a measurement could set a scale for the 0νββ nuclear matrix elements and help to discriminate between the different nuclear structure models in which calculated MF0ν may differ by as much as a factor of 5 (that translates to about 20% difference in the total M0ν).