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

By making use of the isospin conservation by strong interaction, the Fermi $0\nu \beta \beta$ nuclear matrix element $M_F^{0\nu }$ is transformed to acquire the form of an energy-weighted double Fermi transition matrix element. This useful representation allows reconstruction of the total $M_F^{0\nu }$ 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 $0\nu \beta \beta$ nuclear matrix elements and help much to discriminate between different nuclear structure models in which calculated $M_F^{0\nu }$ may differ by as much as the factor of 5.