The possibility of observing neutrinoless double $\beta$ decay offers the opportunity of determining the effective neutrino mass if the nuclear matrix element were known. Theoretical calculations are uncertain, and measurements of the occupations of valence orbits by nucleons active in the decay can be important. The occupation of valence neutron orbits in the ground states of ${}^{76}\mathrm{Ge}$ (a candidate for such decay) and ${}^{76}\mathrm{Se}$ (the daughter nucleus) were determined by precisely measuring cross sections for both neutron-adding and removing transfer reactions. Our results indicate that the Fermi surface is much more diffuse than in theoretical calculations. We find that the populations of at least three orbits change significantly between these two ground states while in the calculations, the changes are confined primarily to one orbit.

• Received 2 October 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.112501