Nuclear structure relevant to neutrinoless double<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:math>decay: The valence protons in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Ge</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>76</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Se</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>76</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>

The possibility of observing neutrinoless double $\ensuremath{\beta}$ decay offers the opportunity of determining the effective neutrino mass if the nuclear matrix element were known. Theoretical calculations are uncertain, and the occupation of valence orbits by nucleons active in the decay is likely to be important. The occupation of valence proton orbits in the ground states of $^{76}\mathrm{Ge}$, a candidate for such decay, and $^{76}\mathrm{Se}$, the corresponding daughter nucleus, is determined by precisely measuring cross sections for proton-removing transfer reactions. As in previous work on neutron occupation, we find that the Fermi surface for protons is much more diffuse than previously thought, and the occupancies of at least three orbits change significantly between the two ${0}^{+}$ ground states.

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