Proton pair correlations and the neutrinoless double-$\beta$ decay of ${}^{76}$Ge

Proton pair correlations relevant for the neutrinoless double-$\beta$ decay of ${}^{76}$Ge have been probed via the ${}^{74,76}$Ge(${}^3$He,$n$) reactions at 16 MeV. No evidence for pairing vibrations in either nucleus is observed at sensitivity limits of $\sim$6$\%$ and $\sim$19$\%$ of the ground-state strength in ${}^{76}$Se and ${}^{78}$Se, respectively. These results are relevant for the understanding of matrix elements for neutrinoless double-$\beta$ decay. The lack of pairing vibrations is consistent with a simple BCS structure for the ground states of ${}^{76}$Ge and ${}^{76}$Se, assumed in quasiparticle random phase approximation (QRPA) models of the process.