The (3he,t) Reaction On76ge, and the Double-Β…

A ${}^{76}$Ge(${}^{3}$He,$t$)${}^{76}$As charge-exchange experiment at an incident energy of 420 MeV has been performed with an energy resolution of 30 keV. The Gamow-Teller GT${}^{\ensuremath{-}}$ strength distribution in ${}^{76}$As, which is the intermediate nucleus in the double-beta ($\ensuremath{\beta}\ensuremath{\beta}$) decay of ${}^{76}$Ge, has been extracted. An unusually strong fragmentation of the GT${}^{\ensuremath{-}}$ strength is observed even at low excitation energies of ${E}_{x}\ensuremath{\leqslant}5\phantom{\rule{0.16em}{0ex}}\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$. By combining the data with those for GT${}^{+}$ transitions from a recent ${}^{76}$Se($d$,${}^{2}$He)${}^{76}$As measurement, the nuclear matrix element for the ${}^{76}$Ge $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay has been evaluated. A lack of correlation among the GT transition strengths feeding the same levels from the two different directions is observed. The impact on the ${}^{76}$Ge $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay nuclear matrix element is discussed.