High-resolution<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mrow/><mml:mn>96</mml:mn></mml:msup></mml:math>Zr(<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mrow/><mml:mn>3</mml:mn></mml:msup></mml:math>He,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>t</mml:mi></mml:math>) experiment and the matrix element for double-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>decay

The Gamow-Teller (GT) strength distribution has been investigated in a high-resolution (${}^{3}$He,$t$) charge-exchange experiment on the double-beta ($\ensuremath{\beta}\ensuremath{\beta}$) decaying nucleus ${}^{96}$Zr. The experiment was carried out at the Osaka University Research Center for Nuclear Physics (RCNP) with a 420 MeV incident ${}^{3}$He beam and the Grand Raiden magnetic spectrometer. A final-state energy resolution of 32 keV was achieved. A large fraction of the low-energy GT${}^{\ensuremath{-}}$ strength is identified in a single state at 694 keV. A similar observation has been made in a ${}^{96}$Mo($d$,${}^{2}$He)${}^{96}$Nb experiment at 120 keV resolution for the GT${}^{+}$ strength. It is found that this single state makes up nearly 100$%$ of the nuclear matrix element for the ${}^{96}$Zr two-neutrino double-beta ($2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decay.