We have used the $(d,{}^2\mathrm{He})$ reaction to obtain the GT${}^{+}$ strength distribution for ${}^{116}\mathrm{Sn}\to {}^{116}\mathrm{In}$ transitions. Here, ${}^{116}\mathrm{In}$ is the intermediate nucleus in the second-order perturbative description of ${}^{116}\mathrm{Cd}$ double beta $(\beta \beta )$ decay. In this paper we will review what is known about the nuclear matrix elements for the ${}^{116}\mathrm{Cd}$ $2\nu \beta \beta$ decay, discuss the single-state dominance hypothesis and combine our new data with other existing data from charge-exchange reactions to obtain a $2\nu \beta \beta$-decay half-life. The deduced value $T_{1/2}=(4\pm 1)\times {10}^{19}$y compares well with the one known from direct counting experiments.

• Received 18 February 2005

DOI:https://doi.org/10.1103/PhysRevC.71.054313