Nuclear matrix elements for double-{\beta} decay

Background: Direct determination of the neutrino mass through double-$\beta$ decay is at the present time one of the most important areas of experimental and theoretical research in nuclear and particle physics. Purpose: We calculate nuclear matrix elements for the extraction of the average neutrino mass in neutrinoless double-$\beta$ decay. Methods: The microscopic interacting boson model (IBM-2) is used. Results: Nuclear matrix elements in the closure approximation are calculated for ${}^{48}$Ca, ${}^{76}$Ge, ${}^{82}$Se, ${}^{96}$Zr, ${}^{100}$Mo, ${}^{110}$Pd, ${}^{116}$Cd, ${}^{124}$Sn, ${}^{128}$Te, ${}^{130}$Te, ${}^{148}$Nd, ${}^{150}$Nd, ${}^{154}$Sm, ${}^{160}$Gd, and ${}^{198}$Pt decay. Conclusions: Realistic predictions for the expected half-lives in neutrinoless double-$\beta$ decay with light and heavy neutrino exchange in terms of neutrino masses are made and limits are set from current experiments.