Two-neutrino double beta decay within Fully-Renormalized QRPA: Effect of the restoration of the Ikeda sum rule

The recently proposed Fully-Renormalized QRPA (FR-QRPA), which fullfils the Ikeda sum rule (ISR) exactly, is applied to the two-neutrino double beta decay of $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{116}$Cd, $^{128}$Te and $^{130}$Xe. The results obtained are compared with those of other approaches, standard QRPA and self-consistent QRPA (SCQRPA). The similarities and the differences among the methods are discussed. The influence of the restoration of the Ikeda sum rule on the $2\nu\beta\beta$-decay amplitude is analyzed.