The renormalized proton-neutron quasiparticle random-phase approximation model (RQRPA) has been used to calculate double-β-decay matrix elements and associated transition half-lives for two-neutrino double β decay of parent nuclei ${}^{76}\mathrm{Ge},$ ${}^{78}\mathrm{Kr},$ ${}^{82}\mathrm{Se},$ ${}^{96}\mathrm{Zr},$ ${}^{106}\mathrm{Cd},$ and ${}^{130}\mathrm{Te}$ to the ground state and excited one- and two-phonon states of their daughter nuclei. The results are compared to ordinary proton-neutron QRPA and experiments. In addition, the violation of the Ikeda sum rule in the RQRPA is examined and discussed.

• Received 31 May 1996

DOI:https://doi.org/10.1103/PhysRevC.55.2314