Abstract
The renormalized proton-neutron quasiparticle random phase approximation approach has been used to study double \ensuremath{\beta} decay matrix elements and associated transition half-lives for neutrino-accompanied double \ensuremath{\beta} decay to the first excited ${2}^{+}$ state for five medium-heavy parent nuclei ${}^{76}$Ge, ${}^{82}$Se, ${}^{96}$Zr, ${}^{100}$Mo, and ${}^{116}$Cd. The results of these calculations are compared with the normal approach and experiments where available. The dependence on the size of the single particle basis is also discussed.
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