A many-body Hamiltonian involving the mean field for a projected spherical single-particle basis, the pairing interactions for like nucleons, a repulsive dipole-dipole proton-neutron interaction in the particle-hole channel, and an attractive dipole-pairing interaction is treated by a gauge-restored and fully renormalized proton-neutron quasiparticle random-phase approximation formalism. The resulting wave functions and energies for the parent and the daughter nuclei are used to calculate the $2\nu \beta \beta$ decay rate and the process half-life for the emitters: ${}^{48}$Ca, ${}^{76}$Ge, ${}^{82}$Se, ${}^{96}$Zr, ${}^{104}$Ru, ${}^{110}$Pd, ${}^{128,130}$Te, ${}^{148,150}$Nd, ${}^{154}$Sm, and ${}^{160}$Gd. The results of our calculations are compared with the corresponding experimental data as well as with those obtained through other methods. The Ikeda sum rule is obeyed.

• Received 2 June 2011

DOI:https://doi.org/10.1103/PhysRevC.84.064322