Restoration of the Ikeda sum rule in self-consistent quasiparticle random-phase approximation

The so-called self-consistent quasiparticle random phase approximation, accounting for a better treatment of ground-state correlations, is applied to a schematic Hamiltonian, describing the Fermi beta decay process. The self-consistent procedure coupling the BCS minimum with the quantum fluctuations yields an exact fulfillment of the Ikeda sum rule. The role of the ground-state correlations is analyzed in the case of the double beta decay process.