Renormalized QRPA and double beta decay: a critical analysis of double Fermi transitions

Abstract

The proton-neutron monopole Lipkin model, which exhibits some properties which are relevant for those double beta decay ($\beta \beta$) transitions mediated by the Fermi matrix elements, is solved exactly in the proton-neutron two-quasiparticle space. The exact results are compared with the ones obtained by using the Quasiparticle Random Phase (QRPA) and renormalized QRPA (RQRPA) approaches. It is shown that the RQRPA violates the Ikeda Sum Rule and that this violation may be common to any extension of the QRPA where scattering terms are neglected in the participant one-body operators as well as in the Hamiltonian. This finding underlines the need of additional developments before the RQRPA could be adopted as a reliable tool to compute $\beta \beta$ processes.

arXiv comment18 pages, LaTeX, 7 figures included as LaTeX files. Minor changes in title and text

Cited by in corpus (13)

• Double Beta Decay
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• Non-collapsing renormalized QRPA with proton-neutron pairing for neutrinoless double beta decay
• Modified Hartree-Fock-Bogoliubov at finite temperature
• Single- and double-beta decay Fermi-transitions in an exactly solvable model
• Quasiparticle Random Phase Approximation with inclusion of the Pauli Exclusion Principle
• Self consistent random phase approximation within the O(5) model and Fermi transitions
• Double beta decay and the proton-neutron residual interaction
• A large Hilbert space QRPA and RQRPA calculation of neutrinoless double beta decay
• Limitations of the number selfconsistent Random Phase Approximation
• Quasiparticle Random Phase Approximation with an optimal Ground State
• Effective restoration of dipole sum rules within the renormalized random-phase approximation
• The beta-beta two neutrino decay in 48Ca