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

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

1996-02-06

arxiv.org/abs/nucl-th/9602007v2

Phys.Rev.C54:1976-1981,1996

Physics

Nuclear Physics

Nuclear Theory

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

Scientific paper

10.1103/PhysRevC.54.1976

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.

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