Limitations of the number self-consistent random phase approximation

Abstract

The Quasiparticle Random Phase Approximation equations are solved taking into account the Pauli Principle at the expectation value level, and allowing changes in the mean field occupation numbers to minimize the energy while having the correct number of particles in the correlated vacuum. The study of Fermi pn excitations in 76 Ge using a realistic Hilbert space shows that the pairing energy gaps in the modified mean field are diminished up to one half of the experimental value when strong proton-neutron correlations are present. Additionally, the Ikeda sum rule for Fermi transitions is violated due to the lack of scattering terms in the phonon operators. These results call for a critical revision of the double beta decay half-lives estimated using the QRPA extensions when standard QRPA calculations collapse. PACS numbers: 21.60.Jz, 23.40.-s * Fellow of the CONICET, Argentina. On leave

Effects of orbital occupancies on the neutrinoless ββ matrix element of 76Ge

“…From Fig. 5 of [30] one can see that the occupancies of the neutron orbitals in the pfg subspace do not change significantly when the BCS+pnQRPA results are replaced by the self-consistent results. The proton Fermi surface sharpens a bit when going from the BCS+pnQRPA over to the self-consistent approach of [30], but the effect is quite small (anyway, we do not have experimental occupancies available for protons).…”

“…Further support can be sought from calculations that determine the orbital occupancies and the pnQRPA amplitudes X and Y self-consistently [30]. In [30] this kind of scheme was applied in a realistic model space to study Fermi pn excitations in 76 Ge. From Fig.…”

“…This can be justified partly by the good agreement between the calculated and observed properties of the low-lying energy levels in the adjacent odd-mass nuclei. Further support can be sought from calculations that determine the orbital occupancies and the pnQRPA amplitudes X and Y self-consistently [30]. In [30] this kind of scheme was applied in a realistic model space to study Fermi pn excitations in 76 Ge.…”

Neutrinoless doubleβdecay within the self-consistent renormalized quasiparticle random phase approximation and inclusion of induced nucleon currents

“…In Table I with the pn-QRPA and the pn-RQRPA ones. It is due to the mean-field modifications by the number self-consistent approach which use to diminish the pairing gap [19].…”

“…The new calculated pn-SRQRPA results predict considerably larger value for upper limit on m ee in comparison with the pn-QRPA and the pn-RQRPA ones. It is due to the mean-field modifications by the number self-consistent approach which use to diminish the pairing gap [19].…”