Ikeda sum rule, self-consistency and double-beta decay in the renormalized quasiparticle random phase approximation

Abstract

The effect of the inclusion of ground-state correlations into the QRPA equation of motion for the two-neutrino double-beta ( ββ 2 ν ) decay is carefully analyzed. The resulting model, called renormalized QRPA (RQRPA), does not collapse near the physical value of the nuclear force strength in the particle-particle channel, as happens with the ordinary QRPA. Still, the ββ 2 ν transition amplitude is only slightly less sensitive on this parameter in the RQRPA than that in the plain QRPA. It is argued that this fact reveals once more than the characteristic behavior of the ββ 2 ν transition amplitude within the QRPA is not an artifact of the model, but a consequence of the partial restoration of the spin-isospin SU(4) symmetry. It is shown that the price paid for bypassing the collapse in the RQRPA is the violation of the Ikeda sum rule.