Critical view on double-beta decay matrix elements within Quasi Random Phase Approximation-based methods

A systematic study of the two-neutrino and neutrinoless double-beta decay m atrix elements (ME) for the nuclei with A = 76, 82, 96, 100, 116, 128, 130 and 136 is done. The calculations are performed with four different quasi r andom phase approximation (QRPA)-based methods, i.e. the proton-neutron QRP A (pnQRPA), the renormalized proton-neutron QRPA (pnRQRPA), the full-RQRPA and the second-QRPA (SQRPA). First we checked the conservation of the Ikeda sum rule (ISR) and found that it is fulfilled with a good accuracy for the SQRPA, while for the pnRQRPA and full-RQRPA the deviations are up to 17%. Then, we studied the dependence of the ME on the single-particle (s.p.) bas is. For that we performed the calculations using the same set of parameters and two different s.p. basis. For the two-neutrino decay mode the ME manif est generally the largest sensitivity to the choice of the basis when they are calculated with the pnQRPA, while the smallest sensitivity is got with the SQRPA. For all the methods the largest differences between the results were found for Te-128,Te-130 and Xe-136. For the neutrinoless decay mode th e ME display generally a stronger dependence on the basis than for the two- neutrino decay mode, when they are calculated with the pnQRPA, RQRPA and fu ll-RQRPA, while for SQRPA differences in the results are within 30%. A bett er stability against the change of the s.p. basis used and a good fulfillme nt of the ISR allow to reduce the uncertainties in the values of the neutri noless ME predicted by the QRPA-based methods to about 50% from their magni tude. Further, we fixed the values of g(pp) from the two-neutrino calculati ons and according to recent experimental data, and then we used them to com pute the ME for the neutrinoless decay mode. Taking the most recent experim ental limits for the neutrinoless half-lives, we deduce new upper limits fo r the neutrino mass parameter. Finally, there are estimated, for each nucle us, scales for the neutrinoless double-beta decay half-lives that the exper iments should reach for exploring neutrino masses around 0.1 eV. This might guide the experimentalists in planning their setups. (C) 2001 Elsevier Sci ence B.V. All rights reserved.