Neutrinoless double-β-decay matrix elements within the second quasirandom phase approximation method

A computation of the neutrinoless double-{β}-decay matrix elements is performed with the second quasirandom phase approximation method [A. A. Raduta, A. Faessler, S. Stoica, and W. A. Kaminski, Phys. Lett. B 254, 7 (1991); A. A. Raduta, A. Faessler, and S. Stoica, Nucl. Phys. A534, 149 (1991); S. Stoica and W. A. Kaminski, Phys. Rev. C 47, 867 (1993); S. Stoica, ibid. 49, 787 (1994); Phys. Lett. B 350, 152 (1995); S. Stoica and I. Mihut, Nucl. Phys. A602, 197 (1996)] for the nuclei with $A=76,$ 82, 96, 100, 116, 128, 130, and 136. It was found that the Ikeda sum rule is fulfilled with good accuracy and the results display a weak dependence on the single particle basis used. Comparing our calculations with similar ones performed with other quasirandom phase approximation--based methods we estimate more precisely the accuracy of these methods in the prediction of the neutrinoless matrix elements and neutrino mass parameter, which is settled to about 50% from their calculated values. Taking the most recent experimental limits for the neutrinoless half-lives, we also deduced new limits for the neutrino mass parameter.