Estimation of nuclear matrix elements of double-β decay from shell model and quasiparticle random-phase approximation

The nuclear matrix element (NME) of neutrinoless double-beta (0 nu beta beta) decay is an essential input for determining the neutrino effective mass, if the half-life of this decay is measured. Reliable calculation of this NME has been a long-standing problem because of the diversity of the predicted values of the NME, which depends on the calculation method. In this study, we focus on the shell model and the QRPA. The shell model has a rich amount of themany-particle many-hole correlations, and the quasiparticle random-phase approximation (QRPA) can obtain the convergence of the calculation results with respect to the extension of the single-particle space. It is difficult for the shell model to obtain the convergence of the 0 nu beta beta NME with respect to the valence single-particle space. The many-body correlations of the QRPA may be insufficient, depending on the nuclei. We propose a new method to phenomenologically modify the results of the shell model and the QRPA compensating for the insufficiencies of each method using the information of other methods in a complementary manner. Extrapolations of the components of the 0 nu beta beta NME of the shell model are made toward a very large valence single-particle space. We introduce a modification factor to the components of the 0 nu beta beta NME of the QRPA. Our modification method yields similar values of the 0 nu beta beta NME for the two methods with respect to 48Ca. The NME of the two-neutrino double-beta decay is also modified in a similar but simpler manner, and the consistency of the two methods is improved.