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

Abstract

The nuclear matrix element (NME) of the neutrinoless double-β (0νββ) decay is an essential input for determining the neutrino effective mass, if the half-life of this decay is measured. The reliable calculation of this NME has been a long-standing problem because of the diversity of the predicted values of the NME depending on the calculation method. In this paper, we focus on the shell model and the QRPA. The shell model have a rich amount of the many-particle many-hole correlations, and the QRPA can obtain the convergence of the result of calculation with respect to the extension of the single-particle space. It is difficult for the shell model to obtain the convergence of the 0νββ NME with respect to the valence single-particle space. The many-body correlations of the QRPA are insufficient depending on nuclei. We propose a new method to modify phenomenologically the results of the shell model and the QRPA compensating the insufficient point of each method by using the information of other method complementarily. Extrapolations of the components of the 0νββ 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 0νββ NME of the QRPA. Our modification method gives similar values of the 0νββ NME of the two methods for 48 Ca. The discrepancy of the shell model and the QRPA for the NME of the two-neutrino double-β decay is much smaller than that for the 0νββ NME without major modifications.

Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism

“…The obtained NME for Nd 150 is 3.604, not much different from the value 3.14 by the neutron-proton QRPA using the same EDF [125]. Recently, Terasaki and Iwata [129] compared the QRPA and shell-model calculations for the NME of Ca 48 . To compensate the drawbacks of each model, they proposed a phenomenological way to modify each result by introducing an enhancing or quenching factor.…”

“…Unfortunately, it is difficult to reduce the discrepancy between these models because each model has its own phenomenology and uncontrolled approximations. Besides, there are a number of studies based on nuclear models other than the above two, including the proton-neutron quasiparticle random-phase approximation [124,125,126,127,128,90,129], the interacting boson model (IBM) [130,131,132,133,134], or the projected Hartree-Fock-Bogoliubov method using a pairing-plus-quadrupole Hamiltonian [135,136,137]. See the recent discussions on the comparison of the quasiparticle random-phase approximation with IBM [138] and with the shell model [120,129].…”