Relativistic description of nuclear matrix elements in neutrinoless double- β decay

Background: Neutrinoless double-β (0νββ) decay is related to many fundamental concepts in nuclear and particle physics beyond the standard model. Currently there are many experiments searching for this weak process. An accurate knowledge of the nuclear matrix element for the 0νββ decay is essential for determining the effective neutrino mass once this process is eventually measured. Purpose: We report the first full relativistic description of the 0νββ decay matrix element based on a state-of-the-art nuclear structure model. Methods: We adopt the full relativistic transition operators which are derived with the charge-changing nucleonic currents composed of the vector coupling, axial-vector coupling, pseudoscalar coupling, and weak-magnetism coupling terms. The wave functions for the initial and final nuclei are determined by the multireference covariant density functional theory (MR-CDFT) based on the point-coupling functional PC-PK1. Correlations beyond the mean field are introduced by configuration mixing of both angular momentum and particle number projected quadrupole deformed mean-field wave functions. Results: The low-energy spectra and electric quadrupole transitions in Nd150 and its daughter nucleus Sm150 are well reproduced by the MR-CDFT calculations. The 0νββ decay matrix elements for both the 01+→01+ and 01+→02+ decays of Nd150 are evaluated. The effects of particle number projection, static and dynamic deformations, and the full relativistic structure of the transition operators on the matrix elements are studied in detail. Conclusions: The resulting 0νββ decay matrix element for the 01+→01+ transition is 5.60, which gives the most optimistic prediction for the next generation of experiments searching for the 0νββ decay in Nd150.