Study On 0νββ-decay Nuclear Matrix Elements With Beyond Mean-field Methods

0νββ decay is only the practical way to reveal whether neutrinos are the Majorana particles.Its discovery will also determine the mass scale and mass hierarchy of neutrinos,provided that the corresponding nuclear matrix elements(NMEs)M0ν are known.However,the discrepancy of M0" from different nuclear models vary up to a factor around three times.To understand such a discrepancy and obtain a more reliable M0ν,we develop the calculation approach of M0ν based on the self-consistent quasiparticle random phase approximation plus quasiparticle-vibration coupling(QRPA+QPVC)model,which can incorporate the strengths of the two widely used models in this field,i.e.,quasiparticle random phase approximation(QRPA)model and the interacting shell model(ISM).Because QRPA+QPVC model takes into account the higher-order correlations beyond QRPA model and its model space is large,a more reliable M0ν would be obtained.So far,2νββ-decay half-lives of 11 nuclei have been measured.Their corresponding NMEs provide a test ground to check nuclear models.Therefore,we first study the single-state or lowlying-states dominance hypothesis of M2ν based on the self-consistent Skyrme QRPA model.In the systematical calculations of the M2ν for the 11 nuclei with experimental data,the negative contributions from higher-lying states of the intermediate nuclei in the running sums of NMEs are usually found,which play important roles in the fulfillment of the single-state or low-lying-states dominance hypothesis.Such negative contributions are due to the enhanced ground-state correlations,which are tuned by strong isoscalar pairing interaction.Second,we study the M0ν based on the self-consistent Skyrme QRPA model.The uncertainty in the nuclear matrix elements(NMEs)of 0νββ decay is investigated by using 18 Skyrme interactions supplemented with two kinds of pairing interactions.The NMEs for the isotopes concerned are less sensitive to the particle-hole(ph)interactions,while strongly dependent on the employed isovector particle-particle(pp)pairing interactions.The results indicate that a precise determination of the isovector pp pairing interaction in the Skyrme energy density functional is of importance to reduce the uncertainty in the NMEs within the QRPA framework.Finally,we develop the calculation approach of M0ν based on the self-consistent Skyrme QRPA+QPVC model.We analyze the influence of higher-order many-body correlations on the M0ν.Compared to the QRPA model,the M2ν obtained by the Skyrme QRPA+QPVC model decreases more rapidly when increasing the strength of isoscalar pairing.The QPVC effects on the M0ν are small and make it 10%larger than that obtained by Skyrme QRPA model.As an application of the Skyrme RPA+PVC model,we additionally study the γ decay of giant resonances to low-lying states.Results indicate that there are larger amount of 1p-1h-1phonon components in the wave function of the giant quadrupole resonance than that of the giant dipole resonance.