Beyond Mean-field Description Of Nuclear Giant Resonances Based On Skyrme Density Functional Theory

The research on nuclear giant resonances(GRs)is of great importance for studying the nuclear structure,constraining the nuclear equation of state(EoS),and understanding the origin of heavy elements.Currently,the most widely used microscopic theory for GRs is the(quasiparticle)random-phase approximation[(Q)RPA]theory,which considers the GRs as a superposition of oneparticle-one-hole(two quasiparticles)excitations.Although the(Q)RPA theory has achieved great success in describing GRs energies,it cannot provide self-consistent descriptions of the widths,decay properties,and spectrum’s fine structures due to the lack of contributions from higher-order configurations.Therefore,it is of great significance for the theoretical studies of the GRs by considering the contributions of higher-order configurations.In this thesis,we have developed a fully self-consistent quasiparticle random-phase approximation(QRPA)+quasiparticle-vibration coupling(QPVC)theory on top of Skyrme density functionals.The pairing effects are included by the Bogoliubov transformation,while the beyond mean-field effects are taken into account by the couplings between two quasipariticles and phonons.Utilizing the(Q)RPA and(Q)RPA+(Q)PVC theories,we studied the nuclear isoscalar giant monopole resonance(ISGMR)and the isovector giant dipole resonance(IVGDR).The nuclear ISGMR is crucial for constraining the nuclear incompressibility coefficient K∞.Current studies have shown that models that can provide a reasonable description of ISGMR energy in Pb often overestimate the ISGMR energies of Sn isotopes by about 1 MeV,indicating that the EoS in Sn isotopes is more "soft",and therefore,It is hard to constrain K∞ reasonably.In the investigation of ISGMR,we calculated the ISGMR in Ca,Sn,and Pb isotopes by using the newly developed(Q)RPA+(Q)PVC theory,and found that the(Q)PVC effects may reconcile the discrepancy in ISGMR energies in Sn and Pb to a large extent.By the inclusion of(Q)PVC effects,the shifts of ISGMR energy to lower energy in Sn and Ca are about 0.4 MeV more than the one in 208Pb,which leads to the well descriptions of ISGMR in Ca,Sn,and Pb at the same time.In the investigation of nuclear IVGDR,we studied the IVGDR energies and electric dipole polarizabilities αD in O,Ca,Sn,and Pb isotopes utilizing the(Q)RPA and(Q)RPA+(Q)PVC theories.It is found that the(Q)RPA theory may provide a good description of the IVGDR energies and αD in 208Pb,120Sn,and 48Ca simultaneously,but it cannot provide a good description of the IVGDR energies and αD in 16O and 208Pb simultaneously.These conclusions remain valid when the(Q)PVC effects are taken into account.Comparing with the(Q)RPA theory,(Q)PVC effects do not change the total αD,but it can provide a better agreement for running sum rule of αD with the experimental data due to the inclusion of spreading width.Due to the fact that the total αD is not affected by the QPVC effects,we studied the constraints on the nuclear isovector properties on top of QRPA theory by taking Sn isotopes as examples.It is found that αD and nuclear isovector properties,such as the slope parameter of symmetry energy L and neutron skin thickness ΔRnp,present good linear correlations in the neutron-rich Sn isotopes,which provide an effective way to constrain L and ΔRnp.The good linear correlations between αD and nuclear isovector properties in neutron-rich Sn isotopes can be attributed to the occurrence of pygmy dipole resonance and paring effects.Further,utilizing the experimental αD values in stable nuclei,we predicted the αD in neutron-rich Sn isotopes,and gave constraints on L and ΔRnp.