Microscopic Study Of Shape Coexistence And Low-lying Spectrum In Odd Nuclei Within Covariant Density Functional Theory

With the construction and operation of a new generation of large-scale radioactive nuclear beam devices around the world,people have discovered many novel phenomena or laws about nuclear structure by detecting their excitation and fission in unstable exotic nuclei,which has brought new understanding to nuclear physics research.In the experiment,the internal structure information of the nucleus is mainly analyzed by measuring the low excitation spectrum of the nucleus,such as shell structure evolution,quantum phase transition,shape coexistence,etc.In particular,the shape coexistence of nuclei,that is,the coexistence of two or more eigenstates with different shapes in finite quantum many-body systems,has become one of the frontier topics in nuclear physics research in recent years.At present,people have carried out a series of research work on the shape coexistence of even-even nuclei.Compared with even-even nuclei,odd-mass nuclei have more complex structures due to the presence of unpaired odd nucleons,and the number of odd-mass nuclei is about twice that of even-even nuclei.Therefore,the research on the low excitation spectrum and shape coexistence of odd-mass nuclei has become an important research content in the field of nuclear structure.Covariant density functional theory（CDFT）can self-consistently describe the ground state properties of nuclei in the whole nuclide layout.The collective Hamiltonian method based on CDFT achieves a unified self-consistent description of the low-lying excitation spectra of even-even nuclei with quadrupole or octupole deformation,and the microscopic mechanism of the coexistence of even-even nuclei shape is discussed in depth.The microscopic core-quasiparticle coupling（CQC）model based on CDFT has been developed to study the low excitation spectrum and shape coexistence of odd-mass nuclei,including the quasiparticle freedom.In this paper,the following work has been carried out under the framework of the microscopic CQC model:1)The low excitation spectra and shape coexistence of odd-A nuclei ¹³⁹Gd,¹³⁷Sm,¹³³Nd and ¹³¹Ce are studied.The theoretical calculations reproduce the experimental data well,predicts many excitation bands that have not been observed in the experiment,and gives the wave function configuration distribution,electromagnetic transition probability,quadrupole shape invariant and deformation parameters.The study shows that there is the cross-shell excitation mode of particle-hole and the configuration structure of single nucleon coupling core excitation band in this region,which has the characteristics of shape coexistence.2)In order to study the parity double band structure and energy level splitting of odd-A nuclei in the actinide region,we optimized the microscopic CQC model by introducing the monopole-monopole interaction,and systematically studied the octupole deformation and low-energy negative parity bands of even-even nuclei and odd-A nuclei in the actinide region.The theoretical calculation reproduces the experimental data well,verifies the applicability and accuracy of the microscopic CQC model based on the CDFT in the actinide region,reveals the microscopic mechanism and physical image of the formation of the parity double band,predicts the multiple parity double band structure and gives the wave function configuration distribution.