Multi-Reference Covariant Density Functional For Collective Excitations Of Quadrupole-Octupole Deformed Nuclei

The study on spectroscopy is of great importance to disclose and recognize the underling law of nature in microscopic world. The spectroscopic properties of nuclear low-lying states reveal rich structure information of atomic nuclei, providing a key way to deepen our knowledge of nuclear structure and uncover the new physic, playing an essential role in understanding the phenomena of nuclear shell structure evolution, shape coexistence, shape transition and clustering structure. The collective excitation of most atomic nuclei can be described with quadrupole deformation degree of freedom. Besides, there are nuclei in some specific mass region, possessing an alternative-parity doublet bands, which is similar to the spectra of di-atomic molecular. The most obvious way to describe the spectra of such nuclei is to introduce octupole deformation degree of freedom. Moreover, previous studies have indicated that the octupole deformation also plays an important role in the phenomena of nuclear clustering structure, cluster decay and fission process. Therefore, the study of low-lying states of octupole deformed nuclei is significant.In this thesis, we establish a multi-reference covariant density functional theory for the low-lying states of quadrupole-octupole shaped nuclei(QO-MR-CDFT) by introducing parity projection, particle number projection, angular momentum projection and Generator Coordinate Method in the framework of covariant density functional theory. The QO-MR-CDFT is composed of three parts: 1) The nuclear intrinsic wavefunctions with different quadrupole-octupole deformations are obtained through the relativistic mean-field calculation with a constraint on the mass quadrupole-octupole moments; 2) The Parity Projection, Particle Number Projection and Angular Momentum Projection method are used to project out the wave functions with designed parity, particle number and angular momentum; 3) Generator Coordinate Methods is used to mix the projected wavefunctions with designed parity, particle number and angular momentum but different intrinsic deformations. We introduced the Broyden method to accelerate the speed of the iterations in the mean-field calculations. The Pfaffian method is adopted to calculate the norm overlap. Moreover, the parallel technique OpenMP is implemented to calculate the transition densities and currents to save the computation time.We applied the newly developed QO-MR-CDFT to study the clustering structure and molecular-like α+16O structure in the low-lying states of 20 Ne. The energy spectra and electric multiple transition strengths of the parity doublet bands have been reproduced after including the dynamic octupole deformation degree of freedom. In particular, we found that the molecular-like is weakening with the increase of angular momentum. Our studies indicate that the special deformation dependent moment of inertia is a possible mechanism responsible for the rotation-induced dissolution of the α+16O molecular structure in 20 Ne. It is worth mentioning that the newly developed OC-MR-CDFT is the most advanced method for the low-lying states of quadrupole-octupole deformed nuclei.