Microscopic Study Of Multiple Shape Coexistence Within Covariant Density Functional Theory

The coexistence of nuclear shape is one of the frontier issues in nuclear physics,which is related to many important scientific issues such as the evolution of the shell structure and the microscopic origin of collectivity.Since the discovery of the coexistence of the three shapes in ¹⁸⁶Pb in 2000,and the recent experimental confirmation of the coexistence of multiple shapes in ^110,112Cd nuclei,it has changed people’s understanding of traditional nuclear structures and also presented new challenges to nuclear theoretical models.At present,the theoretical methods used to study the nuclear coexistence mainly include configuration interaction shell model and density functional theory.In particular,density functional theory can carry out global research on the entire nuclide layout,and has made great achievements in describing the nature of the ground state of nuclei.In order to study the coexistence of nuclear shapes systematically,it is necessary to describe not only the properties of the ground states,but also the properties of the low-lying states microscopically and self-consistently.To this end,it is indispensable to extend the density functional theory of the mean field approximation.In recent years,a microscopic collective Hamiltonian model（5DCH-CDFT）has been developed based on the covariant density functional theory by the supervisor’s group,and it self-consistently includes the dynamic correlation effects of beyond mean field and achieves a unified and self-consistent description of the low-lying spectra of nuclei.This paper uses the 5DCH-CDFT model to systematically study the multiple shapes coexistence of Cd isotopes and neutron-deficient Pb isotopes based on the successful PC-PK1 functional.The specific research results are as follows:1).The studies of the potential energy surfaces of even-even ¹⁰⁶Cd-¹²⁰Cd has revealed that the multiple shapes of the prolate,oblate and triaxial deformation with moderate deformation（β～0.2）coexist in the ^110-116Cd isotopes,and reproduced the experimental low-lying spectra of ^110,112Cd.By analyzing the distribution of the collective wave function,it is predicted that large prolate deformations（β～0.4）exist in the even-even ^110-116Cd;2).The study of the collective potential energy surfaces of neutron-deficient ^182-190Pb has revealed that there are multiple shapes coexistence of spherical,prolate and oblate in Pb isotopes.Further,the study of excitation spectrum and wave functions confirmed the existence of prolate and oblate shapes,but did not display an obvious spherical configuration.