Green's Function Relativistic Mean Field Theory For Single-particle Resonances

With the operation of the worldwide new radioactive ion beam facilities and the developments in the detection techniques,the study of exotic nuclei has become a very challenging topic in nuclear physics.In order to describe those nuclei,theoretically,we must deal with the continuous spectrum properly.And the Single particle resonant state in the continuum is very important for those exotic nuclei.The covariant density functional theory has achieved great success in the description of the nuclear structure.The Green's function method can give both the energies and widths of the resonant states strictly,and taking into account the correct diffuse spatial density distribution.In this paper,using the green's function method to deal with the continuum based on the covariant density functional theory,the following work are completed.(1)We extended the covariant density functional theory based on the Green's function method to study hypernuclei.Firstly,taking the hypernucleus ?61Ca as an example,the single-particle resonant states for hyperons are investigated by analyzing the density of states,and the corresponding energies and widths are given.It is found that the distributions of the very narrow 1f5/2 and 1f7/2 states are very similar to bound states while those of the wide 1g7/2 and 1g9/2 states are like scattering states.Besides,the energy level structure of hyperons in the Ca hypernucleus isotopes with mass number A = 53-73 are studied;obvious shell structure and small spin-orbit splitting are found for the single-spectrum.Finally,the impurity effect of hyperons on the single-neutron resonant states is investigated.For most of the resonant states,both the energies and widths decrease with adding more hyperons due to the attractive AN interaction.(2)We extended the covariant density functional theory based on the Green's function method to study deformed nuclei.Since the majority of open-shell nuclei are deformed,the deformation can change the order of single particle energy levels near the continuum threshold.In this paper,the Green's function method is applied to solve the coupled-channel Dirac equation with a quadrupole-deformed Woods-Saxon potential for the first time.Detailed formalism for the partial-wave expansion of Green's function is presented and relevant calculation program is developed.Numerical checks are carried out by comparing with our previous implementation of spherical Green's function method and the results from the deformed analytical continuation of the coupling constant and scattering phase shift methods.Besides,taking the recently reported p-wave halo candidate nucleus 37Mg as an example,the Nilsson levels for bound and resonant orbitals are presented and some decisive hints of p-wave halo formation in this nucleus is discussed by the deformed Green's function method,namely,crossing between the configurations 1/2[321]and 5/2[312]at deformation parameter ?>0.5 may enhance the probability to occupy the 1/2[321]orbital coming from 2p3/2.