Study Of Single-particle Resonant States With Green's Function Method

The single-particle resonant state in the continuum plays a crucial role in the properties of exotic nuclei.In recent years,people have proposed a variety of methods to study the resonant states.Green's function?GF?method is one of the simple and effective methods.In previous work,the single-particle resonances are identified by comparing the density of states displayed by nucleons moving in the mean-field potentials and those by free particles,and this method could not give a wide resonance.In this paper,a new idea is proposed,that is,the resonant state can be determined by searching the poles of Green's function or extremes for density of state and accurate energy and width can be given for both narrow resonance and wide resonance.Based on this,this article studies the single-particle resonant states of spherical nuclei and deformed nuclei,mainly including:?1?In the case of a sphere,taking the¹²⁰Sn atomic nucleus as an example,the single-neutron resonant state was studied using Green's function with relativistic mean-field theory.In coordinate space,the dependence of the resonance energy,width and density distribution on the size of the space was checked,and the results were very stable.Compared with the traditional method,four new wide resonances2g_7/2,2g_9/2,2h_11/2and 1j_13/2are observed in this work,and the width accuracy of the narrow resonance state 1h_9/2is improved to 1×10^-8Me V.?2?The Green's function method is extended to deformed nuclei.The coupled-Dirac equation with quadrupole-deformed Woods-Saxon potentials is solved in the coordinate space.Numerical checks are carried out by comparing with our previous implementation of the spherical GF method and the results from the deformed complex momentum representation?CMR?,the analytical continuation of the coupling constant?ACCC?,and the scattering phase shift?SPS?methods,and it is proved that the GF method is very effective and reliably for describing resonance states,no matter they are narrow or broad,spherical or deformed.Finally,as an application,the Nilsson energy level of the bound state and resonance state of³⁷Mg of the halo candidate nucleus was calculated using the deformed Green function method,and the key clues to the formation of p-waveform halo were given.