Exploration Of The Single-particle Resonances In Nuclei By Using The Complex Momentum Representation Method

The single-particle resonant states play a crucial role in the study of exotic phenomenons in nuclei.Many methods have been developed for studying the single-particle resonant states in nuclei.In this paper,we explore the single-particle resonant states by applying the Complex Momentum Representation(CMR)method.Taking 17O and 31Ne as examples,the novel phenomena in nuclei is analyzed.The main contents are as follows:Firstly,the physical meanings of resonant states is explained.The methods to explore the single-particle resonances are briefly introduced.These methods include the R matrix method,the S matrix method,the J matrix method,the K matrix method,the real stability method(RSM),the analytic continuation in the coupling constant(ACCC),complex scale method(CSM),and Green function method.Secondly,the complex momentum representation method is introduced and the theoretical formalism for the spherical nuclei is presented.With 17O as an example,the single-particle resonant states is studied and the dependence of energy and width on the numerical parameters is analyzed.The calculated results are compared with those obtained by the other methods in satisfactory agreement.Thirdly,the theoretical formalism of the CMR method for the deformed nuclei is derived out.The single particle resonances in 31Ne is explored and the relationship between the resonance energy and width and the quadruple deformation parameters is analyzed.Compared with other methods,not only the narrow resonances but also broad resonances are obtained using the present method.To understand the physical mechanism for 31Ne halo,we have calculated the single-particle energies for the bound and resonant states together with their evolution with deformation.The results show that a p wave resonance appears clearly in the complex momentum plane accompanied by a p-f inversion in the single-particle levels,which implies that the halo in 31Ne maybe devoted to the deformation and level inversion.The calculated probability of single-particle level occupancy,the rms radius,and the density distribution support the conclusion of a deformation halo for 31Ne.