Probing The Resonant States In Exotic Nuclei By CGF And CMR Methods

The resonant states exist widely in nature,which can be traced in molecular,atom-ic,nuclear physics.Moreover,the resonance is also considered to be extremely remark-able in the scattering experiments.Furthermore,the resonant states play a critical role in the formation of many physical phenomena,such as halo,giant halo,disappearance of magic numbers,and so on.With the complex scaled Green's function(CGF)method and the RMF-CMR method by combining relativistic mean field(RMF)with complex momentum representation(CMR),we mainly study the single particle resonant states of exotic nuclei in this paper.Based on the methods,it is shown that the resonance is important in nuclear physics,especially in nuclear structure.The paper can be divided into two parts and as follows:Firstly,taking the neutron-rich nucleus⁴³S as an example,the CGF method is extended from the axially symmetrical case to non-axially symmetric deformation,that is,the case of triaxial deformation.By subtracting the background term,we minimize the dependence of the continuum level density on?.So the peaks of the resonances can be clearly displayed and the parameters can be obtained accurately.Considering the influence of the triaxial deformation parameters?,?on the energies and widths of the resonant states,the levels structure in⁴³S changes greatly.In addition,compared with CSM(the complex scaling method),the CGF method can obtain more lower energy resonant states,which indicates that CGF method is more suitable for more complex deformation cases.Due to the success of the CGF method in describing neutron-rich nuclei,we ex-tend the CGF method to study the single particle resonant states of proton-rich nuclei and take the nuclei¹⁵F and¹¹N as examples.As the width of the 5/2⁺still has large uncertainty for¹⁵F,many experiments and theoretical studies are devoted to the investi-gations for the first excited state.Based on the CGF method,we calculated the energy and width of the first excited state 5/2⁺after fitting the experimental single-proton separation energy of¹⁵F.Compared with the CSM method,scattering phase shift and cross section,it is shown that our results are reliable.The available results are also close to the experimental value and Fortune's new estimation that is based on the shell model.In addition,we also discuss how the potential parameters and deformation ef-fect influence the resonant states,levels structure and shells evolution.In the spherical case,there is an obvious sd level inversion.In the deformed case,the formation con-dition of halo phenomenon is not sufficient,which brings us enlightenment for further exploring the nature of¹⁵F and the experimental scheme in the future.We also focus on another extremely proton-rich nucleus¹¹N.With the same parameters,results of the CSM,CGF method and S-matrix are very similar.Without the deformation,the levels inversions still exist.When the deformation parameter?is introduced,the condition for halo formation is not full.So we believe that halo phenomenon of¹¹N need further study.At the same time,we also consider the effect of deformation on levels structure.From the results,the complex scaled Green's function method is suitable for the study of exotic nuclei.Secondly,with the newly developed RMF-CMR method,we have studied the sin-gle particle resonant states for Pb isotopes,and their pseudospin and spin symmetries.The obtained energies and widths decrease monotonously with the increasing mass number.Meanwhile,the magic number N=184 appears in the clear shell structures.In the neutron-richer nuclei,the extracted pseudospin and spin splittings become small-er.The extent of the splittings depends on the quantum numbers and position of the states lying in mean field.Good pseudospin and spin symmetries are expected in the neutron-rich nuclei and the single states with lower orbital momentum and lying near the continuum threshold.Especially,it is found that both lower(upper)components of the every pseudospin(spin)doublet look similar for not only bound states but also res-onant states,which confirms the presence of the pseudospin(spin)symmetry although the corresponding energy splitting is slightly large.Moreover,for every pseudospin(spin)doublet,the upper(lower)components of Dirac spinors satisfy the radial node relation,which is the same in the bound states and resonant states.