Study On The Exotic Properties Of Nuclei With The Complex Momentum Representation Method

Neutron halos and proton halos are one of the most remarkable phenomena in the study of exotic nuclei.The typical characteristic of the halo structure is that the weakly binding of valence nucleons and a loose distribution of the density of matter around core,whose radius is much larger than that of stable nucleus with the same number of nucleons.Those nuclei are called halo nuclei.The continuum,especially the resonant states near the continuum threshold,plays an important role in the formation of halo and other exotic phenomena because of the weakly binding of valence nucleons.Therefore,we need to develop a new method that the contribution of continuum need to be considered to explore the structure and properties of exotic nuclei.In this paper,we develop the relativistic mean-field theory in complex momentum representation with the BCS approximation for pairing correlations for exotic nuclei.The bound states and resonant states are treated on the same footing and the physical resonant states are considered self-consistently in the present calculations.Therefore,the method is applicable not only to stable nuclei but also to exotic nuclei with a diffused matter density distribution.Considering that the neutron-rich Zr and Ce isotopes have special characteristics,in many theoretical studies,it is found that giant halos exist in neutron-rich Zr isotopes with 122 Zr as the core,and halos and giant halos exist in neutron-rich Ce isotopes with 184 Ce as the core.In the thesis,Zr and Ce isotopes are chosen as examples,and their ground state properties are systematically studied.The role of resonant state in the formation of exotic phenomena is explored with the newly developed RMF-BCS-CMR method.The main contents are as follows:Firstly,we introduce the significance of resonances,the methods for resonances,and the progress of studying resonant states in recent years.Because the resonant state plays an important role in the formation of exotic phenomena,this paper focuses on several methods for studying halo phenomena.Secondly,we introduce the theoretical framework,which includes the relativistic mean field theory(RMF),the complex momentum representation method(CMR),and the BCS approximation formula.And we establish the RMF-BCS-CMR method.Lastly,we adopted the RMF-BCS-CMR method to explore the exotic properties of Zr and Ce isotopes.(1)For Zr isotopes,the calculated binding energies,two-neutron separation energies,and root-mean-square radii are in excellent agreement with the available data as well as the relativistic Hartree-Bogoliubov calculations.Especially,several resonant states lying near the continuum threshold are found to play important roles in the formation of exotic phenomena and support the prediction of giant halo in the Zr isotopes.The physical mechanism of halo in 124 Zr is clarified,which comes from a resonant state of p-wave.(2)For Ce isotopes,the energy,width,occupation probabilities,and the contribution of orbits to nuclear density distribution near Fermi surface are obtained.It is found that fairly diffuse density distributions is caused by several resonant orbits with low-angular momentum,which may result in the appearances of halo and giant halo in Ce isotopes close to the neutron drip line.The conclusion agrees well with the predication of the RHB calculations.The obtained wavefunctions for 198Ce supports this conclusion that it may be a giant halo nucleus.The results show these nuclei 186Ce,188Ce,and 190Ce hold d-wave halo structure,and 192Ce,194Ce,196Ce,and 19gCe hold s-and d-wave giant halo structures.The formation mechanism of these halos and giant halos was clarified.