Research On The Exotic Structure Of The Neutron-rich Nuclei In The Medium-mass Region

There are about 300 kinds of stable nuclides in nature.By studying those nuclei close to the β-stability line,physicists have obtained rich knowledge on nuclear structure and properties and established many corresponding nuclear models.In recent years,the neutron-rich（or proton-rich）nuclei,far from the β-stability line,have attracted the attention of the physicists.Since the end of the 20th century,a number of large radioactive nuclear beam installations and related detection equipment have been built in many countries,which is an opportunity for scientists to explore these exotic nuclei.The research of those exotic nuclei has become one of the important scientific frontiers in nuclear physics.Nowadays,physicists have made great success in exploring those nuclei with these devices.In this paper,we develop the theory describing exotic nuclei,which is used to study the structure and properties of those nuclei in the medium-mass region.Up to now,the heaviest halo nucleus that has been explored in experiment is ³⁷Mg.One wants to know whether there are halo structures in the heavier nuclei.For the purpose,the physicists pay attention to the study about the exotic structure of the neutron-rich nuclei in the medium-mass region,which will be very challenging in the nuclear physics.In this paper,we develop the covariant density functional theory（CDFT）in the complex momentum representation（CMR）,and the CDFT-CMR method is established.The covariant density functional theory is one of the most successful microscopic models to describe the structure and properties of the nuclei.The CDFT includes two theoretical model that are the relativistic mean-field（RMF）theory and relativistic Hartree-Fock（RHF）theory respectively.In this paper,the complex-momentum representation method is combined with the relativistic-mean-field theory,and the RMF-CMR method is developed.Then,we use this method to study the exotic structures of the deformed neutron-rich nuclei in medium-mass region.Moreover,the complex-momentum representation method is combined with the Green’s function method,and the CMR-GF method is developed.Then,the CMR-GF method is used to study the n-α scattering.The scattering phase shift and scattering cross section are obtained,which are in good agreement with the experimental data.The contents are listed in the following:1.To develop the CDFT-CMR theoretical methodThe RMF theory can not only describe the ground state properties of stable nuclei very well,such as the binding energy,the root-mean-square radius,and the density distribution of the nucleon,but also describe the exotic properties of the nuclei far from the stable line,such as the halo（skin）phenomena,the energy-level inversion,the magic number change and so on.It is quite effective to describe both the spherical nuclei and deformed nuclei.In this paper,the complex momentum representation is combined with the covariant density functional theory,and the RMF-CMR theoretical model is established.Starting from the Lagrange density,the Dirac equation describing the nuclear motion,the Klein-Gordon equation of the meson and the electromagnetic-field equation of the photon are obtained with the classical variational principle.Furthermore,the wave function describing the nuclei is expanded with the momentum base（?）.The Dirac equation is solved in the momentum space.The theoretical formula is derived and the numerical program is designed.This model is adopted to study the exotic properties of the neutron-rich nuclei in the medium-mass region.The potential energy surface is obtained and the shape evolution of the medium-mass nuclei is analyzed.2.The research about the exotic structure of nuclei ⁷⁵Cr and ⁷⁷Fe in medium-mass region with the CDFT-CMR modelThe exotic nuclei in medium-mass region have attracted extensive attention in nuclear physics recently.The resonant states are thought to play a critical role at the formation of these exotic phenomena.In this work,the RMF-CMR theory with the parameter of NL3*is first proposed to study the deformed nuclei in medium-mass region.Taking ⁷⁵Cr and ⁷⁷Fe as examples,we obtain the results of the potential energy surface,the single particle energy level（bound state and resonances）and its evolution with deformation parameters,the wave-function configuration occupation probabilities and the radial density distribution of the energy level occupied by the last valence nucleon,respectively.Based on these results,it could be found that the exotic halo phenomena appear in the deformed nuclei ⁷⁵Cr and ⁷⁷Fe.This conclusion is in good agreement with the results calculated by other theoretical method.It is quite important for experimenters to explore the exotic halo structure of deformed nuclei in medium mass region.3.The systematic study on the exotic structure for Fe and Cr isotopesSince the RMF-CMR method is successful in describing the exotic nuclei ⁷⁵Cr and ⁷⁷Fe,we adopt this method to systematically study the even-even ^66-86Fe and ^54-80Cr isotopes.Similarly,we obtain the single particle energy levels（the bound states and resonances）and their evolution with the mass number A,the root-mean-square（rms）radius and the radial density distribution of the levels occupied by the valence neutrons.From the calculated results,we find that the valence neutrons in ⁷⁸Fe,⁸⁴Fe and ⁷⁶Cr occupy the weakly bound level.In addition,it is also seen that the rms radius increase abnormally and the radial density diffuses prominently in the nuclei ⁷⁸Fe、⁸⁴Fe and ⁷⁶Cr.It is meaning that the neutron-rich nuclei ⁷⁸Fe,⁸⁴Fe and ⁷⁶Cr are most likely halo candidates in the medium mass region,which can provide guides for exploring the exotic nuclei in medium-mass region in experiment.4.The development of the CMR-GF method and its application to the n-αscatteringThe resonant states play an important role in the nuclear scattering.In order to study the elastic scattering of n-αsystem,the Green’s function method is combined with the complex momentum representation,and the complex momentum-representation-Green-function approach is established.By transforming the Schr?dinger integral equation into the symmetrical matrix equation,we can obtain the bound states,resonant states and continuous spectra of the system.The resonant states can be separated from the continuum and clearly exposed in the complex plane.We study the resonances and its effect on the continuum level density,phase shift,and cross section.The results indicate that there is a close relationship between the resonances and scattering,the peaks in the physical quantities of the scattering are mainly derived from the contribution of the resonant states.The results obtained from the theoretical calculation are in good agreement with the experimental data.