Research On The Resonant States By The Complex Scaling Method

In this thesis, we have first introduced the importance of resonances in physics, and the methods of exploring resonances, as well as the recent progress on the resonance researches. It is pointed out that the study of resonances has important significance in understanding the physical properties of weakly bound nuclei. Secondly, we have presented the theoretical formalism of complex scaling method, and shown the starting point of complex scaling transformation by introducing a coordinate transformation râ†'eiθr, and the requirements of the complex scaling transformation being to meet the ABC theorem. Then we have introduced our development on the complex scaling method, i.e., the relativistic expansion of complex scaling method,(Dirac-CSM and RMF-CSM). Several examples on the applications of Dirac-CSM and RMF-CSM have also been introduced in two aspects.Firstly, we have applied the Dirac-CSM to study the resonances of a Dirac particle in a Morse potential. The applicability of the method is demonstrated with the results compared with the available data. It is shown that the present calculations in the nonrelativistic limit are in excellent agreement with the nonrelativistic calculations. Further, the dependence of the resonant parameters on the shape of the potential is checked with the sensitivity to the potential parameters analyzed. By comparing the energies and widths of the pseudospin doublets, well pseudospin symmetry is discovered in the present model. The relationship between the pseudospin symmetry and the shape of the potential is investigated by changing the Morse potential shaped by the dissociation energy, the equilibrium intermolecular distance, and the positive number controlling the decay length of the potential.Secondly, we have developed a complex scaling method for describing the resonances of deformed nuclei and presented a theoretical formalism for the bound and resonant states on the same footing. With31Ne as an illustrated example, we have demonstrated the utility and applicability of the extended method and have calculated the energies and widths of low-lying neutron resonances in31Ne. The bound and resonant levels in the deformed potential are in full agreement with those from the multichannel scattering approach. The width of the two lowest-lying resonant states shows a novel evolution with deformation and supports an explanation of the deformed halo for31Ne.Finally, we give the summary and outlook of this paper.