Progress in research of the complex scaling method

Abstract

In this paper 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. Secondly, we have presented the theoretical formalism of complex scaling method. 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. 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. With 31Ne 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 in 31Ne. The bound and resonant levels in the deformed potential are in full agreement with those from the multichannel scattering approach. Finally, we give the summary of this paper.