复标度方法对共振态的研究
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摘要
本文首先介绍了单粒子共振态的研究意义、研究方法及研究进展。指出单粒子共振态的研究对于了解奇特核的物理性质具有重要意义。其次给出了复标度方法的理论框架,指出其出发点是引入坐标变换r→eiθr,且复标度变换要求满足ABC定理。接下来给出了复标度方法的相对论拓展,即Dirac-CSM方法和RMF-CSM方法。复标度方法研究共振态的几个实例也一并介绍。本文着重介绍了两个方面问题：第一、复标度方法被用于研究指数势和Morse势中Dirac粒子的共振问题。为了论证本文方法的适用性,计算结果和其它文献提供的结果进行了比较,可以发现,本文结果的非相对论极限值和其它的非相对论计算吻合得相当好。共振参数对势场形状的依赖性被进一步检查,敏感性被详尽分析。通过比较贋自旋双重态的能量和宽度,在本文模型中,很好的贋自旋对称性被发现。通过改变控制势场形状的三个参数,贋自旋对称和势场形状之间的关系被进一步研究。第二、我们发展了描述形变核共振态的理论。在描述形变核的Schrodinger方程中,通过引入复标度变换了统一描述束缚态和共振态的理论。以31Ne为例,检验了这种理论的适用性和有效性,并用这个理论系统研究了31Ne的单中子共振态,通过比较发现,我们获得的31Ne的单中子共振态的能量和宽度与耦合道方法的计算结果一致。尤其,我们获得的最低的两个共振能级和宽度呈现特殊的变化规律,能够很好地解释31Ne的形变晕现象。最后给出了本文的总结和展望。
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 r→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.
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 r→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.
引文
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