标题： 经典分支与量子壳的增强——反射非对称变形振子的系统分析—— 显示英文标题

标题： Classcial Bifurcation and Enhancement of Quantum Shells --- Systematic Analysis of Reflection-Asymmetric Deformed Oscillator ---

摘要： 研究了反射不对称变形谐振子模型的经典周期轨道与量子壳层结构之间的对应关系，作为四极和八极变形参数的函数。 周期轨道理论揭示了该不可积系统的量子能级结构的几个方面。 在量子能级密度的傅里叶变换中得到了良好的经典-量子对应，并证明了周期轨道分岔的重要性。 对二维变形参数空间中壳层能量的局部极小值进行系统的调查表明，在八极参数的有限值处确实出现了显著的壳层结构。 研究了表现出强壳层效应的区域与经典分岔线之间的对应关系，并指出了这些分岔的重要性。 显示英文摘要

摘要： Correspondence between classical periodic orbits and quantum shell structure is investigated for a reflection-asymmetric deformed oscillator model as a function of quadrupole and octupole deformation parameters. Periodic orbit theory reveals several aspects of quantum level structure for this non-integrable system. Good classical- quantum correspondence is obtained in the Fourier transform of the quantum level density, and importance of periodic orbit bifurcation is demonstrated. Systematic survey of the local minima of shell energies in the two-dimensional deformation parameter space shows that prominent shell structures do emerge at finite values of the octupole parameter. Correspondences between the regions exhibiting strong shell effects and the classical bifurcation lines are investigated, and significance of these bifurcations is indicated.