【作者】 高嵩；

【导师】 林圣路；

【作者基本信息】 山东师范大学 ， 原子与分子物理， 2007， 博士

【摘要】 强场中原子光吸收谱的强共振特性已引起人们的多年的关注,它是研究和发展量子混沌概念的一个典型实例。这种现象涉及高里德堡态原子结构和极端条件下物质抗磁性、电子关联及不可积体系运动规律等基本问题。半经典闭合轨道理论由于具有物理图像清晰、可近乎解析处理等特点被普遍用来解释原子或离子在强外场中的光吸收现象,成为实现联结经典理论和量子世界的重要桥梁。同时,该理论具体展现了强场条件下原子分子动力学行为。标度律及傅立叶变换的应用构成全新的回归谱学方法,成为原子分子谱学新进展。随着应用范围的扩展,原来的理论方法面临新的挑战,主要困难来自两方面:一是在能量或外场达到某些特殊点时,有分岔现象产生。由于轨道分岔形成的聚焦作用,导致波函数在分岔点附近发散,闭合轨道理论在分岔点附近不再适用;另一方面是对于多电子原子,由于原子实的散射,使轨道数目迅速增加,增加了问题的复杂性。这些闭合轨道多为不稳定组合轨道,没有有效的识别和分类方法,难以得到收敛结果。因此,有必要在半经典理论框架中对原有理论方法进行适当的改进和推广。从本质上看,回归谱学是有限分辨率的,为了发展高精度谱分析,在适当情况下,把回归谱量子化是可行的。调和反演就是可供选择的有效方法之一。针对上述问题,我们主要进行了以下几个方面的研究:1、研究了分岔现象对平行电磁场中H ?光剥离电子流分布的影响。在这里我们研究的对象为远离核的垂直于外场的平面上电子流的分布情况。在这里我们将闭合轨道理论推广到开轨道,提出一种具有复杂结构的光剥离显微术。这一方法可以用于精确测定激光和场参数。分析了电子轨道在垂直于外场的平面上的分布情况:以磁场由小到大逐渐变化为例,分别利用相空间中ρ- p_ρ的关系曲线（ρ为光剥离电子到达观测平面上的点到Z的距离, p_ρ为其相应的动量）和ρ-θ₀曲线（θ₀是光剥离电子的初始出射角）随磁场变化。讨论了折叠式焦散点的产生和对电子轨道数目的影响。为了得到在垂直于场的平面上H^-光剥离电子流通量的分布,在焦散点附近,可以利用统一近似的方法对波函数进行修正,消除发散,得到了符合实际的结果。近两年来国际上其他研究小组也发表了几篇关于平行电磁场中的负离子光剥离电子流通量的文章,但他们考虑的是各向同性的离子源（s波）,而我们采用的H ?的波函数是各向异性的（p波）,因而具有较强的方向选择性。利用坐标和相应动量的关系曲线随系统参数（如磁场）的变化而导致的曲线拓扑结构的变化分析分岔和反分岔现象,是我们提出的一种全新的分析轨道变化趋向的方法,比前人所用的方法简便而且更为直观。2、研究了分岔对电场中锂原子的回归谱的影响利用包含模型势作用的分区自洽迭代方法,引进标度律和有效普朗克常数eff的概念,以使理论计算结果能与将来的实验（量子谱）进行直接比较。用上述方法计算了Li里德堡原子在电场中的回归谱。从中明显看出,由于原子实散射而出现的新的共振结构可以归结为相应氢原子的标准闭合轨道的组合的贡献。应用正则方程计算高激发态电子的经典运动情况,讨论了分岔和反分岔产生的边界能所满足的条件,分析了轨道分岔的基本原因和形式,得到了实轨道存在的区域和鬼轨道存在的依据。选取的标度能量为ε=-2.7,在这个能量附近,轨道分岔很多。我们既考虑了实散射影响,又考虑了轨道的分岔效应。为了解决由于轨道分岔引起的波函数的发散问题,我们采用统一近似方法对电场中的Li原子Stark谱进行了修正。我们的工作既是对半经典理论的推广,又是对该理论的验证和完善。另外,因为Li原子体系是一个在实验上可以被测量的体系,所以从另一方面来说,我们得到的结果对于实验研究具有重要的参考意义,同时也有助于开展对更复杂原子体系以及外场结构情况的研究。3、利用调和反演的方法对电场中锂原子回归谱进行的高精度分析,即把回归谱量子化,抽取相应的本征值。引入了一种高精度的谱分析的方法——调和反演,对以上得到的回归谱进行进一步的分析。调和反演的方法,突破了常规傅立叶变换中测不准关系的限制,得到了原来闭合轨道理论或周期轨道理论得不到的本征值,从而给出高分辨率的谱。这里,首次将此分析方法引入到非氢里德堡原子的情况中。无论是对于闭合轨道理论还是对调和反演这种高分辨率分析方法的发展都起到了推动作用。论文共分为6章。第一章为综述,主要从总体上介绍了半经典闭合轨道理论的要点及其发展,我们所选的课题的意义及本文重点进行的工作。第二章详细地分析了平行电磁场中H ?光剥离电子轨道的分岔情况,讨论了当外场（特别是磁场）变化时,在探测平面上电子轨道的变化情况。第三章讨论了分岔现象对于垂直于外场的平面上电子流通量的影响,说明光剥离显微术的原理。第四章介绍了分区自洽迭代方法,引进标度律和回归谱概念。分析了锂原子Stark效应中的轨道分岔现象,并采用统一近似方法描述了电场中分岔点附近的波函数,同时考虑了组合轨道的影响,对半经典闭合轨道理论所得结果进行了修正。第五章是对于电场中锂原子回归谱利用调和反演的方法进行分析,得到了高精度的谱。第六章是本文的总结,对已有的工作做简要概括并讨论了应用半经典闭合轨道理论所遇到的问题和困难,对今后发展前景进行了展望。更多还原

【Abstract】 The strong resonance structures of photo-absorption spectra of high Rydberg atoms and molecules in strong external fields have attracted much interest in recent years. They have been typical examples for studying the semiclassical theory and quantum chaos. And these phenomena involve many basic questions such as high Rydberg atoms’structure, the matter diamagnetism in extreme conditions and electron correlation, etc. Semiclassical closed-orbit theory has been a powerful tool for investigating photo-absorption properties of atoms, negative ions and molecules in externally applied strong fields since it was proposed in the 1980s, due to its clear physical picture and wide availability, and has become an important link to connect the classical and quantum theory. In the past decades, the closed-orbit theory has successfully been applied to highly excited states of atom in various external fields; the validity of the closed-orbit theory has been fully confirmed.However, with the development of researches, there are two new challenges for the primary theory: The first one is because that the effect of bifurcation is obvious at some special value of the parameters, where the closed-orbit theory is failure because the wave-function would become infinite at a focus or caustic passed through the origin. The other one is for the reason of core-scattering. The number of closed-orbits increases rapidly; and most orbits are unstable and are not easily realized recognized and classified, which makes the problem more difficult to work with. So it is imperative to correct and extend the primitive closed-orbit theory due to the closed orbit theory is essentially low resolution.Pursuing above problems, we have mainly done the following work here:1. We investigate the effects of bifurcations on electron motion and then the flux distribution of photo-detached electrons of H^- in parallel electric and magnetic fields. We pay our attention particularly to the interference of electron waves far from the atomic core in configuration space. Considering the electron orbits are no longer“closed”and the system possesses axis symmetry, the electron’s classical motion and the bifurcation of classical orbits can be described inρ-pρandρ-θ₀ diagrams. （hereρis the distance from the original of the observation plane, p_ρis the corresponding momentum, andθ0 is the angle between the initial outgoing direction and the z-axis, respectively.）The divergence in the wave function associated with the bifurcation of classical orbit is specified by using a semiclassical uniform approximation. We calculate the detached-electron flux distribution images on the screen using the mixed position and momentum representation for the detached-electron. It is demonstrated that the major features of the detached-electron images are rings, which can be controlled by adjusting the magnetic field. Recently several interesting articles have appeared addressing the theoretical questions of detached-electron distribution in parallel fields. A point source was used to simulate the initial detached-electron in all these works. An isotropic point-like source was used. However, the results cannot be directly applied to the photo-detachment of H ? because H ? is in an s-wave state and the detached-electron is a p-wave. It is the first time to investigate this phenomenon. What makes the current system more interesting is that the classical orbits of the photo-detached electrons bifurcate with the external parameters such as the photon energy and the magnetic field strength. The relationship between the ring patterns in the detached-electron images and the bifurcation of classical orbits is discussed usingρ-p_ρdiagrams.2. We analyze the effects of bifurcations on the recurrence spectra of Li Rydberg atom in electric field.In this thesis, we present theoretical computation by using region-splitting consistent and iterative method together with the standard model potential, of course, introducing a new scale property and a concept of an effective Planck constant （ eff ） allows us to compare our results with the experiments in the future. From our results, we can see clearly that the new strong resonance structure can be refered by the combined closed-orbits.We study the Li Rydberg atom in electric field. The condition of bifurcation and anti-bifurcation has gotten. The regions for the real orbits and ghost orbits are separately determined. Because the dispersion of the wave function in the vicinity of bifurcation, we analyze the reasons why rising bifurcation and the forms of bifurcation at a constant scaled energyε= ? 2.7, then both the core potential and the bifurcation have to be taken into account. The divergences of Li Rydberg atom’s recurrence spectra in electric field are corrected by using the uniform approximations method. Our works are not only the extension but also the validation and supplement for the closed-orbit theory.3. An extended harmonic inversion method is applied to obtain highly resolved spectra of lithium atom in electric field.A powerful method for both the analysis of quantum spectrum and semiclassical orbit quantization is introduced. This method allows one to circumvent the confines of the conventional Fourier transform and to extract dynamical information from quantum spectra which has been unattainable before. It is the first time for this method to be applied to the nonhydrogen atom.This thesis is divided into six chapters. The first chapter is summarization, which chiefly introduces the development of semiclassical closed-orbit theory, includes its successful and encounters challenges. The bifurcation phenomena are analyzed in the second chapter in detail. The photodetachment electron flux is discussed in the next chapter. The region-splitting consistent iterative method is introduced in chapter 4, and the concepts of scaled law and recurrence spectra are presented. Then, we explain the phenomena of the bifurcations, where the wave function is described in scheme of the uniform approximates method so as to get correct results which include the core-scattered effects. We analyze the recurrence spectrum of Li Rydberg atom in electric field with the harmonic inversion in the chapter 5. Decimating the selected window frequencies and solving a set of nonlinear algebraic equations result in the eigenvalues that evidence corresponding quantum resonances hidden in low resolution spectra. In the last chapter we give some important conclusions of this thesis and an inspection to the challenge and the application of this theory is made.更多还原