【作者】 赵霞；

【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， 硕士

【摘要】 近年来,强外场中高激发态原子的光吸收现象吸引了人们的广泛关注和研究兴趣,主要是由于在趋于电离域附近,原子的量子行为变为经典混沌。半经典闭合轨道理论由于具有物理图像清晰、应用范围广泛等特点被普遍用来解释此类现象,成为实现联结经典理论和量子混沌的重要桥梁,并是研究和发展量子混沌概念的重要手段。对于最简单的氢原子体系,人们已经从量子和经典两方面对其与各种含时和不含时外场相互作用时量子跃迁过程中的多周期现象进行了深入研究,这些外场包括静电场、静磁场、平行电磁场、垂直电磁场、线性极化以及圆极化的微波场等。近金属表面的里德堡原子体系是近年来又一个备受关注的重要的理论模型。在这一模型中,金属板对氢原子的作用充当外场的作用,原子与金属表面间的距离d对里德堡原子的性质起关键性作用。当原子和金属表面间的距离较大时,二者的相互作用较弱,微扰论成立;随着原子和金属表面间距离d的减小,二者的相互作用越来越强,规则运动和不规则运动同时存在,导致混沌现象产生。随着原子与金属表面间距离d的变化,它能够实现多种动力学效应的模拟:可以模拟瞬态的van der waals相互作用;可以模拟原子在强电磁场中的Stark-Zeeman效应;也可以模拟强磁场中的抗磁效应。本课题中,我们首次采用闭合轨道理论的方法,对近金属表面里德堡氢原子的运动性质随着原子与金属表面距离d变化的情况进行了研究,并计算了常标度能量下近金属表面里德堡氢原子的回归谱。(1)首先给出近金属表面原子体系的理论模型,推导出体系的哈密顿量,介绍了标度律,进行了半抛物变换消除哈密顿量的库仑奇异性,并描述了体系的动力学性质和闭合轨道理论下的物理图像。(2)简单介绍EBKM量子化方案和态密度理论,在此基础上提出闭合轨道理论的基本物理思想,并运用闭合轨道理论推导出反映原子光吸收现象的平均振子强度密度。为了解决闭合轨道对激发态能量的依赖性,我们在标度律的基础上引入了回归谱的概念。(3)根据经典正则方程,我们找出了近金属表面氢原子电子稳定的闭合轨道,并由这些轨道计算得到回归谱。由计算结果分析得出,临界距离d c附近是个分界点,此处轨道数目最多。当d > dc时,轨道越来越少;当d < dc时,亦是如此。在临界距离d c附近,当d =1800,即ε=?1.44时,电子的运动性质和轨道性质等特征与电场加平行弱磁场中氢原子电子的特征相像。为此,我们计算了此时金属表面氢原子的回归谱,并对电场中氢原子从标度能ε=?2.0到ε=?0.8做了谱计算,我们将两种情况下的谱逐一作了比较,结果表明,ε=?1.4时,二者对应最好。本论文共分为五章。第一章为综述,主要从总体上介绍了闭合轨道理论提出的历史背景及发展情况,同时介绍了近金属表面里德堡原子体系的特点及研究现状。第二章介绍了近金属表面里德堡氢原子体系的理论模型和物理图像,并介绍了体系的标度性。第三章给出闭合轨道理论。第四章是我们的计算结果。在这一章中,我们计算给出了近金属表面里德堡氢原子的闭合轨道,并分析了轨道随着原子与金属表面距离变化的情况。我们通过对d =1800时电子的运动情况分析出,此时金属板的作用近似于电场加平行弱磁场。为了验证我们的推论,我们将氢原子在近金属表面的回归谱与电场中的谱进行了比较,结果表明二者在标度能接近时有大体的对应。第五章是本文的结束语,简要的对本论文进行了总结,并为今后的工作进行了展望。更多还原

【Abstract】 Last a few years, the photo-absorption phenomena of highly excited atoms in strong external fields has attracted much interests and investigation. Largely because these non-separable quantum systems turn classically chaotic as they approach the ionization limit. The semiclassical closed-orbit theory has been extensively applied to explain the phenomena due to its clear physical picture and wide availability. It has already become an important link between classical theory and quantum world, as well as a powerful tool to study quantum chaos.For the simplest system, the hydrogen atom, much researching works of the multi-period phenomena in the photoabsorption process by interacting with time-independent and time-dependent external fields have been achieved, which fall into the quantum and classical aspects. Some of the external fields are: static electric field, static magnetic field, combined electric and magnetic fields in parallel configuration, combined electric and magnetic fields in perpendicular configuration, mass anisotropy,and linearly and circularly polarized microwave fields. Recently much attention is focused on the system of Rydberg atom near a metal surface. In this model the metal surface acts for the external field and the distance d between the metal surface and the hydrogen atom plays a critical role in the dynamical properties of the system. When the distance d is large, their interaction is weak, so perturbation theorem may be applied. Whereas for strong interplay, regular and irregular motions merge with each other and chaos appear. With the varying of the metal-surface distance, the system can cover many dynamical effects-- instantaneous van der Waals interaction, Zeeman-Stark effects, diamagnetic effects in strong fields and so on.In this thesis, we study how the dynamics of the hydrogen atom near a metal surface vary with the atom-surface distance using the closed orbit theory for the first time. And, withal, we calculate the recurrence spectra at a constant scaled energy.(1) Firstly we introduce the theoretical model of hydrogen atom near a metal surface, derive its Hamiltonian,introduce the scaling rule, make a semi-parabolic transformation to remove the Coulomb singularity and describe its physical picture under the scheme of the closed-orbit theory.(2) We introduce the EBKM theorem and density of states theory simply, then represent the physical idea of the closed-orbit theory. Finally we display the formula of average oscillating density based upon the theory. In order to solve the dependence of the orbits on the energy, we apply the concept of the recurrence spectroscopy.(3) According to the classical canonical equation, we find all the steady closed orbits and consequently calculate the recurrence spectra. It demonstrates that the critical distance d c is the critical point. Here the number of the orbits is the most. Whereas in the region d > dc the number of the orbits gets lesser and lesser, this also does for d < dc. In the vicinity of d c, with the distance of d =1800, namelyε=?1.44, the effects of the movement of the electron and the orbits is most like that in electric field plus a parallel weak static magnetic field. Thereby we calculate the recurrence spectra of the hydrogen atom in a electric field with the scaled energy range fromε=?2.0 toε=?0.8, then compare them with the spectra of the hydrogen near a metal surface. It shows that they have the best correspondences whenε=?1.4.The thesis works include five chapters. The first chapter is summarization, which briefly introduces the background and the development of the closed-orbit theory. We also describe the trait and progress on the hydrogen atom near a metal surface in this passage. Chapter two presents the theoretical model and physical picture of the system and explains the scaled properties of the system. In chapter three, we reconsider the closed-orbit theory and its form at present. Chapter four is our calculation. In this section, we first calculate the closed orbits of the hydrogen atom near a metal surface, analyze then the varying of the orbits along with the atom-surface distances. We find that when d =1800, the movement of the electron is analogous to the applied static electric field plus a parallel weak static magnetic field. In evidence we calculate the recurrence spectra of the hydrogen atom in a electric field, and compare it with the spectra of the hydrogen near a metal surface. It is shown that there is a consonance between them when their scaled energy approaches to each other. As the conclusion, in the last chapter, we briefly summarize the total subject and give an expectation for the future work.更多还原