Li原子在平行电磁场中回归谱的半经典研究

【作者】 张秋菊；

【导师】 林圣路；

【作者基本信息】 山东师范大学 ， 原子与分子物理， 2001， 硕士

【摘要】 半经典闭合轨道理论由于具有物理图象清晰、应用范围广泛的特点，被普遍用来解释原子或离子在外场中的光吸收现象。该理论为研究量子谱的经典对应提供了强有力的工具；在研究经典混沌的量子体现中已取得很大成功。不论对规则运动的可积体系还是不规则运动的不可积体系都可以给出清楚的物理解释。该理论在研究H^-在各种外场下的光吸收以及氢原子、Li原子、He原子和O₃等在电场或磁场中的光激发，波包动力学等问题已经得到广泛的应用。 通过对多电子原子强场行为的实验和理论研究，人们发现，在其回归谱中存在着由氢原子轨道不能解释的强共振结构。这说明，研究多电子原子必须考虑离子实的作用，而且回归谱中应该有实散射峰的贡献。但当把闭合轨道理论推广到多电子原子时，主要由于离子实散射的作用，使轨道数目迅速增加，且多为不稳定轨道，不易进行分类，增加了问题的复杂性。本文采用了量子实散射的分区自洽迭代方法，就是利用量子亏损表示离子实的作用，实散射的轨道全都由氢原子的轨道组合而成。从而克服了这一困难，把闭合轨道理论应用到了平行电磁场中的Li原子上。 在本论文的工作中，我们在两个不同的标度能量下，应用包括实散射的半经典闭合轨道理论，计算了平行电磁场中Li原子的回归谱；讨论了该体系的标度性；并与同样情况下的氢原子回归谱作了比较， 硕士学位论文 摘要得出了预期的结果。主要进行了以下几项工作： （l）研究了该体系电于的经典运动规律，计算出了两个不同标度能量时的基本闭合轨道数目，以及每一个闭合轨道的出射角和返口时间。 （2）用半经典闭合轨道理论推导计算每条轨道第一次返口以及第n 次返回的雅可比量、经典振幅、经典作用量以及马斯洛夭指标等，从而定出电于的半经典波函数。 门)根据包括实散射的闭合轨道理论，进行标度变换和迭代计算。 （4）通过傅立叶变换，将光吸收谱由能量的函数转换成标度经典作用量的函数，得出平行电磁场中的回归谱图象，并与氢原于的结果相比较。验证了离于实对多电子原子回归谱的重要贡献。 在这一研究领域中，前人只是对电场或磁场单独存在的情况进行了理论分析和解释。对于电磁场同时存在的情况，这是第一次进行理论研究，这既是对半经典理论应用范围的推广，又是对该理论的验证和完善。另外，以前的绝大部分研究中，都是选取的电离阈以下的能量范围，即E＜0的范围，本文则选取了E＞0的范围。因为 ＊ 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，同时有助于对更复杂的体系，如 He、O；体系的研究。更多还原

【Abstract】 The success of the semiclassical closed-orbit theory lie in its clear physical picture and wide application sphere, so it can be used widely to explain photoabsorption of atom or ion in external fields. This theory has provided the strong tool for studying the classical correspondences of quantum spectra; and has gained the very big success for the quantum manifestations of classical chaos. No matter for integrable system associated with regular motion or the unintegrable system in irregular motion, and all can be given a clear physical explanation. The theory has got the extensive application in descripting the photoabsorption of H - in the various external fields , as well as the high excited states of hydrogen atom, Li atom, He atom and 03 etc in electric field or magnetic field,and Rydberg wave packet dynamics. Through the experimental and theoretical researches of the nonhydrogenic atoms in strong external feud, it is found that in the recurrence spectra of nonhydrogenic atoms there exist the new strong resonance structure, which can not be explained by the orbits of hydrogen atom , and it is neccesary to take the effects of the ionic core into account in case of the nonhydrogenic atoms,and the scattering peaks originated from ionic core should contribute to their recurrence spectra. When this 3 Abstract semiclassical closed-orbits theory is extended to nonhydrogenic atoms, the number of closed-orbits increase rapidly due to the effect of core-scattering, and most of those are unstable and are not easily classified , that make the problem more complicated. In this thesis, we have used region-splitting consistent and iterative method together with the quantum core-scattering that is by using of the quantum defects to show the core effects, and core- scattering orbits are all combinated by closed-orbits of hydrogen atom. Thus, having surmount these difficulties, semiclassical closed-orbit theory can be applied to Li atom in parallel electric and magnetic fields. Employing the semiclassical closed-orbit theory including quantum core-scattering, we calculated the recurrence spectra of Li atom in parallel electric and magnetic fields for two different scaled energy and compared it with the corresponding hydrogenic system, arrived at the expected results; we also carried out a scaling transformations, and checked the convergency. Our efforts are as follows: (1) We analysised the classical motion in two different scaled energy (s = 0.58 ands = 0.OO6at fixed scaled electric fields strengthf 0.036), obtained the number of closed-orbits, the outgoing angles, and the returning times. (2) In the semiclassical closed-orbit theory framework, we calculated the Jacobian and semiclassical amplitude and classical action as well as the Maslov index. We got the semiclassical wave function thus. (3) Based on the extending semiclassical approach, we made the scaling transformation and calculate the iterative solutions. (4) Via Fourier trasformation, the photoabsorption spectra can be written as the function of scaled classical action from the function of energy. Then, 4 Abstract we obtained the recurrence更多还原