【作者】 王大理；

【导师】 黄时中；

【作者基本信息】 安徽师范大学 ， 原子与分子物理， 2004， 硕士

【摘要】 本文以双电子原子结构的拉卡理论和类氦离子的非相对论原子结构的计算结果为基础，利用不可约张量理论，较为系统地研究了类氦离子的相对论效应和精细结构，包括相对论质量修正、达尔文修正、电子与电子之间接触相互作用、轨道-轨道相互作用、自旋-自旋相互作用、自旋-其它轨道相互作用以及自旋-轨道相互作用。具体内容包括： 首先，借助角动量耦合理论，将多电子原子哈密顿算符中的自旋-自旋、自旋-其它轨道以及轨道-轨道相互作用全部改用球张量表示，这种球张量形式的优点在于已将原子哈密顿算符中的径向、角向和自旋部分完全分开，从而便于计算矩阵元，而且角向矩阵元可以方便地利用不可约张量理论来进行计算。 然后，利用不可约张量理论，在|LSM_LM_S〉表象中导出了双电子原子中各种相对论效应，包括相对论质量修正、达尔文修正、电子间接触相互作用以及轨道-轨道相互作用对非相对论性能量进行修正的理论计算式；在|LSJM_J〉表象中导出了双电子原子精细结构能级(包含自旋-自旋、自旋-其它轨道和自旋-轨道相互作用)的一般表达式，同时导出了与光谱实验数据密切联系的自旋-自旋精细结构参数和自旋-轨道精细结构参数的理论计算式。在这些推导中，完成了所有角向积分和自旋求和计算，相应的结果用3j、6j、9j符号和待定的径向矩阵元来表示。这部分推导工作是严格的，没有引进任何近似，其中轨道-轨道相互作用、自旋-自旋相互作用和自旋-其它轨道相互作用能的理论计算式的推导过程比较复杂，在以前的文献中没有给出这些相互作用能的具体推导过程。 最后，以上述工作为基础，具体计算了类氦离子的(1s2p)组态的各种相对论修正项的量值和精细结构能级之值。这部分工作的重点是计算径向矩阵元。在这一工作中，我们对单电子径向函数作了近似处理，即只取斯莱特型单电子径向波函数(STO)的领头项，其形式与类氢离子的径向函数相似。采用这种近似的优点是计算过程的中间步骤非常清晰，不足之处是计算结果的精确度(与实验相比较)只能达到99％。我们也开展了采用斯莱特型单电子径向波函数进行计算的工作，但由于工作量大，目前尚未完成。 总之，本文为双电子原子能级的相对论修正和精细结构的理论计算提供了一种新的方法，包括原子哈密顿算符的球张量表示方法、原子哈密顿中各种相互作用项的角向矩阵元和自旋求和的计算方法，以及径向矩阵元的近似计算方法.并将这些方法具体用于计算类氦离子的有关能态，计算精度可以达到99%。更多还原

【Abstract】 In this thesis, based on Racah method of two-electron atom and non-relativistic energy structure for Helium-like atoms, the relativistic corrections and the fine structure of Helium-like atoms, including the relativistic mass correction, the Darwin correction terms, the electron-electron contact terms, the orbit-orbit interaction, the spin-orbit interaction, the spin-other-orbit interaction and the spin-spin interaction, are studied systemically using irreducible tensor. Concretely, the main works of this thesis are as follows.Firstly, with the help of angular momentum coupling theory, the Hamiltonian for multi-electron adorns is rewritten in terms of spherical tensors. The advantage of this form is that the radial, angular and spin parts are separated completely, which makes it easy to calculate the angular matrix elements by means of irreducible tensor. Secondly, Theoretical expressions of the relativistic corrections including the relativistic mass correction, the Darwin correction terms, the electron-electron contact terms and the orbit-orbit interaction which contribute to the non- relativistic energyfor two-electron atom are theoretically derived in the LSMLMS scheme. Generalexpressions of the fine structure energy levels for two-electron atom including the spin-spin interaction, the spin-orbit interaction and the spin-other-orbit interaction inthe LSJMJ scheme are derived. Theoretical expressions of the spin-spin andspin-orbit interaction fine structure parameters that are generally determined by experimental data of spectroscopy are derived. In the course of these derivation, the orbital integrations and the summations over spin are completed and are presented3j, 6j, 9j symbols and the radial matrix elements. These derivations are strict andno approximate are introduced. The derivations for the orbit-orbit interaction, the spin-spin interaction and spin-other-orbit interaction, which are fairly complicated, have not been given in the previous literatures.Finally, the value of the various rclativistic corrections and the fine structureenergy levels for (1s2p) configuration of Helium-like atoms are calculatedconcretely. The calculation of the radial matrix elements is particularly important in this part. In this work, we have made an approximate to the one-electronics radial function, namely only the leading term of Slater-type orbital (STO), which is the same as the modified hydrogen-like wave function, are taken into consideration. The advantage of using this approximate is that the middle step of the calculation course is very distinct, while the shortcoming is that the precision of calculated results, comparing with the experiment, can only be up to 99%. The work that uses Slater-type orbital to calculate the radial matrix elements is in progress. Because the workload is big, it has not been accomplished at present.In a word, a new method that theoretically calculates the relativistic corrections and the fine structure of the energy levels in two-electron atom, including the atomic Hamiltonian expressed by spherical tensors, the calculation of the angular matrix elements and the summations over spin of the various interactions in the atomic Hamiltonian, and the approximate calculation of the radial matrix elements, has been provided in this thesis. The method is concretely applied to calculate the concerned energy states of Helium-like atoms, and the calculation precision can be up to 99%.更多还原