Investigation On The Relativistic Corrections And The Fine Structure Of The Energy Levels In Helium-like Atoms

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%.