| The polarizability, a fundamental property of the atom, can be considered as a measure of the response of the charge cloud to an external electric field. Studies of polarizabilities of neutral atoms and ions have been of great interest in many different physical applications which includes atomic clock and cold atomic physics. For exam-ple, the knowledge of static multi-pole polarizabilities of clock transition states are used to evaluate the blackbody radiation (BBR) shifts and Stark shifts; the knowledge of dynamic polarizabilities of atomic states can be used to identify the magic wave lengths in optical lattices, and construct the long-range dispersion potential which plays an important role in ultracold physics environment. However, precise measurement of po-larizabilities is quite challenging. The experimental values of polarizabilities of many elements are still not available, especially for the excited states. Therefore, accurate theoretical studies of atomic and ionic polarizabilities are of particular interest and importance. In this work, we apply relativistic configuration interaction method, rela-tivistic atomic structure model method and perturbed all-order method to calculate the polarizabilities of two electron atomic system, monovalent atomic system and close-shell atomic system, respectively. The main constants include the following four parts:(1) Using B-spline configuration interaction method, the convergence of S-wave single and triplet states and the ground state for He are studied. At the same time, we also investigate the contribution from negative energies states. Then we compute the fine structure energies of2P states and the static dipolar polarizabilites of low-lying states for He-like ions, and highlight the importance of relativistic effects and the Breit interaction effects for polarizabilities.(2) Since the complexity of ab initial many-body methods, we develop a simple and effective relativistic atomic structure model method. We apply this method to calculate the static polarizabilities and two-body dispersion coefficients of alkali metal atoms, and have a comprehensive comparison with ab initial many-body methods. On the other hand, we compute the dynamic polarizabilities of the low lying states of Ca+, and determine a number of magic wavelengths at convenient photon energies for transition states4S1/2--4p1/2,4S1/2--4p3/2,4S1/2--3d3/2and4S1/2--3d5/2. We also discuss how to use these magic wave lengths in the experiment case.(3) Combing relativistic atomic structure model method with many-body pertur-bation theory method, we calculate the hyperfine structure constants for alkali metal atoms. According to the basic physical mechanism of hyperfine interaction, an effective interaction potential model is constructed to approximate the hyperfine interaction. Then we use this model method calculate the hyperfine Stark shifts of the ground s-tates for alkali metal atoms, and compare with many-body perturbation method and experiment measurements available.(4) Applying many-body perturbation theory method, we calculate the second and third correlation energies of He, Ne and Ar. We also investigate the reason of slow convergence for the third correlation energies. On the other hand, we calculate the correlation energies of O6+and Ne using all-order method. We also highlight how to deal with the Breit interaction in all-order method by comparing with relativistic configuration interaction method. Finally, we develop a so called perturbed all-order method which is based on perturbation theory and all-order theory. Then we apply perturbed all-order method to calculate the static polarizabilities of some close-shell atomic systems, and discuss the contributions from different many-body parts to total polarizabilities. |
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