近年来，人们利用魔法囚禁(magic-tranpping)技术，实验上已实现了精度为10^{-18}的光学原子钟，进一步提高原子钟的精度成为下一步研究目标。由于超极化率以及光与原子的高阶相互作用可以导致10^{-17}到10^{-19}的不确定度，因此，对这些效应的研究将变得非常重要。本项目拟基于非相对论半经验极化势组态相互作用（CICP）方法，发展一套L-Spinor基的全相对论CICP方法和程序，并结合多组态Dirac-Fock方法，精确计算单电、双价电子原子体系的波函数和偶极以及多极跃迁矩阵元，详细研究这些原子的偶极极化率、多极极化率以及超极化率。同时，我们将系统地研究动态超极化率以及光与原子的高阶相互作用对动态Stark效应的贡献，进一步确定高精度的魔法波长（magic-wavelength）和调谐波长（tune-out wavelength)，为相关实验提供理依据。

Recently，the fractional uncertainty of optical lattice clock has achieved 10^{-18} by using particular magic wavelengths. Further development of even more precise is a destination for the researchers. Because the fractional shifts of the clock frequency due to hyperpolarizablility of the atoms and the multipole interactions of atom-lattice field are in the range of 10^{-17}-10^{-19}, to this end, the role of the higher-order and multipole atom-lattice interaction should be considered in the further studies. In the present project, based on the configuration interactions with a semi-empirical core potential (CICP) approach, a full relativistic configuration interactions with a semi-empirical core potential (RCICP) method and program will be developed. In this method, the L-Spinor basis which has been developed by Grant and Quiney (Phys. Rev. A 62, 022508 (2000)) will be used. Combining RCICP method and the Multi-Configuration Dirac-Fock (MCDF) method and corresponding packages GRASP92/2K, the wave functions and dipole and multipole matrix elements of one-electron and two-electron atom systems will be calculated. Meanwhile, the dipole and multi-pole polarizabilities and hyperpolarizabilities for these atoms will be studied. The contributions of the hyperpolarizabilities and atom-lattice multipole interactions on the ac stark shift will be studied systematically. Further more, the high accuracy magic wavelength will be determined, in which the high order effects will be considered in detail.