| Alkaline-earth metal ions constitute of a close shell core and a single valence electron, and are important research systems in precision measurement and cold atomic physics for their simple electronic structures. Theoretical calculations of the atomic structure and experimental measurements of transition spectrum for alkaline-earth metal ions have important applications in exploring the basic physical constant variation, the study of atomic PNC and the development of optical frequency standard. Polarizability as the basic properties of the atom, describes the response of the atomic electronic cloud distribution on external electric field. Researchers pay more and more attention to the polarization study of alkaline-earth metal ions. Be+ has the simplest electronic structure in alkaline earth metal ions, and is also one important member of few body systems. The precision calculation of its polarizability can be used as a reliable way to testing new many-body calculation methods. Be+、Mg+、Ca+、Ba+ can be used as the coolants in the sympathetic cooling of other ions. For the long lifetime of the dJ state, Ca+、Sr+、Ba+、Ra+ would be good candidates for the optical clocks. Ca+ and Sr+ optical clock have been well developed, and their uncertainties have reached to 10-17. Ba+ optical clock and Ra+ optical clock are still on the stage of research. The accurate calculation of their polarizabilities can provide reliable theoretical input values for the experiment on cooling and trapping ion, analyzing blackbody radiation frequency shift and Ac/Dc stark frequency shift. In addition, the specific experimental measurement of atomic polarizability is challenging, and the available polarizability of experimental measurements is limited. Therefore, the reliable theoretical value of atomic polarizability becomes very significant.In this thesis, the Dirac-Fock plus core polarization (DFCP) method is employed to calculate the valence electronic wavefunctions and energy level structures, with the semi-empirical model potential as foothold and the Dirac-Fock equation as a starting point. The semi-empirical method can effectively avoid the complexity of ab initial methods, and can greatly improve computing speed of the energy levels, wavefunctions and transition matrix elements. What is more, the Dirac-Fock plus core polarization method can provide enough precise theoretical calculation value of static polarizability and reliable theoretical calculation value of dynamic polarizability and magic wavelength. The main works in this theses includes:(1) Using the core polarization potential method, the ground-state dipole polarizabilities of alkaline-earth metal ions and the electric quadrupole polarizabilities are calculated, as well as the dipole polarizabilities of first four low-lying excited states. The present calculated results have been compared with the values of the first principle calculation, and some transition matrix elements and their corresponding static polarizability contributions are given.(2) The dynamic dipole polarizabilities of the ground state and the first four low-lying excited states for alkaline earth metal ions are calculated, and analyzed by plotting the curves. According to the curves of the dynamic poaprizabilities of Mg+, Ca+, Sr+, Ba+ and Ra+, we identified all magic wavelengths up to the ultraviolet regime for s1/2-p1/2、s1/2-p3/2、s1/2-d3/2、 s1/2-d5/2 transitions. Furthermore, for Ca+, Sr+, Ba+ and Ra+, the contributions of the individual transitions to the dynamic polarizabilites of s1/2, d3/2, d5/2 states at the magic wavelength are shown.(3) We discussed the applications of magic wavelength in determining reduced matrix elements and theoretical estimation of heating rate of the ion in the laser field at the magic wavelength. |
