Research Of The Polarizability And Electric Quadrupole Momnet Of Cadmium And Ytterbium Ions

Cadmium（Cd）atom and Ytterbium（Yb）ion are important atomic system for precise measurement of time frequency,where Cd 5s^{2 1}S₀-5s5p ³P₀ and Yb⁺6s^{2 2}S_1/2-4f¹³6s ²F_7/2 clock transition will become new generation time frequency standard.In this paper,the relativistic multi-electron structure calculation of the precise spectra of Cd atoms and Yb⁺ ion is carried out.In the calculations,the relativistic effect and electron correlation are strictly considered,the energy level structure and transition properties of clock transition are studied,and the the physical origin of various errors is discussed.The main content includes:（1）The method of deal with multi-electron atomic system by relativistic couple-cluster method is analyzed.The finite field fitting formulas of electric dipole polarization and electric quadrupole moment are given,the electronic correlation effect caused by various couplecluster is compared and analyzed,and the calculation scheme of different couple-cluster methods is proposed according to the energy level structure characteristics of the specific atomic system.（2）The high-precision data of energy levels and atomic properties of Cd 5s^{2 1}S₀ ground state and 5s5p ³P_0,1,2,¹P₁ low-excited states are widely used in optical frequency standard.The electric dipole polarization and electric quadrupole moment of Cd 5s^{2 1}S₀ ground state and 5s5p ³P_0,1,2,¹P₁ low-excited states of the spin angular momentum resolution are calculated,and the high-precision data are recommended.Through the base group optimization and an increase in the level of electronic coupling,we control the finite field calculations accuracy at 0.1-4.6%（electric dipole polarization）and 2.7-4.8%（electric quadrupole moment）.Based on the spin dependent relativistic couple-cluster calculations data,we evaluate the contribution of spin-orbit coupling effects to the scalar and tensor polarizability of the Cd atom.Our results show that the finite field method can be effectively applied to the calculation of high-precision data,the calculations include polarization of the candidate optical atom clocks.Farther more,it provides an effective way for the theoretical evaluation of the various energy level frequencies of the clock transition.（3）Extending the computational model to the 4f open shell layer electronic structure of the Yb⁺ion.The Yb⁺ion two clock translations of 6s ²S_1/2-5d ²D_5/2 and Yb⁺6s ²S_1/24f¹³6s ²F_7/2 are studied.First,the accurate energy level data of Yb⁺6s ²S_1/2 ground state and ²P_3/2,²D_3/2,5/2,²F_5/2,7/2 low-excited states are obtained by relativistic couple-cluster theory.Farther more,the high-precision data of electric quadrupole moment of Yb⁺5p ²P_3/2,5d ²D_3/2,5/2 and 4f¹³6s ²F_5/2,7/2 low-excited states are obtained under the framework of finite field theory.Our results are consistent with the experimental data available,where the data of the electric quadrupole moment of the Yb⁺²F_7/2 state are different from the early theoretical results of the expectation method,however ²F_7/2 state data consistent with experimental data.Then the electric quadrupole moment data Yb⁺5p ²P_3/2 are given for the first time.Above results will be helpful for the accurate evaluation of the electric quadrupole moment frequency shift of the current Yb⁺ion optical clock experiment.