| dc.description.abstract | The investigations in the field of the quantum computer brings the importance of the understanding of the Quantum Electrodynamics (QED) properties of particles to the front line. By the various techniques of molecular cooling and trapping we remove the kinetics characteristics of the system. Thus, when the particle is trapped and doesn’t perform any movement we can test the physical characteristics such as total electronic energies of atoms and ions, energies of optical and X-ray transitions, hyperfine splitting constants that show the energy levels splitting, g-factors of bound electrons, that describe the magnetic and angular momentum of a particle, isotopic shifts, probabilities of electrical and magnetic transitions in atoms etc. The objective of this thesis is the high precision calculations of G-factor and Hyperfine structure splitting of different elements. By considering the existing results and literature, we perform the high accuracy calculations on H-like (one electron and nucleus), Li-like(three electrons orbiting nucleus) and B-like(five electrons orbiting nucleus) elements. Moreover working closely with experimental groups we perform calculations on lanthanide atoms. For these type of calculations, different type of contributions are to be taken into account, including correlation, relativistic, quantum electrodynamic, higher radiative corrections, and the contribution of the negative Dirac spectrum. It is also necessary to calculate the corrections arising from the the electric charge distribution and nucleus magnetic moment. We propose the approximate radiative single-particle potential that significantly improves the high-accuracy of the non empirical calculations of the QED corrections for calculating the electronic structure of atoms and molecules. In conjunction with the experimental measurements and fits, using the Multi Configurational Dirac-Fock-Sturm method (MCDFS), we have executed the extensive high-precision calculation for the electronic structure calculations of one of the lanthanide atoms, the Er. The interest of these calculations is explained in their multiple unpaired valence electrons, that have rich atomic energy spectra and exhibit various types of coupling between the electronic angular momentum J and the nuclear spin I of the atom. These calculations allowed us to obtain the magnetic dipole and electric quadrupole constants for the only stable fermionic isotope, 167Er and thus explain the theory behind the experiment of the laser cooling transitions. We then do various calculations to improve existing results for the determina- tion of the fine-structure constant. The approach of the calculations by the MCDFS method has been proposed for the calculations for the specific weighted differences of the g-factors of H-and Li-like ions of the same element. An accurate formula was obtained for the weight parameter, determined by requiring cancellation of the non- relativistic finite nuclear size corrections to various orders. We then demonstrated that weighted differences can be used for an effective cancellation of nuclear struc- tural effects. This independent scheme may be used to extract the fine-structure constant from a comparison of experimental and theoretical bound-electron g-factors with an accuracy improvement by orders of magnitude. The future prospect of the calculations for the many-electron systems like B-like particles are also outlined. | en_GB |
