Application of many-body theory methods to atomic problems.

There is strong interest in atomic and nuclear physics to the study of superheavy elements by the search for the island of stability in the region Z=104 to Z=126. There are many experimental efforts and theoretical works devoted to these study in measuring the spectra and chemical properties. In this thesis, calculations of the spectra and the hyperfine structure of some superheavy elements have been performed in an attempt to enrich our knowledge about the elements and even may help in their detection.We perform the high-precision relativistic calculations to determine the spectra of the superheavy element Z=119 (eka-Fr) and the singly-ionized superheavy element Z=120+ (eka-Ra+). Dominating correlation corrections beyond relativistic Hartree-Fock are included to all orders in the residual electron interaction using the Feynman diagram technique and the correlation potential method. The Breit interaction and quantum electrodynamics radiative corrections are considered. Also, the volume isotope shift is determined.We present the relativistic calculations for the energy levels of the superheavy element Z=120. The relativistic Hartree-Fock and configuration interaction techniques are employed. The correlations between core and valence electrons are treated by means of the correlation potential method and many-body perturbation theory.We also try to address the absence of experimental data on the electron structure and energy spectrum of the Uub element (Z=112) by calculating its energy levels. The relativistic Hartree-Fock and configuration interaction methods are combined with the many-body perturbation theory to construct the many-electron wave function for valence electrons and to include core-valence correlations. The hyperfine structure constants of the lowest s and p1/2 states of superheavy elements Z=119 and Z= 120+ are calculated. Core polarization, dominating correlation, Breit and quantum electrodynamic effects are considered. The dependence of the hyperfine structure constants on nuclear radius is discussed. Measurements of the hyperfine structure combined with our calculations will allow one to study nuclear properties and distribution of magnetic moment inside nucleus.Finally, we discuss the possibility of measuring nuclear anapole moments in atomic Zeeman transitions and perform the necessary calculations. Advantages of using Zeeman transitions include variable transition frequencies and the possibility of enhancement of parity nonconservation effects