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.

This dissertation applies covariant density functional theory (CDFT), one of the modern theoretical approaches for describing finite nuclei and neutron stars, to investigate the density distribution of nuclei, which is a manifestation of the nodal structure of the single-particle states in physical phenomena, including charge radii and bubbles. A systematic global investigation of differential charge radii has been performed within the CDFT framework for the first time. Available experimental data is compared with theoretical charge radii across the neutron shell closures at N = 28, 50, 82, and 126. Odd-even staggering (OES) in charge radii are believed to be primarily caused by the pairing. Our research proposes a new approach where a considerable contribution to OES in charge radii is provided by the fragmentation of the single-particle content of the ground state in odd-mass nuclei due to particle-vibration coupling. The proton-neutron interaction explained with the nodal structure of the products of the proton and neutron wave functions. However, proton core is responsible for a major contribution to the buildup of differential charge radii. This interaction between protons and neutrons causes a rearrangement of the single-particle density of occupied proton states, which affects the charge radii. According to our microscopic analysis, the shape of the proton potential, the overall proton density, and the energies of the single-particle proton states are all influenced by self-consistency effects, but they have a minimal impact on the differential charge radii. A detailed and microscopic analysis of bubble physics strongly suggests that single-particle processes are primarily responsible for the creation of bubble shapes in superheavy nuclei. The creation of bubble structure is also influenced by nuclear saturation processes and self-consistency effects, and it is dependent on the availability of low-�� single-particle states for occupation since single-particle densities. For the first time, we investigated how nuclear bubbles are formed in the central classically prohibited area at the bottom of the wine bottle potentials, resulting in decreased s state densities at r = 0.

Covariant density functional theory (CDFT) is a modern theoretical tool for the description of nuclear structure phenomena. Different physical observables of the ground and excited states in even-even nuclei have been studied within the CDFT framework employing three major classes of the state-of-the-art covariant energy density functionals. The global assessment of the accuracy of the description of the ground state properties and systematic theoretical uncertainties of atomic nuclei have been investigated. Large-scale axial relativistic Hartree-Bogoliubov (RHB) calculations are performed for all Z < 106 even-even nuclei between the two-proton and two-neutron drip lines. The sources of theoretical uncertainties in the prediction of the two-neutron drip line are analyzed in the framework of CDFT. We concentrate on single-particle and pairing properties as potential sources of these uncertainties. The major source of these uncertainties can be traced back to the differences in the underlying single-particle structure of the various CEDFs. A systematic search for axial octupole deformation in the actinides and superheavy nuclei with proton numbers Z = 88 - 126 and neutron numbers from two-proton drip line up to N = 210 has been performed in CDFT. The nuclei in the Z ~ 96, N ~ 196 region of octupole deformation have been investigated in detail and their systematic uncertainties have been quantified. The structure of superheavy nuclei has been reanalyzed with inclusion of quadrupole deformation. Theoretical uncertainties in the predictions of inner fission barrier heights in superheavy elements have been investigated in a systematic way. The correlations between global description of the ground state properties and nuclear matter properties have been studied. It was concluded that the strict enforcement of the constraints on the nuclear matter properties (NMP) defined in Ref. [1] will not necessary lead to the functionals with good description of ground state properties. The different aspects of the existence and stability of hyperheavy nuclei have been investigated. For the first time, we demonstrate the existence of three regions of spherical hyperheavy nuclei centered around (Z ~ 138, N ~ 230), (Z ~ 156, N ~ 310) and (Z ~ 174, N ~ 410) which are expected to be reasonably stable against spontaneous fission.

Multidimensional quantum tunnelling is an important tool that is used in many areas of physics and chemistry. Sub-barrier fusion reactions of heavy-ions are governed by quantum tunnelling. However, the complexity of the structures of heavy-ions does not allow us to use simple one-dimensional tunnelling equations to and the tunnelling probabilities. Instead of this one should consider all the degrees of freedom which affect the phenomenon and accordingly the intrinsic structure or the deformation of the nuclei must be taken into account in the modelling of heavy-ion fusion. These extra degrees of freedom result in a coupling potential term in the Schrodinger equation of the fusing system. In this thesis 16O + 238 U system is considered. Only the rotational deformation of Uranium is assumed and the coupling potential term is calculated for this system by using two diffrent potential types, namely the Woods-Saxon potential and the double folding potential. Using this term in the Schrodinger equation fusion probability and theoretical cross section are calculated. A discussion that addresses then necessity of multidimensional formulation is given. Besides this point the effects of the choice of the potential type are shown.