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.