Covariant density functional theory (CDFT) is one of the modern theoretical tools for the description of finite nuclei and neutron stars. Its performance is defined by underlying covariant energy density functionals (CEDFs) which depend on a number of parameters. Several investigations within the CDFT framework using the relativistic Hartree-Bogoliubov (RHB) approach are discussed in this dissertation. Statistical errors in ground state observables and single-particle properties of spherical even-even nuclei and their propagation to the limits of nuclear landscape have been investigated in the covariant energy density functionals with nonlinear density dependency. The parametric correlations are studied in different classes of CEDFs; the elimination of these correlations reduces the number of independent parameters to five or six without affecting the performance of CEDFs on a global scale. Moreover, this study reveals the need to include information on deformed nuclei for the improvement of fitting protocols. A new technique for incorporating deformed nuclei data into the fitting protocol is described. Different CEDFs are optimized using this approach, resulting in a significant improvement in the nuclear mass description. A systematic investigation of the ground state and fission properties of even-even actinides and superheavy nuclei with proton numbers Z = 90 - 120 located between the two-proton and two-neutron drip lines has been performed. These results provide a necessary theoretical input for the modeling of the nuclear astrophysical rapid neutron capture process (r-process) taking place in the mergers of neutron stars. The state-of-the-art CEDFs, namely, DD-PC1, DD-ME2, NL3*, and PC-PK1, are employed in this study. Theoretical systematic uncertainties in the physical observables and their evolution as a function of proton and neutron numbers have been quantified and their major sources have been identified. The extension of the nuclear landscape to hyperheavy nuclei is investigated. The transition from ellipsoidal-like nuclear shapes to toroidal shapes is crucial for the potential expansion of the nuclear landscape to hyperheavy nuclei. The physical reasons for the stability of toroidal nuclei in the Z ~ 134 region are discussed.

High precision measurements of a weak interaction decay were conducted to search for possible variation of the decay rate parameter caused by an antineutrino flux. The experiment searched for variation of the ⁵⁴Mn electron capture decay rate parameter to a level of precision of 1 part in ∼10⁵ by comparing the difference between the decay rate in the presence of an antineutrino flux ∼3×10¹² cm^-2sec^-1 and no flux measurements. The experiment is located 6.5 meters from the reactor core of the High Flux Isotope Reactor (HFIR) in Oak Ridge National Laboratory. A measurement to this level of precision requires a detailed understanding of both systematic and statistical errors. Otherwise, systematic errors in the measurement may mimic fundamental interactions. <div><br></div><div>The gamma spectrum has been collected from the electron capture decay of ⁵⁴Mn. What differs in this experiment compared to previous experiments are, (1) a strong, uniform, highly controlled, and repeatable source of antineutrino flux, using a reactor, nearly 50 times higher than the solar neutrino flux on the Earth, (2) the variation of the antineutrino flux from HFIR is 600 times higher than the variation in the solar neutrino flux on the Earth, (3) the extensive use of neutron and gamma-ray shielding around the detectors, (4) a controlled environment for the detector including a fixed temperature, a nitrogen atmosphere, and stable power supplies, (5) the use of precision High Purity Germanium (HPGe) detectors and finally, (6) accurate time stamping of all experimental runs. By using accurate detector energy calibrations, electronic dead time corrections, background corrections, and pile-up corrections, the measured variation in the ⁵⁴Mn decay rate parameter is found to be δλ/λ=(0.034±1.38)×10^-5. This measurement in the presence of the HFIR flux is equivalent to a cross-section of σ=(0.097±1.24)×10^-25cm². These results are consistent with no measurable decay rate parameter variation due to an antineutrino flux, yielding a 68% confidence level upper limit sensitivity in δλ/λ <= 1.43×10^-5 or σ<=1.34×10^-25cm² in cross-section. The cross-section upper limit obtained in this null or no observable effect experiment is ∼10⁴ times more sensitive than past experiments reporting positive results in ⁵⁴Mn.</div>