Relativistic Hartree-Fock Description Of Nuclear Ground State Properties

Pairing correlations is one of the most important mechanisms which play curial roles in describing nuclear structure properties. In this work, the odd-even staggering (OES) of nuclear binding energies, which reflect the pairing effect be-tween nucleons in nucleus, are studied systematically within both the relativistic Hartree-Bogoliubov (RHB) theory and the relativistic Hartree-Fock-Bogoliubov (RHFB) theory, where the finite-range Gogny pairing force D1S are utilized as the effective pairing interactions. It is shown that, both the two employed models can provide appropriate descriptions on the OESs of nuclear binding energies for C,O, Ca, Ni, Zr, Sn, Ce, Gd and Pb isotopes as well as for N=50and82isotones. While there still exist some systematical discrepancies from the data, i.e., the underestimated OESs in light C and O isotopes and the overestimated ones in heavy region, respectively. Such discrepancies can be eliminated partially by introducing a Z-or N-dependent strength factor into the pairing force Gogny D1S. Besides, the pairing effects are found to depend not only on the pairing interactions but also on the mean-field effect, namely, the experimental OESs can be better reproduced by PKA1in RHFB theory which contains the p-tensor couplings. Successful descriptions of nuclear ground state properties such as the occupation numbers of Sn isotopes are achieved within the optimized Gogny pairing force.With worldwide development of Radioactive Ion Beam (RIB) facilities, the investigations on shell structure of exotic nuclei have formed a new frontier in modern nuclear physics. One particular example is the exotic phenomenon of nuclear shell evolutions in the neutron-rich region. Since the magic character of68Ni was proposed in1982by Bernas et al, the shell evolution of N=40has attracted much interest from both experimental and theoretical sides due to the important roles played by the corresponding nuclei in figuring r-and rp-process paths. As the second work of this thesis, the tensor effects in the shell evolution of N=40are studied for the first time within both the non-relativistic Skyrme-Hartree-Fock-Bogoliubov and the relativistic Hartree-Fock-Bogoliubov theories. The tensor forces are found to play a crucial role by both theories, that is to say, with the inclusion of the tensor force, both theories present the same trend of the N=40shell evolutions as the β-decay experiments indicated. On the contrary, the opposite trends are given by both the non-relativistic and relativistic theories when the tensor force are omitted.Moreover, the important roles played by the exchange term of relativistic Hartree-Fock-Bogoliubov theory are illustrated by studying the binding energy, two neutron separation energy and the charge radii for about1000even-even nuclei throughout the periodic table.