Theoretical Researches On Parity-violating Electron Scattering And Nuclear Symmetry Energy

Parity-violating electron scattering (PVS) and nuclear symmetry energy are two hot research issues in nuclear physics nowadays. This dissertation mainly covers t-wo parts: the extraction of the nuclear neutron density distributions from the parity-violating scattering and the theoretical studies on nuclear symmetry energy based on the nuclear density distributions. Numerical codes of relativistic partial waves method are developed for calculating the Dirac equation of the polarized electrons' motion in the nuclear potential. By this method, we can determine the phase shifts of the scat-tering waves and calculate the elastic scattering cross sections. Then we can obtain the parity-violating asymmetry of the scattering electrons. Combined with recent experi-mental progress, electron scattering off exotic nuclei near the drip line is systematically studied. We analyze the positions and regularity of minima of the cross sections and form factors, which can be a useful theoretical reference for the upcoming experiment about electron scattering off the double magic nucleus 132Sn. In the research on the parity-violating electron scattering, we focus on the neutron radius experiments about 208Pb and 48Ca in the Jefferson Laboratory. Taking into considerations of the weak interaction between electrons and neutrons during the calculations, the parity-violating asymmetry can be solved by the partial wave method, and then we can obtain the properties about nuclear neutron density distributions. Besides, because the nuclear symmetry energy as well as its density denpendence are uncertain, even at the satura-tion density, we extract the symmetry energy from the properties of finite nuclei. The nuclear ground state properties can be determined very well through a large number of experiments, therefore it is reasonable also important to deduce the properties of nuclear matter from the finite nuclei.During the researches on the parity-violating electron scattering, we first present the theoretical framework about the parity-violating scattering and the mean field mod-el in describing the nuclear ground state properties. Then we systematically investigate the sensitivity of parameters of nuclear mean field models to the parity-violating asym-metry Apv. The nuclear ground state properties, such as the charge RMS radius and binding energies, can be described very well by the nuclear mean field model, however,because of the uncertainties of the isovector sector in the model, different parameter sets can lead to large differences in the neutron skin thickness. In this dissertation, by changing the ?-? meson coupling term ?v we obtain different neutron density distri-butions and calculate the corresponding parity-violating asymmetry Apv. By this way we can analyze the influence of parameters of mean field model on the parity-violating asymmetry. By measuring the experimental parity-violating asymmetry Apv, we can constrain the parameters of isovector meson in the mean field model.After presenting the theoretical framework of parity-violating electron scattering,we combine the theory with the ongoing and upcoming experiments and systematically study the extraction of the neutron density distributions. At present, due to limitation of experiment condition, the parity-violating asymmetry can only be measured at only a single value of momentum transfer in the Jefferson Lab. By systematically calculating the parity-violating asymmetry Apv with different parameter sets, the linear relation between Apv and the neutron RMS radius Rn can be obtained. With this relation, we can extract the nuclear neutron radius from the limited number of measurements. Next,supposing the nuclear neutron density distribution is the Helm model distribution with two parameters, we obtain an empirical formula between Apv and the Helm model parameters R0 and ? of the neutron density distribution. Based on this formula, we can extract the nuclear neutron density distribution from two PVS measurements.The symmetry energy of nuclear matter and its density denpendence are a hot topic of nuclear physics. The nuclear neutron skin thickness and the slope of nuclear symmetry energy at the saturation density are closely linked. In this paper, we study the extraction of the symmetry energy from the properties of finite nuclei. The neu-tron skin thickness ?Rnp and the slope parameter L of nuclear symmetry energy at the saturation density are calculated with different mean field model parameter set-s. There exists strong linear correlation between ?Rnp and L. If we can measure the neutron skin thickness ?Rnp with a model independent method, for example the parity-violating electron scattering, we can determine the slope parameter L. Because the results of L calculated from different parameter sets are largely different with each other, we further investigate the symmetry energy Csym(?) and the slope parameter L at the saturation density by the local density approximation. Under the local densi-ty approximation, the properties of nuclear matter can be deduced from the density distributions of finite nuclei. By analyzing the change tendency of the local density asymmetry X(r) =?n(r)-?p(r)/?(r) with the nuclear radius, we find that the local density approximation has a better applicability for the neutron rich nuclei with large isospin asymmetry. We extract L with different parameter sets and the results lie in a fairly narrow band. Taking into consideration of L extracted from different isotopic chain-s, we finally obtain the value of the slope parameter and its corresponding error bar:L ? 66 ± 7 MeV. These researches are helpful to understand the other properties of finite nuclei and the properties of neutron stars.