Self-Consistent Field Theory For The Nuclear Many-Body System

In nuclear many-body physics, there are many problems that can not be solved analytically. To avoid the many-body interaction complexity, researchers develop some proper approximate methods for solving nuclear many-body problems. The self-consistent mean-field theory is one of the successful approximate methods. Its main idea is to replace all interactions by an effective mean-field interaction. Then, every single particle is affected by the effective mean-field interaction. On the other hand, the mean-field interaction is affected by all single-particle states. Based on the energy min-imization principle, this coupled problem can be solved self-consistently. In this thesis, we study various nuclear many-body systems within the framework at the hadron level or at the quark level.Firstly, we present a model based on the quark-meson coupling method for the description of nuclear matter and finite nuclei, and at the same time, for the study of medium modifications of nucleon properties. The nucleons are described in the Friedberg-Lee model as nontopological solitons which interact through the self-consistent exchange of scalar and vector mesons. The model explicitly incorporates quark degrees of freedom into nuclear many-body systems and provides satisfactory results on the nuclear properties. The present model predicts a significant increase of the nucleon radius at normal nuclear matter density, which is consistent with the EMC effect. It is very interesting to see the nucleon properties change from the nuclear sur-face to the nuclear interior.Secondly, we study the role of the form factor in meson-exchange interactions within the relativistic Hartree-Fock (RHF) approach. We calculate finite nuclei prop-erties with different cutoff parameters inσandωexchange interactions, and find that the results are quite sensitive to the choice of the cutoff parameters. It is essential to include the form factors in the one-boson-exchange potential (OBEP) model, also the form factor can change the single-particle spectra of nuclei. We discuss the different treatment of theπ-pseudovector coupling andρ-tensor coupling in the RHF model. It is found that the results with the form factors are different from those without the form factors and with theδ-function pieces, while the removal of theδ-function pieces can dramatically alter the contributions fromπandρexchanges.Thirdly, we study the effects of K and K* exchange between the A hyperon and the nucleon in a A hypernucleus, where the nuclear core is described by a success- ful relativistic mean-field (RMF) model. In general, K and K* are responsible for strangeness exchange in the OBEP model, which are absent in the RMF calculation. We investigate the contribution of Fock terms derived from K and K* exchange. We use a pseudovector coupling for K exchange, which is found to provide a repulsive potential for the A particle in hypemuclei. Both vector and tensor couplings for K* ex-change are taken into account, whose combined effect on the A single-particle energy is found to be small.