The Study About The Phase Structure And The Medium Effect Of Hot And Dense Nuclear Matter

Nuclear matter is a system contains a large number of nucleons. The studying method for the nuclear matter is the relativistic nuclear many-body theory. Starting from the dynamics of the constituent particle of the system, this theory can be used to discuss the properties of the nuclear matter according to the principle of the statistic thermodynamics. From the relativistic quantum hadrodynamic (QHD) model, some properties of the hot and dense nuclear matter has been studied in this paper under the formalism of finite temperature field theory.For the first part of the thesis, the varization of the effective nucleon mass (M*) as the function of the temperature (T) and the chemical potential (n} is investigated within the QHD-I model in detail, in particular the behavior of M* at high temperature. The multi-value for the selfconsistent equation of the effective nucleon mass has been found in the high temperature region. From this phenomenon we assume that there may be a phase transition in this region. Consequently, we verified the liquid-gas (L-G) phase transition by giving the P - p phase diagram at high temperature. At the same time we conclude that the multi-value for the effective nucleon mass corresponds to the existence of the phase transition of the nuclear system. To verify this conclusion, we take the well-known L-G at the low temperature as an example. It is found that the effective nucleon mass at the region of the phase transition presents the multi-solution. It is worth to note that the new phase at high temperature is still at hadron level since there is no quark in the model we discussed. The phase transition at high temperature is also found in QHD-II model.It is widely accepted that all the thermodynamic phase transition must have the dynamic background. Following the same method which has been used to analyse the phase transition at the mocular level, we investigate the behavor of the nucleon-nucleon intera-tion potential at different temperature and chemical potential through calculating the Debye screening massses of the mesons in the nuclear matter. We found that the temperature and the chemical potential when the potential well disappears accords to the critical ones for the phase transition given by the: P - p diagram. Thus the dynamical background for the phase transition at the nucleon level is provided from the disappearance of the nucleon-nucleon interacting potential well and the disaggregation of the nucleon abound.In recent years, the investigations on the in-mediium fields attract special attentionsbecause they have different behaviors from those in free space. On the one hand, the concepts of the quasi-particle or excitation mode are introduced to describe the medium effect of a hot and dense system, many interesting jobs are performed to study the in-medium properties of the bosons and fermions, such as the dispersion relation, effective mass, damping (decay rate) and width (lifetime), etc.. On the other hand, the medium characters related to the in-medium fields should be reflected by two simple functions, the dielectric function (e) and magnetic permeability (u-1). These two quantities remark the in-medium effect from the point of view of the modified electric field and magnetic field, from which the hot and dense medium effects can also be investigated.The dielectric function and magnetic permeability are are proposed to describe the medium properties in the classical electrodynamics originally and then applied to study the behavior of the Quantum Electrodynamics (QED). There the dielectric function and magnetic permeability are defined by the modifications of the in-medium fields from their vacuum values. It is noted that the field tensor of the QCD can also be decomposed into a electon-like and a magnet-like components as in the QBD theory. The color dielectric function and the color magnetic permeability ajre proposed to describe the color dielectric properties of the QCD medium. In order to discuss the difference for the properties of the in-medium meson and the in-v...