The Study Of Effective Nucleon Mass In Hot And Dense Nuclear Matter

There are two frameworks the temperature field theory and the relativistic hadronic model theory for studying nuclear matter at finite temperature and finite density. The finite temperature field theory have two formalisms imaginary time and real time formalisms. In this thesis, we only introduce imaginary time formalism. Through this formalism, we can apply the technics of calculation in quantum field theory to statistical thermodynamics. The relativistic hadronic model theory includes quantum hadrodynamics(QHD) and its mean field theory. QHD is a relativistic quantum field theory of hadronic degrees of freedom. As hadrons are not point-like particles. They constitute of quarks and gluons. The basic theory dealing with quarks and gluons is quantum chromodynamics(QCD). Generally speaking. QCD is the fundamental theory of strong interaction. However, the perturbative calculation in QCD is only available at high energy. The hadrons belong to intermediate and low energy area. So it's very difficult to study nuclear phenomenon with QCD. While QHD is a low energy effective theory which describes hadronic physics very well. Through mean field approximation, this theory gives good prediction to the experiments. In QHD theory, there are many hadronic models. Among them, QHD-I model (also called Walecka model) is most fundamental. Through this model and using finite temperature field theory, we can write down the partition function of the system. After mean field approximation, the partition function can be derived. So the thermodynamic properties of nuclear matter could be studied.Here by applying QHD-I model and ZM model, we have mainly discussed the effective nucleon mass in hot and dense nuclear matter. Our discussion can be divided into three aspects . The first aspect is that, in QHD-I model, it is generally accepted that there is a first-order liquid-gas phase transition, but the properties of effective nucleon mass under this phase transition haven't been thoroughly studied. We have discussed this problem and found that there are multiple solutions of the effective nucleon mass in the phase transition area. The second aspect: in ZM model, under mean field approximation, the zero-point energy of vaccum is often neglected. After our careful analysis, we find that there are finite part which is temperature dependent in this zero-point energy. So we have separated this part and discussed its influence to the effective nucleon mass. The result shows that this part has remarkable contribution at high temperature. The third aspect: as is known, the main reason of proposing ZM model is to improve the properties of effective nucleon mass in QHD-I model. By introducing the nonlinear coupling constant. ZM model has improved the effective nucleon mass indeed. But the physics mechanism is not deeply disclosed. Here, through expanding the nonlinear coupling constant, we have discussed this mechanism. In addition, we find that the phase transition at high temperature in QHD-I model has been suppressed in ZM model. This phenomenon can explain why there is no phase transition at high temperature in ZM model.