Mean Field Theory And Higher Order Contribution In Nuclear Matter

In nuclear physics, the mean field theory is an effective method to study the nu-clear many-body system. Unfortunately, the pion can not be contained in the Hartreeapproximation. Thus we need perform Hartree-Fock calculation to include the pion. Inorder to consider the tensor force, we need2p-2h correction. These higher order termsare known very important to determine the properties of nuclear matter. In this thesis,we study both the mean field theory and the higher order terms, and also discuss thechiral symmetry of Lagrangian.Firstly, we study the1S0superfluidity of Λ hyperons in neutron star matter andneutron stars. We use the relativistic mean field (RMF) theory to calculate the prop-erties of neutron star matter. In the RMF approach, the meson-hyperon couplings areconstrained by reasonable hyperon potentials that include the updated information fromrecent developments in hypernuclear physics. To examine the1S0pairing gap of Λ hy-perons, we employ several ΛΛ interactions based on the Nijmegen models and usedin double-Λ hypernuclei studies. It is found that the maximal pairing gap obtained isa few tenths of a MeV. The magnitude and the density region of the pairing gap aredependent on the ΛΛ interaction and the treatment of neutron star matter. We calculateneutron star properties and find that whether the1S0superfluidity of Λ hyperons existsin the core of neutron stars mainly depends on the ΛΛ interaction used.Secondly, we study the equation of states of symmetric nuclear matter and pureneutron matter in the Skyrme-Hartree-Fock (SHF) model with tensor corrections. Weare aware now that the pion exchange interaction has a significant contribution to nu-clear structure. The pion generates a strong tensor interaction between two nucleons,which cannot be treated within the Hartree-Fock framework for the spin-saturated sys-tem such as homogeneous nuclear matter. Therefore, we study the role of the tensorinteraction based on the SHF model, in which we extend it by explicitly introducingtwo-particle-two-hole (2p-2h) excitations for the treatment of the tensor interaction insymmetric nuclear matter and pure neutron matter. We are able to describe infinitematter very well using the SHF model with tensor corrections. We also discuss theconnection between the symmetry energy and the tensor interaction in this framework,and extend this model to asymmetric nuclear matter with arbitrary proton fraction.Thirdly, we study the baryon’s mass and axial coupling constant coming from thechiral representation mixing in the SU(3)L SU(3)Rchiral symmetry. We found that the masses derived can not agree with their experimental data if we fit the parameters byaxial coupling constant. Especially the mass of Σ hyperon is too small. Thus we takethe form of Lagrangian as the linear σ model, and break a part of chiral symmetry byconsidering different chiral representation. With this treatment, we can get reasonableresults about both the baryons’ mass and the axial coupling constant.