Theoretical Study On The Relativistic Self-consistent Field Of The Properties Of Asymmetric Nuclear Matter

The interaction between nucleons as one kind of strong interaction,is very important in understanding the properties of finite nuclei and nuclear matter.The equation of state(EOS)of nuclear matter based on the interaction between nucleons has been widely studied.The EOS of symmetric nuclear matter has been understood relatively clearly after long-term studies and verification.However,the uncertainty of EOS of asymmetric nuclear matter(symmetry energy)which is extracted from observational/experimental data is still large.Due to the uncertainty of the slope of the symmetry energy at the saturation density,the symmetry energies at high density predicted by various models are quite different.In fact,even the sign of the symmetry energy at high density is uncertain.In terms of the interaction between nucleons,the uncertainty of high density EOS could be due to the absences of the consideration of some symmetries of the strong interaction.Chiral symmetry as an important symmetry of strong interaction,may constrain the symmetry energy at high densities.One of the main works of this thesis is to explore whether the Nambu-Jona-Lasinio(NJL)model with the chiral symmetry can constrain the symmetry energy at high density.To study the symmetry energy and its slope completely,we add isovector term,isovector-scalar cou-pling term and isovector-vector coupling term in the original NJL model.The isovector-vector coupling term of the NJL model can produce a negative symmetry energy.However,this neg-ative symmetry energy can not stabilize neutron star.With choosing appropriate isovector and isovector-scalar coupling strength,the symmetry energy and the slope of symmetry energy of the NJL model at the saturation point can be within the average domain of extracted values.For a fixed symmetry energy at saturation density,by varying the slope of the symmetry energy,it is found that the symmetry energy of the NJL model tends to be soft at high densities.This result is due to the chiral symmetry of the NJL model,and is independent of the slope of the symmetry energy at saturation density.In addiction to constraint on the symmetry energy at high densities given by chiral symmetry,we also verified whether the predictions of the NJL model can satisfy the neutron star observations.The heaviest neutron star predicted by the NJL model is well above 2.14 M_?.The radius of the neutron star given by the NJL model decreases as the slope of the symmetry energy decreases.The predicted radius of 1.4 M_?neutron star with the NJL model can satisfy the observational domain(10-13.6km).Besides,we also study the properties of the crust-core transition of neutron stars with various properties of symmetry energy.The symmetry energy of the NJL model can be soft at both low density and high den-sity,which is different from the general relativistic mean field(RMF)models.When the radius of a 1.4 M_?neutron star is relatively large,the fraction of the crustal moment of inertia could be greater than 7%,and can explain the glitches of the neutron star.With a given slope of the symmetry energy,the increase of the symmetry energy will increase the crust-core transition density and the corresponding transition pressure.The increase in the crust-core transition pres-sure will ensure the crust to contain more mass.Thus,the fraction of crustal moment of inertia could be greater than 7%,which could also explain the glitches of the neutron star.In addiction to the study of the properties of neutron stars,we also use the Gibbs conditions to calculate the phase transition between nuclear matter and quark matter,and then study the properties of hybrid stars.With a fixed quark NJL model,the nucleon-quark phase transition density is studied by varying the coupling strength of the NJL model of nuclear matter.The nucleon-quark phase transition density with the stiff EOS of nuclear matter is lower than the one with the soft EOS of nuclear matter.With a fixed quark model,no matter how the EOS of nuclear matter changes,the predicted maximum mass of hybrid stars is almost the same.This result implies that the theoretically predicted maximum mass of a hybrid star strongly depends on the EOS of quark matter.Chiral symmetry is one of the main symmetries of strong interaction.How to explore the chiral symmetry is also a concern of this thesis.The in-medium nucleon-nucleon(NN)scat-tering cross section,as an input of the transport model,is very important in understanding the experimental data of heavy ion collisions.Based on the relativistic impulse approximation(RI-A),this thesis uses the NJL model to study the symmetry potential and in-medium NN scattering cross section.As the baryon density increases,the chiral symmetry may be partially restored or restored,so that the scalar density decreases.This result is obviously different from the one from the usual RMF models whose scalar density increases with increasing the baryon densi-ty.Therefore,there are significant differences in the symmetry potential and the in-medium nucleon-nucleon scattering cross section calculated by the chiral symmetry model and RMF model without chiral symmetry.Especially,as long as the chiral symmetry is partially restored,the nucleon-nucleon scattering cross section of the medium will increase sharply,which pro-vides a reference for the use of transport models to study heavy ion collision experiments.In addiction to the above research based on the RMF models,this thesis also studies the effect of the nucleon high momentum distribution beyond the mean field approximation,which will also change the EOS of nuclear matter.Neither the relativistic nor the non-relativistic mean field theory can produce the nucleon high momentum distribution.Beyond the mean field theory,many approaches can produce the nucleon high momentum distribution by introducing three-body or multi-body correlation.Although Walecka and its extended models have achieved great success in studying nuclear matter and nuclei,they can not produce the nucleon high momentum distribution.We have added a second-order Feynman diagram under the Walecka model,deduced the formalism,and found the relationship between the three-body correlation and high momentum distribution of nucleons.