Relativistic Effective Theory Of Landau Parameters And Its Development In Nuclear Matter

Landau parameter is a significant physical quantity to describe the interaction between quasi-particles in Fermi-liquid theory.Nuclear matter can be described theoretically as Fermi liquid.The extracted information of Landau parameter is helpful to understand the basic properties of nuclear matter,the related excitation characteristics of finite nucleus,and can be used as the input for nuclear astrophysics research.At finite densities,the results of Landau parameters in nuclear matter are sensitive to the accurate description of in-medium effect of nuclear force.The treatment methods of different theoretical models for each component of nuclear force will affect the calculation results of Landau parameters,and the in-medium effect and related characteristics of nuclear force still need to be further clarified.In this paper,based on the covariant density functional theory,the density-dependent relativis-tic mean field(DDRMF)and relativistic Hartree-Fock(DDRHF)approximations are used,and the Fermi-liquid theory is introduced to derive the specific expressions of Landau parameters in nuclear matter.By exploring the evolution behavior of Landau parameters with density in symmetric nu-clear matter,the contribution of each meson exchange coupling channel is revealed.The isospin dependence of Landau parameters is further studied by extending to asymmetric nuclear matter,and the isospin splitting effect of neutron and proton contributions to Landau parameters is revealed.As an application of Landau parameters,the density dependence and isospin dependence of sound velocity is discussed in nuclear matter.In symmetry nuclear matter,due to the different consideration of the in-medium effect of nu-clear force,Landau parameters given by DDRMF,which include the density dependent in-medium effect,systematically show weaker density dependence in the high density region of nuclear matter,compared with the results of nonlinear relativistic mean field(NLRMF)ones.To explain such phe-nomenon further,Landau parameters were decomposed by meson-nucleon coupling channel.On account of the introduction of density dependent in-medium effect,the contribution of the vector channel of the Landau parameters can be suppressed,leading to less density dependence to Landau parameters in high-density region of nuclear matter.In addition,the introduction of isospin-vector scalar meson degree of freedom can reduce the density dependence of Landau parameter₀,and the effect of such meson degree enhances with the increase of density.Besides,because of the den-sity dependence of the constant between nuclear and mesone,there will exist rearrangement terms in the Landau parameters.Due to these rearrangement terms,on one hand the density dependence of Landau parameters shall be weaken correspondingly,one the other hand the description of the incompressibility to nuclear matter is also affected.In the case of asymmetric nuclear matter,it is found that the isospin effect in the high den-sity region significantly reduces the density dependence of Landau parameters,which is caused by the different contributions of neutrons and protons.The density-dependent effects of the rearrange-ment terms given by different DDRMF Landau parameters are quite different.The meson-nucleon coupling channel decomposition of Landau parameters exhibit that such difference is shown by the rearrangement terms on the isospin vector channel of the Landau parameters.The contribution of neutrons and protons in the Landau parameters is further decomposed,and it is found that the sen-sitivity of Landau parameters to the proton contribution is obviously stronger than that of neutrons in the nuclear matter when approaching to higher isospin asymmetry,due to the seperation of Fermi surface density of state.In addition,there exists a good linear correlation between the difference of neutron and proton contribution splitting to Landau parameters and isospin asymmetry,while the linear correlation will reduced gradually with the increase of isospin asymmetry and density.By further analyzing such linear correlations,a formula between isospin splitting of Landau parameter₁and Landau mass is established.As the application of Landau parameters,based on the Landau parameters of RMF theory,the physical quantities related to sound velocity of nuclear matter are calculated respectively.The results show that there is systematic difference between the zero and first sound velocities in high density region of nuclear matter,due to the different consideration of in-medium effect.With the increase of isospin asymmetry,the critical density of the first sound velocity is more likely to move towards to the region of low density of nuclear matter,while the case of the zero sound velocity is on the contrary.In addition,the zero sound velocity calculated by the Landau parameters in pure neutron matter,considering the density dependent in-medium effect,is closer to the results obtained by the chiral meson nucleon field theory(Ch NM).In summery,this work extend the study of Landau parameters to asymmetric nuclear matter in covariant density functional theory,clarify the effects of in-medium effect of nuclear force and isospin correlation to the Landau parameters,and establish the relationship between the isospin split-ting of Landau parameters and the Landau mass.Our study paves a way for the deeper exploration and application of Landau parameters of nuclear astrophysics in the following work.