Properties of nuclear matter and neutron stars and their density-dependent correlations are discussed in a nonlinear σ - ω - ρ mean-field approximation with self-interactions and mixed-interactions of mesons. The nonlinear interactions are renormalized as effective masses (MN*, mσ*, mω*, mρ*) and effective coupling constants (gσ*, gω*, gρ*) required by the theory of conserving approximations, which generates a thermodynamically consistent approximation essential to examine density-dependent correlations. The nonlinear σ - ω - ρ mean-field approximation becomes equivalent to Hartree approximation with effective masses and effective coupling constants, and self-consistent structure is clarified. The current nonlinear mean-field approximation is applied to neutron-rich nuclear matter which is defined as isospin asymmetric and beta-equilibrium nuclear matter. The density-dependent correlations between properties of isospin symmetric and asymmetric nuclear matter, the saturation of symmetry energy in high densities are discussed in terms of density-dependent, effective masses and effective coupling constants induced by nonlinear interactions. The accumulating data and accurate measurements of effective masses and effective coupling constants, observables in high energy density will supply significant information in order to understand and testify theoretical consistency of nuclear models. © 2007 Elsevier B.V. All rights reserved.
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