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The conservingσ-ω-ρmean-field approximation with nonlinear interactions of hadrons has been applied to examine properties of nuclear matter and hyperonic neutron stars. The nonlinear interactions that will produce density-dependent effective masses and coupling constants of hadrons are included in order to examine density correlations among properties of nuclear matter and neutron stars such as binding energy, incompressibility,K, symmetry energy,a4, hyperon-onset density, and maximum masses of neutron stars. The conditions of conserving approximations in order to maintain thermodynamic consistency to an approximation are essential for the analysis of density-dependent correlations.

Properties of nuclear and neutron matter are discussed in a nonlinear σ -ω-ρ mean-field approximation with self-and mixed-interactions of mesons and baryons. The nonlinear interactions of mesons are naturally renormalized as effective masses of mesons by thermodynamic consistency required by the theory of conserving approximations. The nonlinear mean-field approximation results in a thermodynamically consistent approximation that maintains Hugenholtz-Van Hove theorem and Landau's requirement of quasiparticles, and it is generally proved that the nonlinear approximation is equivalent to the Hartree approximation with effective masses of baryons and mesons.The approximation is applied to nuclear and neutron matter, which suggests that the lower bound of nuclear compressibility, K ∼ 150 MeV, be required to be consistent with the binding energy (−15.75 MeV at k F = 1.30 fm −1 ) and the maximum mass of neutron stars (M max 2.00M ). Since the contributions of nonlinear interactions are strictly confined as the effective masses of mesons and baryons, properties of nuclear and neutron matter will enable us to study the validity of nonlinear interactions of mesons. The implication of thermodynamic consistency to the hypothesis of naturalness is discussed. The densitydependence of the compressibility, symmetry energy together with effective masses of hadrons will be important constraints for nonlinear mean-field approximations, and the accumulating data together with accurate measurements of observables in high density and energy region will supply significant information in order to testify theoretical consistency of nuclear models.

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