Properties of nuclear and neutron matter in a nonlinear σ– ω– ρ mean-field approximation with self- and mixed-interactions

Abstract

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 ⩾ 2.00 M ⊙ ). 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 density-dependence 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.