arXiv2021
Based on the Hugenholtz-Van Hove theorem, six basic quantities of the EoS in isospin asymmetric nuclear matter are expressed in terms of the nucleon kinetic energy $t(k)$, the isospin symmetric and asymmetric parts of the single-nucleon potentials $U_0(ρ,k)$ and $U_{\text{\text{sym,i}}}(ρ,k)$. The six basic quantities include the quadratic symmetry energy $E_{\text{sym,2}}(ρ)$, the quartic symmetry energy $E_{\text{sym,4}}(ρ)$, their corresponding density slopes $L_2(ρ)$ and $L_4(ρ)$, and the incompressibility coefficients $K_2(ρ)$ and $K_4(ρ)$. By using four types of well-known effective nucleon-nucleon interaction models, namely the BGBD, MDI, Skyrme, and Gogny forces, the density- and isospin-dependent properties of these basic quantities are systematically calculated and their values at the saturation density $ρ_0$ are explicitly given. The contributions to these quantities from $t(k)$, $U_0(ρ,k)$, and $U_{\text{sym,i}}(ρ,k)$ are also analyzed at the normal nuclear density $ρ_0$. It is clearly shown that the first-order asymmetric term $U_{\text{sym,1}}(ρ,k)$ (also known as the symmetry potential in Lane potential) plays a vital role in determining the density dependence of the quadratic symmetry energy $E_{\text{sym,2}}(ρ)$. It is also shown that the contributions from high-order asymmetric parts of the single-nucleon potentials ($U_{\text{sym,i}}(ρ,k)$ with $i>1$) cannot be neglected in the calculations of the other five basic quantities. Moreover, by analyzing the properties of asymmetric nuclear matter at the exact saturation density $ρ_{\text{sat}}(δ)$, the corresponding quadratic incompressibility coefficient is found to have a simple empirical relation $K_{\text{sat,2}}=K_{2}(ρ_0)-4.14 L_2(ρ_0)$.